Do Students Trust in Mathematics or Intuition during Physics Problem Solving? An Epistemic Game Perspective

ERIC Educational Resources Information Center

Yavuz, Ahmet

2015-01-01

This study aims to investigate (1) students' trust in mathematics calculation versus intuition in a physics problem solving and (2) whether this trust is related to achievement in physics in the context of epistemic game theoretical framework. To achieve this research objective, paper-pencil and interview sessions were conducted. A paper-pencil…

Behaviour of mathematics and physics students in solving problem of Vector-Physics context

NASA Astrophysics Data System (ADS)

Sardi; Rizal, M.; Mansyur, J.

2018-04-01

This research aimed to describe behaviors of mathematics and physics students in solving problem of the vector concept in physics context. The subjects of the research were students who enrolled in Mathematics Education Study Program and Physics Education Study Program of FKIP Universitas Tadulako. The selected participants were students who received the highest score in vector fundamental concept test in each study program. The data were collected through thinking-aloud activity followed by an interview. The steps of data analysis included data reduction, display, and conclusion drawing. The credibility of the data was tested using a triangulation method. Based on the data analysis, it can be concluded that the two groups of students did not show fundamental differences in problem-solving behavior, especially in the steps of understanding the problem (identifying, collecting and analyzing facts and information), planning (looking for alternative strategies) and conducting the alternative strategy. The two groups were differ only in the evaluation aspect. In contrast to Physics students who evaluated their answer, mathematics students did not conducted an evaluation activity on their work. However, the difference was not caused by the differences in background knowledge.

Students' conceptual performance on synthesis physics problems with varying mathematical complexity

NASA Astrophysics Data System (ADS)

Ibrahim, Bashirah; Ding, Lin; Heckler, Andrew F.; White, Daniel R.; Badeau, Ryan

2017-06-01

A body of research on physics problem solving has focused on single-concept problems. In this study we use "synthesis problems" that involve multiple concepts typically taught in different chapters. We use two types of synthesis problems, sequential and simultaneous synthesis tasks. Sequential problems require a consecutive application of fundamental principles, and simultaneous problems require a concurrent application of pertinent concepts. We explore students' conceptual performance when they solve quantitative synthesis problems with varying mathematical complexity. Conceptual performance refers to the identification, follow-up, and correct application of the pertinent concepts. Mathematical complexity is determined by the type and the number of equations to be manipulated concurrently due to the number of unknowns in each equation. Data were collected from written tasks and individual interviews administered to physics major students (N =179 ) enrolled in a second year mechanics course. The results indicate that mathematical complexity does not impact students' conceptual performance on the sequential tasks. In contrast, for the simultaneous problems, mathematical complexity negatively influences the students' conceptual performance. This difference may be explained by the students' familiarity with and confidence in particular concepts coupled with cognitive load associated with manipulating complex quantitative equations. Another explanation pertains to the type of synthesis problems, either sequential or simultaneous task. The students split the situation presented in the sequential synthesis tasks into segments but treated the situation in the simultaneous synthesis tasks as a single event.

Using Mathematics and Engineering to Solve Problems in Secondary Level Biology

ERIC Educational Resources Information Center

Cox, Charles; Reynolds, Birdy; Schunn, Christian; Schuchardt, Anita

2016-01-01

There are strong classroom ties between mathematics and the sciences of physics and chemistry, but those ties seem weaker between mathematics and biology. Practicing biologists realize both that there are interesting mathematics problems in biology, and that viewing classroom biology in the context of another discipline could support students'…

Science Modelling in Pre-Calculus: How to Make Mathematics Problems Contextually Meaningful

ERIC Educational Resources Information Center

Sokolowski, Andrzej; Yalvac, Bugrahan; Loving, Cathleen

2011-01-01

"Use of mathematical representations to model and interpret physical phenomena and solve problems is one of the major teaching objectives in high school math curriculum" [National Council of Teachers of Mathematics (NCTM), "Principles and Standards for School Mathematics", NCTM, Reston, VA, 2000]. Commonly used pre-calculus textbooks provide a…

Understanding Student Use of Differentials in Physics Integration Problems

ERIC Educational Resources Information Center

Hu, Dehui; Rebello, N. Sanjay

2013-01-01

This study focuses on students' use of the mathematical concept of differentials in physics problem solving. For instance, in electrostatics, students need to set up an integral to find the electric field due to a charged bar, an activity that involves the application of mathematical differentials (e.g., "dr," "dq"). In this…

Space Mathematics, A Resource for Teachers Outlining Supplementary Space-Related Problems in Mathematics.

ERIC Educational Resources Information Center

Reynolds, Thomas D.; And Others

This compilation of 138 problems illustrating applications of high school mathematics to various aspects of space science is intended as a resource from which the teacher may select questions to supplement his regular course. None of the problems require a knowledge of calculus or physics, and solutions are presented along with the problem…

Problem Solvers: Problem--How Long Can You Stand?

ERIC Educational Resources Information Center

Teaching Children Mathematics, 2010

2010-01-01

Healthy lifestyles are increasingly emphasized these days. This month the authors begin a series of mathematical problems that also address physical activity. They hope that these problems offer opportunities to investigate mathematics and also reinforce the desire to lead a healthy life. In their first problem of the academic year, students…

Current problems in applied mathematics and mathematical physics

NASA Astrophysics Data System (ADS)

Samarskii, A. A.

Papers are presented on such topics as mathematical models in immunology, mathematical problems of medical computer tomography, classical orthogonal polynomials depending on a discrete variable, and boundary layer methods for singular perturbation problems in partial derivatives. Consideration is also given to the computer simulation of supernova explosion, nonstationary internal waves in a stratified fluid, the description of turbulent flows by unsteady solutions of the Navier-Stokes equations, and the reduced Galerkin method for external diffraction problems using the spline approximation of fields.

Problem-solving rubrics revisited: Attending to the blending of informal conceptual and formal mathematical reasoning

NASA Astrophysics Data System (ADS)

Hull, Michael M.; Kuo, Eric; Gupta, Ayush; Elby, Andrew

2013-06-01

Much research in engineering and physics education has focused on improving students’ problem-solving skills. This research has led to the development of step-by-step problem-solving strategies and grading rubrics to assess a student’s expertise in solving problems using these strategies. These rubrics value “communication” between the student’s qualitative description of the physical situation and the student’s formal mathematical descriptions (usually equations) at two points: when initially setting up the equations, and when evaluating the final mathematical answer for meaning and plausibility. We argue that (i) neither the rubrics nor the associated problem-solving strategies explicitly value this kind of communication during mathematical manipulations of the chosen equations, and (ii) such communication is an aspect of problem-solving expertise. To make this argument, we present a case study of two students, Alex and Pat, solving the same kinematics problem in clinical interviews. We argue that Pat’s solution, which connects manipulation of equations to their physical interpretation, is more expertlike than Alex’s solution, which uses equations more algorithmically. We then show that the types of problem-solving rubrics currently available do not discriminate between these two types of solutions. We conclude that problem-solving rubrics should be revised or repurposed to more accurately assess problem-solving expertise.

What Is Physics Problem-Solving Competency? The Views of Arnold Sommerfeld and Enrico Fermi

NASA Astrophysics Data System (ADS)

Niss, Martin

2018-05-01

A central goal of physics education is to teach problem-solving competency, but the description of the nature of this competency is somehwat fragmentary and implicit in the literature. The present article uses recent historical scholarship on Arnold Sommerfeld and Enrico Fermi to identify and characterize two positions on the nature of physics problem-solving competency. The first, Sommerfeld's, is a "theory first, phenomenon second" approach. Here, the relevant problems originate in one of the theories of physics and the goal of the problem-solver is to make a mathematical analysis of the relevant equation(s) and then give a qualitative analysis of the phenomenon that arise from these mathematical results. Fermi's position is a "phenomenon first, theory second" approach, where the starting point is a physical phenomenon that is analyzed and then brought into the realm of a physics theory. The two positions are illustrated with solutions to two problems and it is shown that the two positions are reflected in problem collections of university educations in physics.

Problems Relating Mathematics and Science in the High School.

ERIC Educational Resources Information Center

Morrow, Richard; Beard, Earl

This document contains various science problems which require a mathematical solution. The problems are arranged under two general areas. The first (algebra I) contains biology, chemistry, and physics problems which require solutions related to linear equations, exponentials, and nonlinear equations. The second (algebra II) contains physics…

Pre-Service Physics Teachers’ Problem-solving Skills in Projectile Motion Concept

NASA Astrophysics Data System (ADS)

Sutarno, S.; Setiawan, A.; Kaniawati, I.; Suhandi, A.

2017-09-01

This study is a preliminary research aiming at exploring pre-service physics teachers’ skills in applying the stage of problem-solving strategies. A total of 76 students of physics education study program at a college in Bengkulu Indonesia participated in the study. The skills on solving physics problems are being explored through exercises that demand the use of problem-solving strategies with several stages such as useful description, physics approach, specific application of physics, physics equation, mathematical procedures, and logical progression. Based on the results of data analysis, it is found that the pre-service physics teachers’ skills are in the moderate category for physics approach and mathematical procedural, and low category for the others. It was concluded that the pre-service physics teachers’ problem-solving skills are categorized low. It is caused by the learning of physics that has done less to practice problem-solving skills. The problems provided are only routine and poorly trained in the implementation of problem-solving strategies.The results of the research can be used as a reference for the importance of the development of physics learning based on higher order thinking skills.

Developing Physics E-Scaffolding Teaching Media to Increase the Eleventh-Grade Students' Problem Solving Ability and Scientific Attitude

ERIC Educational Resources Information Center

Saputri, Affa Ardhi; Wilujeng, Insih

2017-01-01

This research aims at revealing (1) the suitability of physics e-scaffolding teaching media with mathematical and image/diagrammatic representation, as well as (2) the effectiveness of the e-scaffolding teaching media with mathematical and image/diagrammatic representation to improve students' problem solving ability and scientific attitude. It is…

On the Formal-Logical Analysis of the Foundations of Mathematics Applied to Problems in Physics

NASA Astrophysics Data System (ADS)

Kalanov, Temur Z.

2016-03-01

Analysis of the foundations of mathematics applied to problems in physics was proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that critical analysis of the concept of mathematical quantity - central concept of mathematics - leads to the following conclusion: (1) The concept of ``mathematical quantity'' is the result of the following mental operations: (a) abstraction of the ``quantitative determinacy of physical quantity'' from the ``physical quantity'' at that the ``quantitative determinacy of physical quantity'' is an independent object of thought; (b) abstraction of the ``amount (i.e., abstract number)'' from the ``quantitative determinacy of physical quantity'' at that the ``amount (i.e., abstract number)'' is an independent object of thought. In this case, unnamed, abstract numbers are the only sign of the ``mathematical quantity''. This sign is not an essential sign of the material objects. (2) The concept of mathematical quantity is meaningless, erroneous, and inadmissible concept in science because it represents the following formal-logical and dialectical-materialistic error: negation of the existence of the essential sign of the concept (i.e., negation of the existence of the essence of the concept) and negation of the existence of measure of material object.

Experimental Mathematics and Mathematical Physics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David

2009-06-26

One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.

The effect of mathematical model development on the instruction of acceleration to introductory physics students

NASA Astrophysics Data System (ADS)

Sauer, Tim Allen

The purpose of this study was to evaluate the effectiveness of utilizing student constructed theoretical math models when teaching acceleration to high school introductory physics students. The goal of the study was for the students to be able to utilize mathematical modeling strategies to improve their problem solving skills, as well as their standardized scientific and conceptual understanding. This study was based on mathematical modeling research, conceptual change research and constructivist theory of learning, all of which suggest that mathematical modeling is an effective way to influence students' conceptual connectiveness and sense making of formulaic equations and problem solving. A total of 48 students in two sections of high school introductory physics classes received constructivist, inquiry-based, cooperative learning, and conceptual change-oriented instruction. The difference in the instruction for the 24 students in the mathematical modeling treatment group was that they constructed every formula they needed to solve problems from data they collected. In contrast, the instructional design for the control group of 24 students allowed the same instruction with assigned problems solved with formulas given to them without explanation. The results indicated that the mathematical modeling students were able to solve less familiar and more complicated problems with greater confidence and mental flexibility than the control group students. The mathematical modeling group maintained fewer alternative conceptions consistently in the interviews than did the control group. The implications for acceleration instruction from these results were discussed.

Introductory Physics Students' Physics and Mathematics Epistemologies

NASA Astrophysics Data System (ADS)

Scanlon, Erin M.

The purpose of this three study dissertation is to investigate why students are enrolled in introductory physics courses experience difficulties in being successful; one possible source of their difficulties is related to their epistemology. In order to investigate students' epistemologies about mathematics and physics, students were observed solving physics problems in groups during a laboratory course (study 1) and while solving physics and mathematics problems individually during office-hour sessions (study 2). The Epistemological Resources theoretical framework was employed (Hammer & Elby, 2002). Using emergent and a priori epistemological resource operationalizations (Jones, 2015), 25 distinct epistemological resources were identified in study 1. Differences in physics epistemological resource usage between students of varying academic background (as measured by their number of previously completed mathematics and science classes were identified. By employing an external (Jones, 2015) and internal (Scanlon, 2016) a priori epistemological resource coding scheme, a total of 17 distinct epistemological resources were identified in study 2. The data were sampled to compare the mathematics and physics epistemological resource usage of participants with consistent and inconsistent sign usage in an energy conservation physics problem in order to provide a meaningful context for discussion. Participants of the same sign usage group employed epistemological resources similarly. Conversely, participants in different groups had significantly different physics epistemological resource usage patterns. Finally, student epistemological resource usage patterns from the first two studies were compared to course outcomes in order to determine implications for practice (study 3). Educators must be aware of and address the epistemological underpinnings of students' difficulties in introductory physics courses.

Physics or Fantasy?

ERIC Educational Resources Information Center

Slisko, Josip; Krokhin, Arkady

1995-01-01

Though the field of physics is moving toward more realistic problems and the use of computers and mathematical modeling to promote insightful treatment of physical problems, artificial problems still appear in textbooks in the field of electrostatics. Discusses physical arguments why one of the most popular textbook applications of Coulomb's Law…

Interactions Between Mathematics and Physics: The History of the Concept of Function—Teaching with and About Nature of Mathematics

NASA Astrophysics Data System (ADS)

Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-07-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (Euler) and heat conduction (Fourier and Dirichlet). The introduction of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student understanding of mathematics and its nature is enhanced by embedding mathematical concepts and theories, within an explicit-reflective framework, into a rich historical context emphasizing its interaction with other disciplines such as physics. Students recognize and become engaged with meta-discursive rules governing mathematics. Mathematics teachers can thereby teach inquiry in mathematics as it occurs in the sciences, as mathematical practice aimed at obtaining new mathematical knowledge. We illustrate such a historical teaching and learning of mathematics within an explicit and reflective framework by two examples of student-directed, problem-oriented project work following the Roskilde Model, in which the connection to physics is explicit and provides a learning space where the nature of mathematics and mathematical practices are linked to natural science.

The Integration of Mathematics in Physics Problem Solving: A Case Study of Greek Upper Secondary School Students

ERIC Educational Resources Information Center

Meli, Kalliopi; Zacharos, Konstantinos; Koliopoulos, Dimitrios

2016-01-01

This article presents a case study that examines the level of integration of mathematical knowledge in physics problem solving among first grade students of upper secondary school. We explore the ways in which two specific students utilize their knowledge and we attempt to identify the epistemological framings they refer to while solving a physics…

What Does the Literature Say about the Persistence of Women with Career Goals in Physical Science, Technology, Engineering, and Mathematics?

ERIC Educational Resources Information Center

Kondrick, Linda C.

The under-representation of women in physical science, technology, engineering, and mathematics (PSTEM) career fields is a persistent problem. This paper summarizes an extensive review of the literature pertaining to the many issues that surround this problem. The review revealed a wide range of viewpoints and a broad spectrum of research…

Representing the Electromagnetic Field: How Maxwell's Mathematics Empowered Faraday's Field Theory

NASA Astrophysics Data System (ADS)

Tweney, Ryan D.

2011-07-01

James Clerk Maxwell `translated' Michael Faraday's experimentally-based field theory into the mathematical representation now known as `Maxwell's Equations.' Working with a variety of mathematical representations and physical models Maxwell extended the reach of Faraday's theory and brought it into consistency with other results in the physics of electricity and magnetism. Examination of Maxwell's procedures opens many issues about the role of mathematical representation in physics and the learning background required for its success. Specifically, Maxwell's training in `Cambridge University' mathematical physics emphasized the use of analogous equations across fields of physics and the repeated solving of extremely difficult problems in physics. Such training develops an array of overlearned mathematical representations supported by highly sophisticated cognitive mechanisms for the retrieval of relevant information from long term memory. For Maxwell, mathematics constituted a new form of representation in physics, enhancing the formal derivational and calculational role of mathematics and opening a cognitive means for the conduct of `experiments in the mind' and for sophisticated representations of theory.

"They [The Lecturers] Have to Get through a Certain Amount in an Hour": First Year Students' Problems with Service Mathematics Lectures

ERIC Educational Resources Information Center

Harris, Diane; Pampaka, Maria

2016-01-01

Drawing on large-scale survey data and interviews with students during their first year at university, and case studies in their institutions, we explore the problems faced by students taking mathematically demanding courses, e.g. physics and engineering. These students are often taught mathematics as a service subject by lecturers of mathematics.…

Identifying potential dropouts from college physics classes

NASA Astrophysics Data System (ADS)

Wollman, Warren; Lawrenz, Frances

Hudson and Rottman (1981) established that mathematics ability is probably a secondary factor influencing dropout from college physics courses. Other factors remain to be found for predicting who will drop out or at least have difficulty with the course. When mathematics ability is coupled with general indicators of performance (total GPA and ACT natural science), prediction of performance for those who complete the course is substantially improved. Moreover, discriminant analyses reveal who will have at least some difficulty, but not who will drop out. The problem of isolating specific weaknesses of students who have difficulty persists. Physics achievement appears to depend on mathematics ability only to the extent that students possess the ability to utilize mathematics knowledge for solving physics problems. Identification of the specific aspects of this ability as well as the specific deficiencies leading to dropout should be the object of future research. For the present, interviews might be more revealing than group testing methods.

Quantum algorithm for solving some discrete mathematical problems by probing their energy spectra

NASA Astrophysics Data System (ADS)

Wang, Hefeng; Fan, Heng; Li, Fuli

2014-01-01

When a probe qubit is coupled to a quantum register that represents a physical system, the probe qubit will exhibit a dynamical response only when it is resonant with a transition in the system. Using this principle, we propose a quantum algorithm for solving discrete mathematical problems based on the circuit model. Our algorithm has favorable scaling properties in solving some discrete mathematical problems.

Material Encounters with Mathematics: The Case for Museum Based Cross-Curricular Integration

ERIC Educational Resources Information Center

de Freitas, Elizabeth; Bentley, Sean J.

2012-01-01

This paper reports on research from a network of high school and museum partnerships designed to explore techniques for integrating mathematics and physics learning experiences during the first year of high school. The foundation of the curriculum is a problem-based, museum-based, and hands-on approach to mathematics and physics. In this paper, we…

Mathematical modeling of moving boundary problems in thermal energy storage

NASA Technical Reports Server (NTRS)

Solomon, A. D.

1980-01-01

The capability for predicting the performance of thermal energy storage (RES) subsystems and components using PCM's based on mathematical and physical models is developed. Mathematical models of the dynamic thermal behavior of (TES) subsystems using PCM's based on solutions of the moving boundary thermal conduction problem and on heat and mass transfer engineering correlations are also discussed.

Playful Physics

NASA Technical Reports Server (NTRS)

Weaver, David

2008-01-01

Effectively communicate qualitative and quantitative information orally and in writing. Explain the application of fundamental physical principles to various physical phenomena. Apply appropriate problem-solving techniques to practical and meaningful problems using graphical, mathematical, and written modeling tools. Work effectively in collaborative groups.

What is behind small deviations of quantum mechanics theory from experiments? Observer's mathematics point of view

NASA Astrophysics Data System (ADS)

Khots, Boris; Khots, Dmitriy

2014-12-01

Certain results that have been predicted by Quantum Mechanics (QM) theory are not always supported by experiments. This defines a deep crisis in contemporary physics and, in particular, quantum mechanics. We believe that, in fact, the mathematical apparatus employed within today's physics is a possible reason. In particular, we consider the concept of infinity that exists in today's mathematics as the root cause of this problem. We have created Observer's Mathematics that offers an alternative to contemporary mathematics. This paper is an attempt to relay how Observer's Mathematics may explain some of the contradictions in QM theory results. We consider the Hamiltonian Mechanics, Newton equation, Schrodinger equation, two slit interference, wave-particle duality for single photons, uncertainty principle, Dirac equations for free electron in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided.

High-Productivity Computing in Computational Physics Education

NASA Astrophysics Data System (ADS)

Tel-Zur, Guy

2011-03-01

We describe the development of a new course in Computational Physics at the Ben-Gurion University. This elective course for 3rd year undergraduates and MSc. students is being taught during one semester. Computational Physics is by now well accepted as the Third Pillar of Science. This paper's claim is that modern Computational Physics education should deal also with High-Productivity Computing. The traditional approach of teaching Computational Physics emphasizes ``Correctness'' and then ``Accuracy'' and we add also ``Performance.'' Along with topics in Mathematical Methods and case studies in Physics the course deals a significant amount of time with ``Mini-Courses'' in topics such as: High-Throughput Computing - Condor, Parallel Programming - MPI and OpenMP, How to build a Beowulf, Visualization and Grid and Cloud Computing. The course does not intend to teach neither new physics nor new mathematics but it is focused on an integrated approach for solving problems starting from the physics problem, the corresponding mathematical solution, the numerical scheme, writing an efficient computer code and finally analysis and visualization.

A Non-Intuitionist's Approach To The Interpretation Problem Of Quantum Mechanics

NASA Astrophysics Data System (ADS)

Grelland, Hans Herlof

2005-02-01

A philosophy of physics called "linguistic empiricism" is presented and applied to the interpretation problem of quantum mechanics. This philosophical position is based on the works of Jacques Derrida. The main propositions are (i) that meaning, included the meaning attached to observations, are language-dependent and (ii) that mathematics in physics should be considered as a proper language, not necessary translatable to a more basic language of intuition and immediate experience. This has fundamental implications for quantum mechanics, which is a mathematically coherent and consistent theory; its interpretation problem is associated with its lack of physical images expressible in ordinary language.

The Epistemological Perceptions of the Relationship between Physics and Mathematics and Its Effect on Problem-Solving among Pre-Service Teachers at Yarmouk University in Jordan

ERIC Educational Resources Information Center

Al-Omari, Wesal; Miqdadi, Ruba

2014-01-01

The purpose of this paper was to examine the perception pre-service teachers hold to the nature of the relationship between physics and mathematics. The study examined this relationship in reference to their performance in problem solving and strategies they used. The results of this empirical study suggested that most participants hold a naïve…

Some Learning Problems Concerning the Use of Symbolic Language in Physics.

ERIC Educational Resources Information Center

De Lozano, Silvia Ragout; Cardenas, Marta

2002-01-01

Draws the attention of teachers of basic university physics courses to student problems concerning the interpretation of the symbolic language used in physics. Reports specific difficulties found in the first physics course related to different kinds of statements expressed in the mathematical language. (Contains 15 references.) (Author/YDS)

Epistemic Views of the Relationship between Physics and Mathematics: Its Influence on the Approach of Undergraduate Students to Problem Solving

ERIC Educational Resources Information Center

Pereira de Ataide, Ana Raquel; Greca, Ileana Maria

2013-01-01

The relationship between physics and mathematics is hardly ever presented with sufficient clarity to satisfy either physicists or mathematicians. It is a situation that often leads to misunderstandings that may spread quickly from teacher to student, such as the idea that mathematics is a mere instrument for the physicist. In this paper, we…

Interactions between Mathematics and Physics: The History of the Concept of Function--Teaching with and about Nature of Mathematics

ERIC Educational Resources Information Center

Kjeldsen, Tinne Hoff; Lützen, Jesper

2015-01-01

In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another…

Gesellschaft fuer angewandte Mathematik und Mechanik, Scientific Annual Meeting, Universitaet Stuttgart, Federal Republic of Germany, Apr. 13-17, 1987, Reports

NASA Astrophysics Data System (ADS)

Recent advances in the analytical and numerical treatment of physical and engineering problems are discussed in reviews and reports. Topics addressed include fluid mechanics, numerical methods for differential equations, FEM approaches, and boundary-element methods. Consideration is given to optimization, decision theory, stochastics, actuarial mathematics, applied mathematics and mathematical physics, and numerical analysis.

What is behind small deviations of quantum mechanics theory from experiments? Observer's mathematics point of view

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khots, Boris, E-mail: bkhots@cccglobal.com; Khots, Dmitriy, E-mail: dkhots@imathconsulting.com

2014-12-10

Certain results that have been predicted by Quantum Mechanics (QM) theory are not always supported by experiments. This defines a deep crisis in contemporary physics and, in particular, quantum mechanics. We believe that, in fact, the mathematical apparatus employed within today's physics is a possible reason. In particular, we consider the concept of infinity that exists in today's mathematics as the root cause of this problem. We have created Observer's Mathematics that offers an alternative to contemporary mathematics. This paper is an attempt to relay how Observer's Mathematics may explain some of the contradictions in QM theory results. We considermore » the Hamiltonian Mechanics, Newton equation, Schrodinger equation, two slit interference, wave-particle duality for single photons, uncertainty principle, Dirac equations for free electron in a setting of arithmetic, algebra, and topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided.« less

Compressed modes for variational problems in mathematics and physics

PubMed Central

Ozoliņš, Vidvuds; Lai, Rongjie; Caflisch, Russel; Osher, Stanley

2013-01-01

This article describes a general formalism for obtaining spatially localized (“sparse”) solutions to a class of problems in mathematical physics, which can be recast as variational optimization problems, such as the important case of Schrödinger’s equation in quantum mechanics. Sparsity is achieved by adding an regularization term to the variational principle, which is shown to yield solutions with compact support (“compressed modes”). Linear combinations of these modes approximate the eigenvalue spectrum and eigenfunctions in a systematically improvable manner, and the localization properties of compressed modes make them an attractive choice for use with efficient numerical algorithms that scale linearly with the problem size. PMID:24170861

Compressed modes for variational problems in mathematics and physics.

PubMed

Ozolins, Vidvuds; Lai, Rongjie; Caflisch, Russel; Osher, Stanley

2013-11-12

This article describes a general formalism for obtaining spatially localized ("sparse") solutions to a class of problems in mathematical physics, which can be recast as variational optimization problems, such as the important case of Schrödinger's equation in quantum mechanics. Sparsity is achieved by adding an regularization term to the variational principle, which is shown to yield solutions with compact support ("compressed modes"). Linear combinations of these modes approximate the eigenvalue spectrum and eigenfunctions in a systematically improvable manner, and the localization properties of compressed modes make them an attractive choice for use with efficient numerical algorithms that scale linearly with the problem size.

How Mathematics Propels the Development of Physical Knowledge

ERIC Educational Resources Information Center

Schwartz, Daniel L.; Martin, Taylor; Pfaffman, Jay

2005-01-01

Three studies examined whether mathematics can propel the development of physical understanding. In Experiment 1, 10-year-olds solved balance scale problems that used easy-to-count discrete quantities or hard-to-count continuous quantities. Discrete quantities led to age typical performances. Continuous quantities caused performances like those of…

Observerʼs mathematics applications to quantum mechanics

NASA Astrophysics Data System (ADS)

Khots, B.; Khots, D.

2014-12-01

When we consider and analyze physical events with the purpose of creating corresponding models we often assume that the mathematical apparatus used in modeling is infallible. In particular, this relates to the use of infinity in various aspects and the use of Newton's definition of a limit in analysis. We believe that is where the main problem lies in the contemporary study of nature. This work considers physical aspects in a setting of arithmetic, algebra, geometry, analysis, and topology provided by Observer's Mathematics (see www.mathrelativity.com). In this paper, we consider Dirac equations for free electrons. Certain results and communications pertaining to solutions of these problems are provided.

The Relation between Students' Math and Reading Ability and Their Mathematics, Physics, and Chemistry Examination Grades in Secondary Education

ERIC Educational Resources Information Center

Korpershoek, Hanke; Kuyper, Hans; van der Werf, Greetje

2015-01-01

Word problems are math- or science-related problems presented in the context of a story or real-life scenario. Literature suggests that, to solve these problems, advanced reading skills are required, in addition to content-related skills in, for example, mathematics. In the present study, we investigated the relation between students' reading…

Online with Integers

ERIC Educational Resources Information Center

Siegel, Jonathan W.; Siegel, P. B.

2011-01-01

Integers are sometimes used in physics problems to simplify the mathematics so the arithmetic does not distract students from the physics concepts. This is particularly important in exams where students should not have to spend a lot of time using their calculators. Common uses of integers in physics problems include integer solutions to…

Essential Mathematics for the Physical Sciences; Volume I: Homogeneous boundary value problems, Fourier methods, and special functions

NASA Astrophysics Data System (ADS)

Borden, Brett; Luscombe, James

2017-10-01

Physics is expressed in the language of mathematics; it is deeply ingrained in how physics is taught and how it's practiced. A study of the mathematics used in science is thus a sound intellectual investment for training as scientists and engineers. This first volume of two is centered on methods of solving partial differential equations and the special functions introduced. This text is based on a course offered at the Naval Postgraduate School (NPS) and while produced for NPS needs, it will serve other universities well.

Mathematical sense-making in quantum mechanics: An initial peek

NASA Astrophysics Data System (ADS)

Dreyfus, Benjamin W.; Elby, Andrew; Gupta, Ayush; Sohr, Erin Ronayne

2017-12-01

Mathematical sense-making—looking for coherence between the structure of the mathematical formalism and causal or functional relations in the world—is a core component of physics expertise. Some physics education research studies have explored what mathematical sense-making looks like at the introductory physics level, while some historians and "science studies" have explored how expert physicists engage in it. What is largely missing, with a few exceptions, is theoretical and empirical work at the intermediate level—upper division physics students—especially when they are learning difficult new mathematical formalism. In this paper, we present analysis of a segment of video-recorded discussion between two students grappling with a quantum mechanics question to illustrate what mathematical sense-making can look like in quantum mechanics. We claim that mathematical sense-making is possible and productive for learning and problem solving in quantum mechanics. Mathematical sense-making in quantum mechanics is continuous in many ways with mathematical sense-making in introductory physics. However, in the context of quantum mechanics, the connections between formalism, intuitive conceptual schema, and the physical world become more compound (nested) and indirect. We illustrate these similarities and differences in part by proposing a new symbolic form, eigenvector eigenvalue, which is composed of multiple primitive symbolic forms.

Computational Modeling and Mathematics Applied to the Physical Sciences.

ERIC Educational Resources Information Center

National Academy of Sciences - National Research Council, Washington, DC.

One aim of this report is to show and emphasize that in the computational approaches to most of today's pressing and challenging scientific and technological problems, the mathematical aspects cannot and should not be considered in isolation. Following an introductory chapter, chapter 2 discusses a number of typical problems leading to…

Fostering Mathematical Understanding through Physical and Virtual Manipulatives

ERIC Educational Resources Information Center

Loong, Esther Yook Kin

2014-01-01

When solving mathematical problems, many students know the procedure to get to the answer but cannot explain why they are doing it in that way. According to Skemp (1976) these students have instrumental understanding but not relational understanding of the problem. They have accepted the rules to arriving at the answer without questioning or…

Video Analysis of a Plucked String: An Example of Problem-based Learning

NASA Astrophysics Data System (ADS)

Wentworth, Christopher D.; Buse, Eric

2009-11-01

Problem-based learning is a teaching methodology that grounds learning within the context of solving a real problem. Typically the problem initiates learning of concepts rather than simply being an application of the concept, and students take the lead in identifying what must be developed to solve the problem. Problem-based learning in upper-level physics courses can be challenging, because of the time and financial requirements necessary to generate real data. Here, we present a problem that motivates learning about partial differential equations and their solution in a mathematical methods for physics course. Students study a plucked elastic cord using high speed digital video. After creating video clips of the cord motion under different tensions they are asked to create a mathematical model. Ultimately, students develop and solve a model that includes damping effects that are clearly visible in the videos. The digital video files used in this project are available on the web at http://physics.doane.edu .

Problem Solving in Physics: Undergraduates' Framing, Procedures, and Decision Making

NASA Astrophysics Data System (ADS)

Modir, Bahar

In this dissertation I will start with the broad research question of what does problem solving in upper division physics look like? My focus in this study is on students' problem solving in physics theory courses. Some mathematical formalisms are common across all physics core courses such as using the process of separation of variables, doing Taylor series, or using the orthogonality properties of mathematical functions to set terms equal to zero. However, there are slight differences in their use of these mathematical formalisms across different courses, possibly because of how students map different physical systems to these processes. Thus, my first main research question aims to answer how students perform these recurring processes across upper division physics courses. I break this broad question into three particular research questions: What knowledge pieces do students use to make connections between physics and procedural math? How do students use their knowledge pieces coherently to provide reasoning strategies in estimation problems? How do students look ahead into the problem to read the information out of the physical scenario to align their use of math in physics? Building on the previous body of the literature, I will use the theory family of Knowledge in Pieces and provide evidence to expand this theoretical foundation. I will compare my study with previous studies and provide suggestions on how to generalize these theory expansions for future use. My experimental data mostly come from video-based classroom data. Students in groups of 2-4 students solve in-class problems in quantum mechanics and electromagnetic fields 1 courses collaboratively. In addition, I will analyze clinical interviews to demonstrate how a single case study student plays an epistemic game to estimate the total energy in a hurricane. My second research question is more focused on a particular instructional context. How do students frame problem solving in quantum mechanics? I will lay out a new theoretical framework based in epistemic framing that separates the problem solving space into four frames divided along two axes. The first axis models students' framing in math and physics, expanded through the second axis of conceptual problem solving and algorithmic problem solving. I use this framework to show how students navigate problem solving. Lastly, I will use this developed framework to interpret existing difficulties in quantum mechanics.

How students process equations in solving quantitative synthesis problems? Role of mathematical complexity in students' mathematical performance

NASA Astrophysics Data System (ADS)

Ibrahim, Bashirah; Ding, Lin; Heckler, Andrew F.; White, Daniel R.; Badeau, Ryan

2017-12-01

We examine students' mathematical performance on quantitative "synthesis problems" with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking, formulation and combination of equations require conceptual reasoning; simplification of equations requires manipulation of equations as computational tools. Mathematical complexity is operationally defined by the number and the type of equations to be manipulated concurrently due to the number of unknowns in each equation. We use two types of synthesis problems, namely, sequential and simultaneous tasks. Sequential synthesis tasks require a chronological application of pertinent concepts, and simultaneous synthesis tasks require a concurrent application of the pertinent concepts. A total of 179 physics major students from a second year mechanics course participated in the study. Data were collected from written tasks and individual interviews. Results show that mathematical complexity negatively influences the students' mathematical performance on both types of synthesis problems. However, for the sequential synthesis tasks, it interferes only with the students' simplification of equations. For the simultaneous synthesis tasks, mathematical complexity additionally impedes the students' formulation and combination of equations. Several reasons may explain this difference, including the students' different approaches to the two types of synthesis problems, cognitive load, and the variation of mathematical complexity within each synthesis type.

Translating across Macroscopic, Submicroscopic, and Symbolic Levels: The Role of Instructor Facilitation in an Inquiry-Oriented Physical Chemistry Class

ERIC Educational Resources Information Center

Becker, Nicole; Stanford, Courtney; Towns, Marcy; Cole, Renee

2015-01-01

In physical chemistry classrooms, mathematical and graphical representations are critical tools for reasoning about chemical phenomena. However, there is abundant evidence that to be successful in understanding complex thermodynamics topics, students must go beyond rote mathematical problem solving in order to connect their understanding of…

Biological system interactions.

PubMed Central

Adomian, G; Adomian, G E; Bellman, R E

1984-01-01

Mathematical modeling of cellular population growth, interconnected subsystems of the body, blood flow, and numerous other complex biological systems problems involves nonlinearities and generally randomness as well. Such problems have been dealt with by mathematical methods often changing the actual model to make it tractable. The method presented in this paper (and referenced works) allows much more physically realistic solutions. PMID:6585837

The Monte Carlo Method. Popular Lectures in Mathematics.

ERIC Educational Resources Information Center

Sobol', I. M.

The Monte Carlo Method is a method of approximately solving mathematical and physical problems by the simulation of random quantities. The principal goal of this booklet is to suggest to specialists in all areas that they will encounter problems which can be solved by the Monte Carlo Method. Part I of the booklet discusses the simulation of random…

Who Teaches Mathematics at Second Level in Ireland?

ERIC Educational Resources Information Center

Ni Riordain, Maire; Hannigan, Ailish

2011-01-01

Ireland's "mathematics problem" is well-documented and extensively reported in the media and elsewhere (Expert Group on Future Skills Needs (EGFSN) 2008; Task Force on the Physical Sciences 2002). Concern primarily lies with post-primary students' underperformance in mathematics coupled with a failure to make a successful transition to…

Carl Neumann versus Rudolf Clausius on the propagation of electrodynamic potentials

NASA Astrophysics Data System (ADS)

Archibald, Thomas

1986-09-01

In the late 1860's, German electromagnetic theorists employing W. Weber's velocity-dependent force law were forced to confront the issue of energy conservation. One attempt to formulate a conservation law for such forces was due to Carl Neumann, who introduced a model employing retarded potentials in 1868. Rudolf Clausius quickly pointed out certain problems with the physical interpretation of Neumann's mathematical formalism. The debate between the two men continued until the 1880's and illustrates the strictures facing mathematical approaches to physical problems during this prerelativistic, pre-Maxwellian period.

Effects of the Problem-Posing Approach on Students' Problem Solving Skills and Metacognitive Awareness in Science Education

NASA Astrophysics Data System (ADS)

Akben, Nimet

2018-05-01

The interrelationship between mathematics and science education has frequently been emphasized, and common goals and approaches have often been adopted between disciplines. Improving students' problem-solving skills in mathematics and science education has always been given special attention; however, the problem-posing approach which plays a key role in mathematics education has not been commonly utilized in science education. As a result, the purpose of this study was to better determine the effects of the problem-posing approach on students' problem-solving skills and metacognitive awareness in science education. This was a quasi-experimental based study conducted with 61 chemistry and 40 physics students; a problem-solving inventory and a metacognitive awareness inventory were administered to participants both as a pre-test and a post-test. During the 2017-2018 academic year, problem-solving activities based on the problem-posing approach were performed with the participating students during their senior year in various university chemistry and physics departments throughout the Republic of Turkey. The study results suggested that structured, semi-structured, and free problem-posing activities improve students' problem-solving skills and metacognitive awareness. These findings indicated not only the usefulness of integrating problem-posing activities into science education programs but also the need for further research into this question.

What Physicist Mean By The Equals Sign In Undergraduate Education

NASA Astrophysics Data System (ADS)

Zohrabi Alaee, Dina; Kornick, Kellianne; Sayre, Eleanor C.; Franklin, Scott V.

2017-01-01

Mathematical concepts and tools have an important role in physics. Faculties want students to think critically about mathematics and the underlying fundamental concepts, rather than simply memorizing a series of equations and answers. The equals sign - ubiquitous in problem solving - carries different conceptual meaning depending on how it is used; this meaning is deeply tied to cultural practices in problem solving in physics. We use symbolic forms to investigate the conceptual and cultural meanings of the equals sign across physics contexts. We built and validated a rubric to classify the ways that physics students use the equals sign in their written work. Our categories are causality, assignments, definitional, balancing, and just math. We analyze students' use of the equals sign in their written homework and exam solutions in an upper-division electrostatics course. We correlate the kinds of equal signs within problem solutions with the difficulty of the problem. We compare they ways students use the equals sign to their course lectures and textbook.

Instructional Strategies for Online Introductory College Physics Based on Learning Styles

ERIC Educational Resources Information Center

Ekwue, Eleazer U.

2013-01-01

The practical nature of physics and its reliance on mathematical presentations and problem solving pose a challenge toward presentation of the course in an online environment for effective learning experience. Most first-time introductory college physics students fail to grasp the basic concepts of the course and the problem solving skills if the…

The Use of Metacognitive Knowledge Patterns to Compose Physics Higher Order Thinking Problems

ERIC Educational Resources Information Center

Abdullah, Helmi; Malago, Jasruddin D.; Bundu, Patta; Thalib, Syamsul Bachri

2013-01-01

The main aspect in physics learning is the use of equation in problem solving. Equation is a mathematical form of theoretical statements, principles, and laws in physics, and describes a relationship between one concept to another by using a specific symbol. In a context of knowledge dimension, equation is a procedural knowledge. Students are…

Mathematical Science Course

ERIC Educational Resources Information Center

Woof, K. R.

1975-01-01

Describes an experimental type of science course which involves theoretical and practical approaches to scientific topics by using mathematics to develop and explain scientific problems and theory. Gives an example of such a course applied to the teaching of physical anthropology. (MLH)

Teaching Guide and Problem Supplement. A Publication of the Exemplary Project Problem Solving Computer Style 1969-1970.

ERIC Educational Resources Information Center

New Orleans Public Schools, LA.

Secondary school teachers incorporating the use of a computer in algebra, trigonometry, advanced mathematics, chemistry, or physics classes are the individuals for whom this book is intended. The content included in it is designed to aid the learning of programing techniques and basic scientific or mathematical principles, and to offer some…

Methods of Mathematical and Computational Physics for Industry, Science, and Technology

NASA Astrophysics Data System (ADS)

Melnik, Roderick V. N.; Voss, Frands

2006-11-01

Many industrial problems provide scientists with important and challenging problems that need to be solved today rather than tomorrow. The key role of mathematical physics, modelling, and computational methodologies in addressing such problems continues to increase. Science has never been exogenous to applied research. Gigantic ships and steam engines, repeating catapult of Dionysius and the Antikythera `computer' invented around 80BC are just a few examples demonstrating a profound link between theoretical and applied science in the ancient world. Nowadays, many industrial problems are typically approached by groups of researchers who are working as a team bringing their expertise to the success of the entire enterprise. Since the late 1960s several groups of European mathematicians and scientists have started organizing regular meetings, seeking new challenges from industry and contributing to the solution of important industrial problems. In particular, this often took the format of week-long workshops originally initiated by the Oxford Study Groups with Industry in 1968. Such workshops are now held in many European countries (typically under the auspices of the European Study Groups with Industry - ESGI), as well as in Australia, Canada, the United States, and other countries around the world. Problems given by industrial partners are sometimes very difficult to complete within a week. However, during a week of brainstorming activities these problems inevitably stimulate developing fruitful new ideas, new approaches, and new collaborations. At the same time, there are cases where as soon as the problem is formulated mathematically, it is relatively easy to solve. Hence, putting the industrial problem into a mathematical framework, based on physical laws, often provides a key element to the success. In addition to this important first step, the value in such cases is the real, practical applicability of the results obtained for an industrial partner who presents the problem. Under both outlined scenarios, scientists and mathematicians are provided with an opportunity to challenge themselves with real-world problems and to work together in a team on important industrial issues. This issue is a result of selected contributions by participants of the meeting that took place in the Sønderborg area of Denmark, one of the most important centers for information technology, telecommunication and electronics in the country. The meeting was hosted by the University of Southern Denmark in a picturesque area of Southern Jutland. It brought together about 65 participants, among whom were professional mathematicians, engineers, physicists, and industrial participants. The meeting was a truly international one, with delegates from four major Danish Universities, the UK, Norway, Italy, Czech Republic, Turkey, China, Germany, Latvia, Canada, the United States, and Finland. Five challenging projects were presented by leading industrial companies, including Grundfos, Danfoss Industrial Control, Unisensor, and Danfoss Flow Division (now Siemens). The meeting featured also the Mathematics for Industry Workshop with several distinguished international speakers. This volume of Journal of Physics: Conference Series on `Methods of Mathematical and Computational Physics for Industry, Science, and Technology' contains contributions from some of the participants of the workshop as well as the papers produced as a result of collaborative efforts with the above mentioned industrial companies. We would like to thank all authors and participants for their contributions and for bearing with us during the review process and preparation of this issue. We thank also all our referees for their timely and detailed reports. The publication of the proceedings of this meeting in Denmark was delayed due to problems with a previous publisher. We are very grateful that Journal of Physics: Conference Series kindly agreed to publish the proceedings rapidly at this late stage. As industrial problems become increasingly multidisciplinary, their successful solutions are often contingent on effective collaborative efforts between scientists, mathematicians, industrialists, and engineers. This volume has provided several examples of such collaborative efforts in the context of real-world industrial problems along with the analysis of important physics-based mathematical models applicable in a range of industrial contexts. Roderick V N Melnik, Professor of Mathematical Modelling, Syddansk Universitet (Denmark) and Professor and Canada Research Chair, Wilfrid Laurier University, Waterloo, Canada E-mail: rmelnik@wlu.ca Frands Voss, Director of the Mads Clausen Institute, Syddansk Universitet (Denmark)

New tools for investigating student learning in upper-division electrostatics

NASA Astrophysics Data System (ADS)

Wilcox, Bethany R.

Student learning in upper-division physics courses is a growing area of research in the field of Physics Education. Developing effective new curricular materials and pedagogical techniques to improve student learning in upper-division courses requires knowledge of both what material students struggle with and what curricular approaches help to overcome these struggles. To facilitate the course transformation process for one specific content area --- upper-division electrostatics --- this thesis presents two new methodological tools: (1) an analytical framework designed to investigate students' struggles with the advanced physics content and mathematically sophisticated tools/techniques required at the junior and senior level, and (2) a new multiple-response conceptual assessment designed to measure student learning and assess the effectiveness of different curricular approaches. We first describe the development and theoretical grounding of a new analytical framework designed to characterize how students use mathematical tools and techniques during physics problem solving. We apply this framework to investigate student difficulties with three specific mathematical tools used in upper-division electrostatics: multivariable integration in the context of Coulomb's law, the Dirac delta function in the context of expressing volume charge densities, and separation of variables as a technique to solve Laplace's equation. We find a number of common themes in students' difficulties around these mathematical tools including: recognizing when a particular mathematical tool is appropriate for a given physics problem, mapping between the specific physical context and the formal mathematical structures, and reflecting spontaneously on the solution to a physics problem to gain physical insight or ensure consistency with expected results. We then describe the development of a novel, multiple-response version of an existing conceptual assessment in upper-division electrostatics courses. The goal of this new version is to provide an easily-graded electrostatics assessment that can potentially be implemented to investigate student learning on a large scale. We show that student performance on the new multiple-response version exhibits a significant degree of consistency with performance on the free-response version, and that it continues to provide significant insight into student reasoning and student difficulties. Moreover, we demonstrate that the new assessment is both valid and reliable using data from upper-division physics students at multiple institutions. Overall, the work described in this thesis represents a significant contribution to the methodological tools available to researchers and instructors interested in improving student learning at the upper-division level.

The Mathematics of High School Physics

NASA Astrophysics Data System (ADS)

Kanderakis, Nikos

2016-10-01

In the seventeenth and eighteenth centuries, mathematicians and physical philosophers managed to study, via mathematics, various physical systems of the sublunar world through idealized and simplified models of these systems, constructed with the help of geometry. By analyzing these models, they were able to formulate new concepts, laws and theories of physics and then through models again, to apply these concepts and theories to new physical phenomena and check the results by means of experiment. Students' difficulties with the mathematics of high school physics are well known. Science education research attributes them to inadequately deep understanding of mathematics and mainly to inadequate understanding of the meaning of symbolic mathematical expressions. There seem to be, however, more causes of these difficulties. One of them, not independent from the previous ones, is the complex meaning of the algebraic concepts used in school physics (e.g. variables, parameters, functions), as well as the complexities added by physics itself (e.g. that equations' symbols represent magnitudes with empirical meaning and units instead of pure numbers). Another source of difficulties is that the theories and laws of physics are often applied, via mathematics, to simplified, and idealized physical models of the world and not to the world itself. This concerns not only the applications of basic theories but also all authentic end-of-the-chapter problems. Hence, students have to understand and participate in a complex interplay between physics concepts and theories, physical and mathematical models, and the real world, often without being aware that they are working with models and not directly with the real world.

The Role of Sign in Students' Modeling of Scalar Equations

ERIC Educational Resources Information Center

Hayes, Kate; Wittmann, Michael C.

2010-01-01

Helping students set up equations is one of the major goals of teaching a course in physics that contains elements of problem solving. Students must take the stories we present, interpret them, and turn them into physics; from there, they must turn that physical, idealized story into mathematics. How they do so and what problems lie along the way…

Dannie Heineman Prize for Mathematical Physics: Applying mathematical techniques to solve important problems in quantum theory

NASA Astrophysics Data System (ADS)

Bender, Carl

2017-01-01

The theory of complex variables is extremely useful because it helps to explain the mathematical behavior of functions of a real variable. Complex variable theory also provides insight into the nature of physical theories. For example, it provides a simple and beautiful picture of quantization and it explains the underlying reason for the divergence of perturbation theory. By using complex-variable methods one can generalize conventional Hermitian quantum theories into the complex domain. The result is a new class of parity-time-symmetric (PT-symmetric) theories whose remarkable physical properties have been studied and verified in many recent laboratory experiments.

Research on Mathematics and Science Education: From Beliefs to Cognition, from Problem Solving to Understanding.

ERIC Educational Resources Information Center

Ahtee, Maija, Ed.; Bjorkqvist, Ole, Ed.; Pehkonen, Erkki, Ed.; Vatanen, Virpi, Ed.

This book contains selected research papers presented at seminars held throughout the year 2000 in Finland by members of the Finnish Association for Research in Mathematics and Science Education (FARMSE) and students at the Finnish Graduate School of Mathematics, Physics, and Chemistry Education. This volume also contains papers professor Laurence…

Comparative evolution of the inverse problems (Introduction to an interdisciplinary study of the inverse problems)

NASA Technical Reports Server (NTRS)

Sabatier, P. C.

1972-01-01

The progressive realization of the consequences of nonuniqueness imply an evolution of both the methods and the centers of interest in inverse problems. This evolution is schematically described together with the various mathematical methods used. A comparative description is given of inverse methods in scientific research, with examples taken from mathematics, quantum and classical physics, seismology, transport theory, radiative transfer, electromagnetic scattering, electrocardiology, etc. It is hoped that this paper will pave the way for an interdisciplinary study of inverse problems.

Mathematical Metaphors: Problem Reformulation and Analysis Strategies

NASA Technical Reports Server (NTRS)

Thompson, David E.

2005-01-01

This paper addresses the critical need for the development of intelligent or assisting software tools for the scientist who is working in the initial problem formulation and mathematical model representation stage of research. In particular, examples of that representation in fluid dynamics and instability theory are discussed. The creation of a mathematical model that is ready for application of certain solution strategies requires extensive symbolic manipulation of the original mathematical model. These manipulations can be as simple as term reordering or as complicated as discovery of various symmetry groups embodied in the equations, whereby Backlund-type transformations create new determining equations and integrability conditions or create differential Grobner bases that are then solved in place of the original nonlinear PDEs. Several examples are presented of the kinds of problem formulations and transforms that can be frequently encountered in model representation for fluids problems. The capability of intelligently automating these types of transforms, available prior to actual mathematical solution, is advocated. Physical meaning and assumption-understanding can then be propagated through the mathematical transformations, allowing for explicit strategy development.

Large-Scale Studies on the Transferability of General Problem-Solving Skills and the Pedagogic Potential of Physics

ERIC Educational Resources Information Center

Mashood, K. K.; Singh, Vijay A.

2013-01-01

Research suggests that problem-solving skills are transferable across domains. This claim, however, needs further empirical substantiation. We suggest correlation studies as a methodology for making preliminary inferences about transfer. The correlation of the physics performance of students with their performance in chemistry and mathematics in…

A new problem in mathematical physics associated with the problem of coherent phase transformation

NASA Astrophysics Data System (ADS)

Grinfeld, M. A.

1985-06-01

The description of heterogeneous coherent phase equilibria in an elastic single component system is shown to lead, in the approximation of small intrinsic deformation, to a new problem in mathematical physics with an unknown bound. The low order terms of the resulting system of equilibrium equations coincide with the equations of the classical linear theory of elasticity (generally speaking, anisotropic); however, the problem remains strongly nonlinear overall, inasmuch as it contains an unknown bound and a boundary condition on it which is quadratic with respect to translation. The formulas obtained are used to find certain explicit solutions to the boundary problems. As an example, the problem of heterogeneous equilibria in an infinite rectangular isotropic beam with free faces and constant loading on the surfaces x squared = const can be examined. A modeling problem for the asymptote of small intrinsic deformation during coherent phase transformation is presented as a scalar analog of the vector problem considered initially.

Exploring New Physics Frontiers Through Numerical Relativity.

PubMed

Cardoso, Vitor; Gualtieri, Leonardo; Herdeiro, Carlos; Sperhake, Ulrich

2015-01-01

The demand to obtain answers to highly complex problems within strong-field gravity has been met with significant progress in the numerical solution of Einstein's equations - along with some spectacular results - in various setups. We review techniques for solving Einstein's equations in generic spacetimes, focusing on fully nonlinear evolutions but also on how to benchmark those results with perturbative approaches. The results address problems in high-energy physics, holography, mathematical physics, fundamental physics, astrophysics and cosmology.

An Object-Oriented Network-Centric Software Architecture for Physical Computing

NASA Astrophysics Data System (ADS)

Palmer, Richard

1997-08-01

Recent developments in object-oriented computer languages and infrastructure such as the Internet, Web browsers, and the like provide an opportunity to define a more productive computational environment for scientific programming that is based more closely on the underlying mathematics describing physics than traditional programming languages such as FORTRAN or C++. In this talk I describe an object-oriented software architecture for representing physical problems that includes classes for such common mathematical objects as geometry, boundary conditions, partial differential and integral equations, discretization and numerical solution methods, etc. In practice, a scientific program written using this architecture looks remarkably like the mathematics used to understand the problem, is typically an order of magnitude smaller than traditional FORTRAN or C++ codes, and hence easier to understand, debug, describe, etc. All objects in this architecture are ``network-enabled,'' which means that components of a software solution to a physical problem can be transparently loaded from anywhere on the Internet or other global network. The architecture is expressed as an ``API,'' or application programmers interface specification, with reference embeddings in Java, Python, and C++. A C++ class library for an early version of this API has been implemented for machines ranging from PC's to the IBM SP2, meaning that phidentical codes run on all architectures.

A Novel Numerical Method for Fuzzy Boundary Value Problems

NASA Astrophysics Data System (ADS)

Can, E.; Bayrak, M. A.; Hicdurmaz

2016-05-01

In the present paper, a new numerical method is proposed for solving fuzzy differential equations which are utilized for the modeling problems in science and engineering. Fuzzy approach is selected due to its important applications on processing uncertainty or subjective information for mathematical models of physical problems. A second-order fuzzy linear boundary value problem is considered in particular due to its important applications in physics. Moreover, numerical experiments are presented to show the effectiveness of the proposed numerical method on specific physical problems such as heat conduction in an infinite plate and a fin.

Using Technology to Facilitate and Enhance Project-based Learning in Mathematical Physics

NASA Astrophysics Data System (ADS)

Duda, Gintaras

2011-04-01

Problem-based and project-based learning are two pedagogical techniques that have several clear advantages over traditional instructional methods: 1) both techniques are active and student centered, 2) students confront real-world and/or highly complex problems, and 3) such exercises model the way science and engineering are done professionally. This talk will present an experiment in project/problem-based learning in a mathematical physics course. The group project in the course involved modeling a zombie outbreak of the type seen in AMC's ``The Walking Dead.'' Students researched, devised, and solved their mathematical models for the spread of zombie-like infection. Students used technology in all stages; in fact, since analytical solutions to the models were often impossible, technology was a necessary and critical component of the challenge. This talk will explore the use of technology in general in problem and project-based learning and will detail some specific examples of how technology was used to enhance student learning in this course. A larger issue of how students use the Internet to learn will also be explored.

Functional Integration

NASA Astrophysics Data System (ADS)

Cartier, Pierre; DeWitt-Morette, Cecile

2006-11-01

Acknowledgements; List symbols, conventions, and formulary; Part I. The Physical and Mathematical Environment: 1. The physical and mathematical environment; Part II. Quantum Mechanics: 2. First lesson: gaussian integrals; 3. Selected examples; 4. Semiclassical expansion: WKB; 5. Semiclassical expansion: beyond WKB; 6. Quantum dynamics: path integrals and operator formalism; Part III. Methods from Differential Geometry: 7. Symmetries; 8. Homotopy; 9. Grassmann analysis: basics; 10. Grassmann analysis: applications; 11. Volume elements, divergences, gradients; Part IV. Non-Gaussian Applications: 12. Poisson processes in physics; 13. A mathematical theory of Poisson processes; 14. First exit time: energy problems; Part V. Problems in Quantum Field Theory: 15. Renormalization 1: an introduction; 16. Renormalization 2: scaling; 17. Renormalization 3: combinatorics; 18. Volume elements in quantum field theory Bryce DeWitt; Part VI. Projects: 19. Projects; Appendix A. Forward and backward integrals: spaces of pointed paths; Appendix B. Product integrals; Appendix C. A compendium of gaussian integrals; Appendix D. Wick calculus Alexander Wurm; Appendix E. The Jacobi operator; Appendix F. Change of variables of integration; Appendix G. Analytic properties of covariances; Appendix H. Feynman's checkerboard; Bibliography; Index.

Functional Integration

NASA Astrophysics Data System (ADS)

Cartier, Pierre; DeWitt-Morette, Cecile

2010-06-01

Acknowledgements; List symbols, conventions, and formulary; Part I. The Physical and Mathematical Environment: 1. The physical and mathematical environment; Part II. Quantum Mechanics: 2. First lesson: gaussian integrals; 3. Selected examples; 4. Semiclassical expansion: WKB; 5. Semiclassical expansion: beyond WKB; 6. Quantum dynamics: path integrals and operator formalism; Part III. Methods from Differential Geometry: 7. Symmetries; 8. Homotopy; 9. Grassmann analysis: basics; 10. Grassmann analysis: applications; 11. Volume elements, divergences, gradients; Part IV. Non-Gaussian Applications: 12. Poisson processes in physics; 13. A mathematical theory of Poisson processes; 14. First exit time: energy problems; Part V. Problems in Quantum Field Theory: 15. Renormalization 1: an introduction; 16. Renormalization 2: scaling; 17. Renormalization 3: combinatorics; 18. Volume elements in quantum field theory Bryce DeWitt; Part VI. Projects: 19. Projects; Appendix A. Forward and backward integrals: spaces of pointed paths; Appendix B. Product integrals; Appendix C. A compendium of gaussian integrals; Appendix D. Wick calculus Alexander Wurm; Appendix E. The Jacobi operator; Appendix F. Change of variables of integration; Appendix G. Analytic properties of covariances; Appendix H. Feynman's checkerboard; Bibliography; Index.

Use of model analysis to analyse Thai students’ attitudes and approaches to physics problem solving

NASA Astrophysics Data System (ADS)

Rakkapao, S.; Prasitpong, S.

2018-03-01

This study applies the model analysis technique to explore the distribution of Thai students’ attitudes and approaches to physics problem solving and how those attitudes and approaches change as a result of different experiences in physics learning. We administered the Attitudes and Approaches to Problem Solving (AAPS) survey to over 700 Thai university students from five different levels, namely students entering science, first-year science students, and second-, third- and fourth-year physics students. We found that their inferred mental states were generally mixed. The largest gap between physics experts and all levels of the students was about the role of equations and formulas in physics problem solving, and in views towards difficult problems. Most participants of all levels believed that being able to handle the mathematics is the most important part of physics problem solving. Most students’ views did not change even though they gained experiences in physics learning.

Success in introductory college physics: The role of gender, high school preparation, and student learning perceptions

NASA Astrophysics Data System (ADS)

Chen, Jean Chi-Jen

Physics is fundamental for science, engineering, medicine, and for understanding many phenomena encountered in people's daily lives. The purpose of this study was to investigate the relationships between student success in college-level introductory physics courses and various educational and background characteristics. The primary variables of this study were gender, high school mathematics and science preparation, preference and perceptions of learning physics, and performance in introductory physics courses. Demographic characteristics considered were age, student grade level, parents' occupation and level of education, high school senior grade point average, and educational goals. A Survey of Learning Preference and Perceptions was developed to collect the information for this study. A total of 267 subjects enrolled in six introductory physics courses, four algebra-based and two calculus-based, participated in the study conducted during Spring Semester 2002. The findings from the algebra-based physics courses indicated that participant's educational goal, high school senior GPA, father's educational level, mother's educational level, and mother's occupation in the area of science, engineering, or computer technology were positively related to performance while participant age was negatively related. Biology preparation, mathematics preparation, and additional mathematics and science preparation in high school were also positively related to performance. The relationships between the primary variables and performance in calculus-based physics courses were limited to high school senior year GPA and high school physics preparation. Findings from all six courses indicated that participant's educational goal, high school senior GPA, father's educational level, and mother's occupation in the area of science, engineering, or computer technology, high school preparation in mathematics, biology, and the completion of additional mathematics and science courses were positively related to performance. No significant performance differences were found between male and female students. However, there were significant gender differences in physics learning perceptions. Female participants tended to try to understand physics materials and relate the physics problems to real world situations while their male counterparts tended to rely on rote learning and equation application. This study found that participants performed better by trying to understand the physics material and relate physics problems to real world situations. Participants who relied on rote learning did not perform well.

Photoelectric effect from observer's mathematics point of view

NASA Astrophysics Data System (ADS)

Khots, Boris; Khots, Dmitriy

2014-12-01

When we consider and analyze physical events with the purpose of creating corresponding models we often assume that the mathematical apparatus used in modeling is infallible. In particular, this relates to the use of infinity in various aspects and the use of Newton's definition of a limit in analysis. We believe that is where the main problem lies in contemporary study of nature. This work considers Physical aspects in a setting of arithmetic, algebra, geometry, analysis, topology provided by Observer's Mathematics (see www.mathrelativity.com). Certain results and communications pertaining to solution of these problems are provided. In particular, we prove the following Theorems, which give Observer's Mathematics point of view on Einstein photoelectric effect theory and Lamb-Scully and Hanbury-Brown-Twiss experiments: Theorem 1. There are some values of light intensity where anticorrelation parameter A ∈ [0,1). Theorem 2. There are some values of light intensity where anticorrelation parameter A = 1. Theorem 3. There are some values of light intensity where anticorrelation parameter A > 1.

Mapping University Students' Epistemic Framing of Computational Physics Using Network Analysis

ERIC Educational Resources Information Center

Bodin, Madelen

2012-01-01

Solving physics problem in university physics education using a computational approach requires knowledge and skills in several domains, for example, physics, mathematics, programming, and modeling. These competences are in turn related to students' beliefs about the domains as well as about learning. These knowledge and beliefs components are…

Comparing the cognitive differences resulting from modeling instruction: Using computer microworld and physical object instruction to model real world problems

NASA Astrophysics Data System (ADS)

Oursland, Mark David

This study compared the modeling achievement of students receiving mathematical modeling instruction using the computer microworld, Interactive Physics, and students receiving instruction using physical objects. Modeling instruction included activities where students applied the (a) linear model to a variety of situations, (b) linear model to two-rate situations with a constant rate, (c) quadratic model to familiar geometric figures. Both quantitative and qualitative methods were used to analyze achievement differences between students (a) receiving different methods of modeling instruction, (b) with different levels of beginning modeling ability, or (c) with different levels of computer literacy. Student achievement was analyzed quantitatively through a three-factor analysis of variance where modeling instruction, beginning modeling ability, and computer literacy were used as the three independent factors. The SOLO (Structure of the Observed Learning Outcome) assessment framework was used to design written modeling assessment instruments to measure the students' modeling achievement. The same three independent factors were used to collect and analyze the interviews and observations of student behaviors. Both methods of modeling instruction used the data analysis approach to mathematical modeling. The instructional lessons presented problem situations where students were asked to collect data, analyze the data, write a symbolic mathematical equation, and use equation to solve the problem. The researcher recommends the following practice for modeling instruction based on the conclusions of this study. A variety of activities with a common structure are needed to make explicit the modeling process of applying a standard mathematical model. The modeling process is influenced strongly by prior knowledge of the problem context and previous modeling experiences. The conclusions of this study imply that knowledge of the properties about squares improved the students' ability to model a geometric problem more than instruction in data analysis modeling. The uses of computer microworlds such as Interactive Physics in conjunction with cooperative groups are a viable method of modeling instruction.

Workshop Physics Activity Guide, Module 3: Heat Temperature and Nuclear Radiation, Thermodynamics, Kinetic Theory, Heat Engines, Nuclear Decay, and Random Monitoring (Units 16 - 18 & 28)

NASA Astrophysics Data System (ADS)

Laws, Priscilla W.

2004-05-01

The Workshop Physics Activity Guide is a set of student workbooks designed to serve as the foundation for a two-semester calculus-based introductory physics course. It consists of 28 units that interweave text materials with activities that include prediction, qualitative observation, explanation, equation derivation, mathematical modeling, quantitative experiments, and problem solving. Students use a powerful set of computer tools to record, display, and analyze data, as well as to develop mathematical models of physical phenomena. The design of many of the activities is based on the outcomes of physics education research.

Resource Letter RPS-1: Research in problem solving

NASA Astrophysics Data System (ADS)

Hsu, Leonardo; Brewe, Eric; Foster, Thomas M.; Harper, Kathleen A.

2004-09-01

This Resource Letter provides a guide to the literature on research in problem solving, especially in physics. The references were compiled with two audiences in mind: physicists who are (or might become) engaged in research on problem solving, and physics instructors who are interested in using research results to improve their students' learning of problem solving. In addition to general references, journal articles and books are cited for the following topics: cognitive aspects of problem solving, expert-novice problem-solver characteristics, problem solving in mathematics, alternative problem types, curricular interventions, and the use of computers in problem solving.

Recent Advances in the Edge-Function Method 1979-1980

DTIC Science & Technology

1980-07-30

the residuals are within the limits within which an engineer can specify the boundary conditions of the problem, then the corresponding Mathematical ...truncation lvel . The consistent preference shown by the solver routine for verteA functions as opposed to polar functions reinforces the expectations of...Accordingly,each solution zr_.-4_des a Mathematical Model for the given physical problem- R.M.S. values provide a practical criterion for the enai--er to

Research on Mathematical Techniques in Psychology. Final Report.

ERIC Educational Resources Information Center

Gulliksen, Harold

Mathematical techniques are developed for studying psychological problems in three fields: (1) psychological scaling, (2) learning and concept formation, and (3) mental measurement. Psychological scaling procedures are demonstrated to be useful in many areas, ranging from sensory discrimination of physical stimuli, such as colors, sounds, etc.,…

An issue encountered in solving problems in electricity and magnetism: curvilinear coordinates

NASA Astrophysics Data System (ADS)

Gülçiçek, Çağlar; Damlı, Volkan

2016-11-01

In physics lectures on electromagnetic theory and mathematical methods, physics teacher candidates have some difficulties with curvilinear coordinate systems. According to our experience, based on both in-class interactions and teacher candidates’ answers in test papers, they do not seem to have understood the variables in curvilinear coordinate systems very well. For this reason, the problems that physics teacher candidates have with variables in curvilinear coordinate systems have been selected as a study subject. The aim of this study is to find the physics teacher candidates’ problems with determining the variables of drawn shapes, and problems with drawing shapes based on given variables in curvilinear coordinate systems. Two different assessment tests were used in the study to achieve this aim. The curvilinear coordinates drawing test (CCDrT) was used to discover their problems related to drawing shapes, and the curvilinear coordinates detection test (CCDeT) was used to find out about problems related to determining variables. According to the findings obtained from both tests, most physics teacher candidates have problems with the ϕ variable, while they have limited problems with the r variable. Questions that are mostly answered wrongly have some common properties, such as value. According to inferential statistics, there is no significant difference between the means of the CCDeT and CCDrT scores. The mean of the CCDeT scores is only 4.63 and the mean of the CCDrT is only 4.66. Briefly, we can say that most physics teacher candidates have problems with drawing a shape using the variables of curvilinear coordinate systems or in determining the variables of drawn shapes. Part of this study was presented at the XI. National Science and Mathematics Education Congress (UFBMEK) in 2014.

Changing the Metacognitive Orientation of a Classroom Environment to Stimulate Metacognitive Reflection Regarding the Nature of Physics Learning

ERIC Educational Resources Information Center

Thomas, Gregory P.

2013-01-01

Problems persist with physics learning in relation to students' understanding and use of representations for making sense of physics concepts. Further, students' views of physics learning and their physics learning processes have been predominantly found to reflect a "surface" approach to learning that focuses on mathematical aspects of…

Upper-Division Student Difficulties with the Dirac Delta Function

ERIC Educational Resources Information Center

Wilcox, Bethany R.; Pollock, Steven J.

2015-01-01

The Dirac delta function is a standard mathematical tool that appears repeatedly in the undergraduate physics curriculum in multiple topical areas including electrostatics, and quantum mechanics. While Dirac delta functions are often introduced in order to simplify a problem mathematically, students still struggle to manipulate and interpret them.…

Supplemental Instruction in Physical Chemistry I

ERIC Educational Resources Information Center

Toby, Ellen; Scott, Timothy P.; Migl, David; Kolodzeji, Elizabeth

2016-01-01

Physical chemistry I at Texas A&M University is an upper division course requiring mathematical and analytical skills. As such, this course poses a major problem for many Chemistry, Engineering, Biochemistry and Genetics majors. Comparisons between participants and non-participants in Supplemental Instruction for physical chemistry were made…

The Pythagorean Roots of Introductory Physics

ERIC Educational Resources Information Center

Clarage, James B.

2013-01-01

Much of the mathematical reasoning employed in the typical introductory physics course can be traced to Pythagorean roots planted over two thousand years ago. Besides obvious examples involving the Pythagorean theorem, I draw attention to standard physics problems and derivations which often unknowingly rely upon the Pythagoreans' work on…

Modeling Physical Systems Using Vensim PLE Systems Dynamics Software

ERIC Educational Resources Information Center

Widmark, Stephen

2012-01-01

Many physical systems are described by time-dependent differential equations or systems of such equations. This makes it difficult for students in an introductory physics class to solve many real-world problems since these students typically have little or no experience with this kind of mathematics. In my high school physics classes, I address…

David crighton, 1942-2000: a commentary on his career and his influence on aeroacoustic theory

NASA Astrophysics Data System (ADS)

Ffowcs Williams, John E.

David Crighton, a greatly admired figure in fluid mechanics, Head of the Department of Applied Mathematics and Theoretical Physics at Cambridge, and Master of Jesus College, Cambridge, died at the peak of his career. He had made important contributions to the theory of waves generated by unsteady flow. Crighton's work was always characterized by the application of rigorous mathematical approximations to fluid mechanical idealizations of practically relevant problems. At the time of his death, he was certainly the most influential British applied mathematical figure, and his former collaborators and students form a strong school that continues his special style of mathematical application. Rigorous analysis of well-posed aeroacoustical problems was transformed by David Crighton.

Large-scale studies on the transferability of general problem-solving skills and the pedagogic potential of physics

NASA Astrophysics Data System (ADS)

Mashood, K. K.; Singh, Vijay A.

2013-09-01

Research suggests that problem-solving skills are transferable across domains. This claim, however, needs further empirical substantiation. We suggest correlation studies as a methodology for making preliminary inferences about transfer. The correlation of the physics performance of students with their performance in chemistry and mathematics in highly competitive problem-solving examinations was studied using a massive database. The sample sizes ranged from hundreds to a few hundred thousand. Encouraged by the presence of significant correlations, we interviewed 20 students to explore the pedagogic potential of physics in imparting transferable problem-solving skills. We report strategies and practices relevant to physics employed by these students which foster transfer.

A transformative model for undergraduate quantitative biology education.

PubMed

Usher, David C; Driscoll, Tobin A; Dhurjati, Prasad; Pelesko, John A; Rossi, Louis F; Schleiniger, Gilberto; Pusecker, Kathleen; White, Harold B

2010-01-01

The BIO2010 report recommended that students in the life sciences receive a more rigorous education in mathematics and physical sciences. The University of Delaware approached this problem by (1) developing a bio-calculus section of a standard calculus course, (2) embedding quantitative activities into existing biology courses, and (3) creating a new interdisciplinary major, quantitative biology, designed for students interested in solving complex biological problems using advanced mathematical approaches. To develop the bio-calculus sections, the Department of Mathematical Sciences revised its three-semester calculus sequence to include differential equations in the first semester and, rather than using examples traditionally drawn from application domains that are most relevant to engineers, drew models and examples heavily from the life sciences. The curriculum of the B.S. degree in Quantitative Biology was designed to provide students with a solid foundation in biology, chemistry, and mathematics, with an emphasis on preparation for research careers in life sciences. Students in the program take core courses from biology, chemistry, and physics, though mathematics, as the cornerstone of all quantitative sciences, is given particular prominence. Seminars and a capstone course stress how the interplay of mathematics and biology can be used to explain complex biological systems. To initiate these academic changes required the identification of barriers and the implementation of solutions.

A Transformative Model for Undergraduate Quantitative Biology Education

PubMed Central

Driscoll, Tobin A.; Dhurjati, Prasad; Pelesko, John A.; Rossi, Louis F.; Schleiniger, Gilberto; Pusecker, Kathleen; White, Harold B.

2010-01-01

The BIO2010 report recommended that students in the life sciences receive a more rigorous education in mathematics and physical sciences. The University of Delaware approached this problem by (1) developing a bio-calculus section of a standard calculus course, (2) embedding quantitative activities into existing biology courses, and (3) creating a new interdisciplinary major, quantitative biology, designed for students interested in solving complex biological problems using advanced mathematical approaches. To develop the bio-calculus sections, the Department of Mathematical Sciences revised its three-semester calculus sequence to include differential equations in the first semester and, rather than using examples traditionally drawn from application domains that are most relevant to engineers, drew models and examples heavily from the life sciences. The curriculum of the B.S. degree in Quantitative Biology was designed to provide students with a solid foundation in biology, chemistry, and mathematics, with an emphasis on preparation for research careers in life sciences. Students in the program take core courses from biology, chemistry, and physics, though mathematics, as the cornerstone of all quantitative sciences, is given particular prominence. Seminars and a capstone course stress how the interplay of mathematics and biology can be used to explain complex biological systems. To initiate these academic changes required the identification of barriers and the implementation of solutions. PMID:20810949

Bell's Inequality: Revolution in Quantum Physics or Just AN Inadequate Mathematical Model?

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei

The main aim of this review is to stress the role of mathematical models in physics. The Bell inequality (BI) is often called the "most famous inequality of the 20th century." It is commonly accepted that its violation in corresponding experiments induced a revolution in quantum physics. Unlike "old quantum mechanics" (of Einstein, Schrodinger Bohr, Heisenberg, Pauli, Landau, Fock), "modern quantum mechanics" (of Bell, Aspect, Zeilinger, Shimony, Green-berger, Gisin, Mermin) takes seriously so called quantum non-locality. We will show that the conclusion that one has to give up the realism (i.e., a possibility to assign results of measurements to physical systems) or the locality (i.e., to assume action at a distance) is heavily based on one special mathematical model. This model was invented by A. N. Kolmogorov in 1933. One should pay serious attention to the role of mathematical models in physics. The problems of the realism and locality induced by Bell's argument can be solved by using non-Kolmogorovian probabilistic models. We compare this situation with non-Euclidean geometric models in relativity theory.

The Pythagorean Roots of Introductory Physics

NASA Astrophysics Data System (ADS)

Clarage, James B.

2013-03-01

Much of the mathematical reasoning employed in the typical introductory physics course can be traced to Pythagorean roots planted over two thousand years ago. Besides obvious examples involving the Pythagorean theorem, I draw attention to standard physics problems and derivations which often unknowingly rely upon the Pythagoreans' work on proportion, music, geometry, harmony, the golden ratio, and cosmology. Examples are drawn from mechanics, electricity, sound, optics, energy conservation and relativity. An awareness of the primary sources of the mathematical techniques employed in the physics classroom could especially benefit students and educators at schools which encourage integration of their various courses in history, science, philosophy, and the arts.

Laplace Boundary-Value Problem in Paraboloidal Coordinates

ERIC Educational Resources Information Center

Duggen, L.; Willatzen, M.; Voon, L. C. Lew Yan

2012-01-01

This paper illustrates both a problem in mathematical physics, whereby the method of separation of variables, while applicable, leads to three ordinary differential equations that remain fully coupled via two separation constants and a five-term recurrence relation for series solutions, and an exactly solvable problem in electrostatics, as a…

Student reasoning about graphs in different contexts

NASA Astrophysics Data System (ADS)

Ivanjek, Lana; Susac, Ana; Planinic, Maja; Andrasevic, Aneta; Milin-Sipus, Zeljka

2016-06-01

This study investigates university students' graph interpretation strategies and difficulties in mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel (isomorphic) mathematics, physics, and other context questions about graphs, which were developed by us, were administered to 385 first-year students at the Faculty of Science, University of Zagreb. Students were asked to provide explanations and/or mathematical procedures with their answers. Students' main strategies and difficulties identified through the analysis of those explanations and procedures are described. Student strategies of graph interpretation were found to be largely context dependent and domain specific. A small fraction of students have used the same strategy in all three domains (mathematics, physics, and other contexts) on most sets of parallel questions. Some students have shown indications of transfer of knowledge in the sense that they used techniques and strategies developed in physics for solving (or attempting to solve) other context problems. In physics, the preferred strategy was the use of formulas, which sometimes seemed to block the use of other, more productive strategies which students displayed in other domains. Students' answers indicated the presence of slope-height confusion and interval-point confusion in all three domains. Students generally better interpreted graph slope than the area under a graph, although the concept of slope still seemed to be quite vague for many. The interpretation of the concept of area under a graph needs more attention in both physics and mathematics teaching.

Construction Method of Analytical Solutions to the Mathematical Physics Boundary Problems for Non-Canonical Domains

NASA Astrophysics Data System (ADS)

Mobarakeh, Pouyan Shakeri; Grinchenko, Victor T.

2015-06-01

The majority of practical cases of acoustics problems requires solving the boundary problems in non-canonical domains. Therefore construction of analytical solutions of mathematical physics boundary problems for non-canonical domains is both lucrative from the academic viewpoint, and very instrumental for elaboration of efficient algorithms of quantitative estimation of the field characteristics under study. One of the main solving ideologies for such problems is based on the superposition method that allows one to analyze a wide class of specific problems with domains which can be constructed as the union of canonically-shaped subdomains. It is also assumed that an analytical solution (or quasi-solution) can be constructed for each subdomain in one form or another. However, this case implies some difficulties in the construction of calculation algorithms, insofar as the boundary conditions are incompletely defined in the intervals, where the functions appearing in the general solution are orthogonal to each other. We discuss several typical examples of problems with such difficulties, we study their nature and identify the optimal methods to overcome them.

Collisional breakup in a quantum system of three charged particles

PubMed

Rescigno; Baertschy; Isaacs; McCurdy

1999-12-24

Since the invention of quantum mechanics, even the simplest example of the collisional breakup of a system of charged particles, e(-) + H --> H(+) + e(-) + e(-) (where e(-) is an electron and H is hydrogen), has resisted solution and is now one of the last unsolved fundamental problems in atomic physics. A complete solution requires calculation of the energies and directions for a final state in which all three particles are moving away from each other. Even with supercomputers, the correct mathematical description of this state has proved difficult to apply. A framework for solving ionization problems in many areas of chemistry and physics is finally provided by a mathematical transformation of the Schrodinger equation that makes the final state tractable, providing the key to a numerical solution of this problem that reveals its full dynamics.

Bush Physics for the 21st Century, A Distance Delivery Physics Course Targeting Students in Rural Alaska and Across the North

NASA Astrophysics Data System (ADS)

Solie, D. J.; Spencer, V. K.

2010-12-01

Bush Physics for the 21st Century brings physics that is engaging to modern youth, and mathematically rigorous, to high school and college students in the remote and often road-less villages of Alaska where the opportunity to take a physics course has been nearly nonexistent. The primary goal of the course is to prepare rural (predominantly Alaska Native) students for success in university science and engineering degree programs and ultimately STEM careers. The course is delivered via video conference and web based electronic blackboard tailored to the needs of remote students. Kinetic, practical and culturally relevant place-based examples from traditional and modern northern life are used to engage students, and a rigorous and mathematical focus is stressed to strengthen problem solving skills. Simple hands-on-lab experiment kits are shipped to the students. In addition students conduct a Collaborative Research Experiment where they coordinate times of sun angle measurements with teams in other villages to determine their latitude and longitude as well as an estimate of the circumference of the earth. Connecting abstract mathematical symbols and equations to real physical objects and problems is one of the most difficult things to master in physics. We introduce Inuktitut symbols to complement the traditional Greek symbols in equations to strengthen the visual/conceptual connection with symbol and encourage an indigenous connection to the physical concepts. Results and observations from the first three pilot semesters (spring 2008, 2009 and 2010) will be presented.

Language of Physics, Language of Math: Disciplinary Culture and Dynamic Epistemology

ERIC Educational Resources Information Center

Redish, Edward F.; Kuo, Eric

2015-01-01

Mathematics is a critical part of much scientific research. Physics in particular weaves math extensively into its instruction beginning in high school. Despite much research on the learning of both physics and math, the problem of how to effectively include math in physics in a way that reaches most students remains unsolved. In this paper, we…

A Physics Show Performed by Students for Kids: "From Mechanics to Elementary Particle Physics"

ERIC Educational Resources Information Center

Dreiner, Herbi K.

2008-01-01

Physics students spend the early part of their training attending physics and mathematics lectures, solving problem sets, and experimenting in laboratory courses. The program is typically intensive and fairly rigid. They have little opportunity to follow their own curiosity or apply their knowledge. There have been many attempts to address this…

Participation in Science and Technology: Young People's Achievement-Related Choices in Late-Modern Societies

ERIC Educational Resources Information Center

Boe, Maria Vetleseter; Henriksen, Ellen Karoline; Lyons, Terry; Schreiner, Camilla

2011-01-01

Young people's participation in science, technology, engineering and mathematics (STEM) is a matter of international concern. Studies and careers that require physical sciences and advanced mathematics are most affected by the problem and women in particular are under-represented in many STEM fields. This article views international research about…

From quantum foundations to applications and back.

PubMed

Gisin, Nicolas; Fröwis, Florian

2018-07-13

Quantum non-locality has been an extremely fruitful subject of research, leading the scientific revolution towards quantum information science, in particular, to device-independent quantum information processing. We argue that the time is ripe to work on another basic problem in the foundations of quantum physics, the quantum measurement problem, which should produce good physics in theoretical, mathematical, experimental and applied physics. We briefly review how quantum non-locality contributed to physics (including some outstanding open problems) and suggest ways in which questions around macroscopic quantumness could equally contribute to all aspects of physics.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'. © 2018 The Author(s).

Introduction to Numerical Methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schoonover, Joseph A.

2016-06-14

These are slides for a lecture for the Parallel Computing Summer Research Internship at the National Security Education Center. This gives an introduction to numerical methods. Repetitive algorithms are used to obtain approximate solutions to mathematical problems, using sorting, searching, root finding, optimization, interpolation, extrapolation, least squares regresion, Eigenvalue problems, ordinary differential equations, and partial differential equations. Many equations are shown. Discretizations allow us to approximate solutions to mathematical models of physical systems using a repetitive algorithm and introduce errors that can lead to numerical instabilities if we are not careful.

Problem-Solving Rubrics Revisited: Attending to the Blending of Informal Conceptual and Formal Mathematical Reasoning

ERIC Educational Resources Information Center

Hull, Michael M.; Kuo, Eric; Gupta, Ayush; Elby, Andrew

2013-01-01

Much research in engineering and physics education has focused on improving students' problem-solving skills. This research has led to the development of step-by-step problem-solving strategies and grading rubrics to assess a student's expertise in solving problems using these strategies. These rubrics value "communication" between the…

Mathematics Ab Ovo: Hans Driesch and Entwicklungsmechanik.

PubMed

Priven, Silvia Waisse; Alfonso-Goldfarb, Ana M

2009-01-01

One of the factors leading to the creation of embryology as a modern discipline at the end of the 19th century was Wilhelm Roux's formulation of the program of Entwicklungsmechanik (developmental mechanics). A look into the work of Hans Driesch, an equal contributor to developmental mechanics, may shed further light on this process. For Roux, developmental mechanics was an anatomical science, but for Driesch it was associated with a mathematical and physical approach to the natural world. Likewise, Roux used the concept of mechanics as an analogy, but Driesch used it literally. Driesch's generation had been trained in a pedagogic context that emphasized mathematics and physics, which may explain why he went a step further than Roux to state that a true "mechanics" of development required the reduction of morphogenetic problems to the known laws of physics. It is argued here that this difference in background is behind the enthusiastic adoption and further development of Roux's program by Driesch's generation, a generation that conceived Entwicklungsmechanik to be the reduction of embryological processes to "the laws of matter in motion." This same mathematical and physical mindset would underscore Driesch's later construction of entelechy as a regulating factor in embryogenesis, through mathematical analysis grounded on the notion of mathematical functions.

Statistical physics of hard combinatorial optimization: Vertex cover problem

NASA Astrophysics Data System (ADS)

Zhao, Jin-Hua; Zhou, Hai-Jun

2014-07-01

Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years, the replica-symmetry-breaking mean field theory of spin glasses and the associated message-passing algorithms have greatly deepened our understanding of typical-case computation complexity. In this paper, we use the vertex cover problem, a basic nondeterministic-polynomial (NP)-complete combinatorial optimization problem of wide application, as an example to introduce the statistical physical methods and algorithms. We do not go into the technical details but emphasize mainly the intuitive physical meanings of the message-passing equations. A nonfamiliar reader shall be able to understand to a large extent the physics behind the mean field approaches and to adjust the mean field methods in solving other optimization problems.

Girls Talk Math - Engaging Girls Through Math Media

NASA Astrophysics Data System (ADS)

Bernardi, Francesca; Morgan, Katrina

2017-11-01

``Girls Talk Math: Engaging Girls through Math Media'' is a free two-week long summer day camp for high-school girls in the Triangle area of NC. This past June the camp had its second run thanks to renewed funding from the Mathematical Association of America Tensor Women and Mathematics Grant. The camp involved 35 local high-school students who identify as female. Campers complete challenging problem sets and research the life of a female scientist who worked on similar problems. They report their work in a blog post and record a podcast about the scientist they researched. The curriculum has been developed by Mathematics graduate students at UNC from an inquiry based learning perspective; problem sets topics include some theoretical mathematics, but also more applied physics-based material. Campers worked on fluid dynamics, special relativity, and quantum mechanics problem sets which included experiments. The camp has received positive feedback from the local community and the second run saw a large increase in the number of participants. The program is evaluated using pre and post surveys, which measure campers' confidence and interest in pursuing higher level courses in STEM. The results from the past two summers have been encouraging. Mathematical Association of America Tensor Women and Mathematics Grant.

Understanding Introductory Students' Application of Integrals in Physics from Multiple Perspectives

ERIC Educational Resources Information Center

Hu, Dehui

2013-01-01

Calculus is used across many physics topics from introductory to upper-division level college courses. The concepts of differentiation and integration are important tools for solving real world problems. Using calculus or any mathematical tool in physics is much more complex than the straightforward application of the equations and algorithms that…

The complexity of proving chaoticity and the Church-Turing thesis

NASA Astrophysics Data System (ADS)

Calude, Cristian S.; Calude, Elena; Svozil, Karl

2010-09-01

Proving the chaoticity of some dynamical systems is equivalent to solving the hardest problems in mathematics. Conversely, classical physical systems may "compute the hard or even the incomputable" by measuring observables which correspond to computationally hard or even incomputable problems.

GENASIS Mathematics : Object-oriented manifolds, operations, and solvers for large-scale physics simulations

NASA Astrophysics Data System (ADS)

Cardall, Christian Y.; Budiardja, Reuben D.

2018-01-01

The large-scale computer simulation of a system of physical fields governed by partial differential equations requires some means of approximating the mathematical limit of continuity. For example, conservation laws are often treated with a 'finite-volume' approach in which space is partitioned into a large number of small 'cells,' with fluxes through cell faces providing an intuitive discretization modeled on the mathematical definition of the divergence operator. Here we describe and make available Fortran 2003 classes furnishing extensible object-oriented implementations of simple meshes and the evolution of generic conserved currents thereon, along with individual 'unit test' programs and larger example problems demonstrating their use. These classes inaugurate the Mathematics division of our developing astrophysics simulation code GENASIS (Gen eral A strophysical Si mulation S ystem), which will be expanded over time to include additional meshing options, mathematical operations, solver types, and solver variations appropriate for many multiphysics applications.

Development and application of unified algorithms for problems in computational science

NASA Technical Reports Server (NTRS)

Shankar, Vijaya; Chakravarthy, Sukumar

1987-01-01

A framework is presented for developing computationally unified numerical algorithms for solving nonlinear equations that arise in modeling various problems in mathematical physics. The concept of computational unification is an attempt to encompass efficient solution procedures for computing various nonlinear phenomena that may occur in a given problem. For example, in Computational Fluid Dynamics (CFD), a unified algorithm will be one that allows for solutions to subsonic (elliptic), transonic (mixed elliptic-hyperbolic), and supersonic (hyperbolic) flows for both steady and unsteady problems. The objectives are: development of superior unified algorithms emphasizing accuracy and efficiency aspects; development of codes based on selected algorithms leading to validation; application of mature codes to realistic problems; and extension/application of CFD-based algorithms to problems in other areas of mathematical physics. The ultimate objective is to achieve integration of multidisciplinary technologies to enhance synergism in the design process through computational simulation. Specific unified algorithms for a hierarchy of gas dynamics equations and their applications to two other areas: electromagnetic scattering, and laser-materials interaction accounting for melting.

Research Prototype: Automated Analysis of Scientific and Engineering Semantics

NASA Technical Reports Server (NTRS)

Stewart, Mark E. M.; Follen, Greg (Technical Monitor)

2001-01-01

Physical and mathematical formulae and concepts are fundamental elements of scientific and engineering software. These classical equations and methods are time tested, universally accepted, and relatively unambiguous. The existence of this classical ontology suggests an ideal problem for automated comprehension. This problem is further motivated by the pervasive use of scientific code and high code development costs. To investigate code comprehension in this classical knowledge domain, a research prototype has been developed. The prototype incorporates scientific domain knowledge to recognize code properties (including units, physical, and mathematical quantity). Also, the procedure implements programming language semantics to propagate these properties through the code. This prototype's ability to elucidate code and detect errors will be demonstrated with state of the art scientific codes.

On determining important aspects of mathematical models: Application to problems in physics and chemistry

NASA Technical Reports Server (NTRS)

Rabitz, Herschel

1987-01-01

The use of parametric and functional gradient sensitivity analysis techniques is considered for models described by partial differential equations. By interchanging appropriate dependent and independent variables, questions of inverse sensitivity may be addressed to gain insight into the inversion of observational data for parameter and function identification in mathematical models. It may be argued that the presence of a subset of dominantly strong coupled dependent variables will result in the overall system sensitivity behavior collapsing into a simple set of scaling and self similarity relations amongst elements of the entire matrix of sensitivity coefficients. These general tools are generic in nature, but herein their application to problems arising in selected areas of physics and chemistry is presented.

Mathematical Physics in Italy in the XIX Century: The Theory of Elasticity

NASA Astrophysics Data System (ADS)

Capecchi, Danilo

In the second half of the nineteenth century there was in Italy an important group of mathematicians who focused their attention on mathematical physics. The most prominent of them were Enrico Betti, Eugenio Beltrami, Gregorio Ricci-Curbastro and some others (Vito Volterra, Carlo Somigliana and Tullio Levi Civita) whose activity persevered for many years in the twentieth century. In this article, I will write about the contribution of this group to the theory of elasticity. The best representative writing on continuum mechanics and elasticity as theories of mathematical physics is presented in the book Teoria della elasticità by Enrico Betti. The book is interesting not only for the particular results found but also for its structure which became paradigmatic for the development of subsequent texts on elasticity, not only those in Italian. Betti's interest was concentrated on the mathematical aspects of a physical theory. Physical principles are not discussed; they are only exposed in the most formal way possible. The objective is to arrive, without discussing epistemological or empirical problems, at the formulation and solution of differential equations that rule elasticity, as had become classic in the emerging mathematical physics. Beltrami wrote no complete books on elasticity; however, his contribution to this field was perhaps more original than that of Betti. A similar consideration holds true for Volterra and Somigliana.

Domain decomposition method for the Baltic Sea based on theory of adjoint equation and inverse problem.

NASA Astrophysics Data System (ADS)

Lezina, Natalya; Agoshkov, Valery

2017-04-01

Domain decomposition method (DDM) allows one to present a domain with complex geometry as a set of essentially simpler subdomains. This method is particularly applied for the hydrodynamics of oceans and seas. In each subdomain the system of thermo-hydrodynamic equations in the Boussinesq and hydrostatic approximations is solved. The problem of obtaining solution in the whole domain is that it is necessary to combine solutions in subdomains. For this purposes iterative algorithm is created and numerical experiments are conducted to investigate an effectiveness of developed algorithm using DDM. For symmetric operators in DDM, Poincare-Steklov's operators [1] are used, but for the problems of the hydrodynamics, it is not suitable. In this case for the problem, adjoint equation method [2] and inverse problem theory are used. In addition, it is possible to create algorithms for the parallel calculations using DDM on multiprocessor computer system. DDM for the model of the Baltic Sea dynamics is numerically studied. The results of numerical experiments using DDM are compared with the solution of the system of hydrodynamic equations in the whole domain. The work was supported by the Russian Science Foundation (project 14-11-00609, the formulation of the iterative process and numerical experiments). [1] V.I. Agoshkov, Domain Decompositions Methods in the Mathematical Physics Problem // Numerical processes and systems, No 8, Moscow, 1991 (in Russian). [2] V.I. Agoshkov, Optimal Control Approaches and Adjoint Equations in the Mathematical Physics Problem, Institute of Numerical Mathematics, RAS, Moscow, 2003 (in Russian).

Distributed Diagnosis and Home Healthcare Conference

DTIC Science & Technology

2006-09-01

and based on physics . The driving force behind the e-health industry, the third pillar of healthcare, will be electronics and mathematics and will...POCT is performed by nurses, perfusionists, and respiratory therapists . Other POCT can be performed by certified nurses and medical assistants...in rural settings to connect patients to providers who they may be unable to reach physically . However, this problem is not a problem of only rural

Mathematical physics approaches to lightning discharge problems

NASA Technical Reports Server (NTRS)

Kyrala, A.

1985-01-01

Mathematical physics arguments useful for lightning discharge and generation problems are pursued. A soliton Ansatz for the lightning stroke is treated including a charge generation term which is the ultimate source for the phenomena. Equations are established for a partially ionized plasma inding the effects of pressure, magnetic field, electric field, gravitation, viscosity, and temperature. From these equations is then derived the non-stationary generalized Ohm's Law essential for describing field/current density relationships in the horizon channel of the lightning stroke. The discharge initiation problem is discussed. It is argued that the ionization rate drives both the convective current and electric displacement current to increase exponentially. The statistical distributions of charge in the thundercloud preceding a lightning dischage are considered. The stability of the pre-lightning charge distributions and the use of Boltzmann relaxational equations to determine them are discussed along with a covered impedance path provided by the aircraft.

BOOK REVIEW: Symmetry and the Monster: One of the Greatest Quests of Mathematics

NASA Astrophysics Data System (ADS)

Szabo, R. J.

2007-04-01

The book Symmetry and the Monster: One of the Greatest Quests of Mathematics describes historical events leading up to the discovery of the Monster sporadic group, the largest simple sporadic group. It also expounds the significance and deep relationships between this group and other areas of mathematics and theoretical physics. It begins, in the prologue, with a nice overview of some of the mathematical drama surrounding the discovery of the Monster and its subsequent relationship to number theory (the so-called Moonshine conjectures). From a historical perspective, the book traces back to the roots of group theory, Galois theory, and steadily runs through time through the many famous mathematicians who contributed to group theory, including Lie, Killing and Cartan. Throughout, the author has provided a very nice and deep insight into the sociological and scientific problems at the time, and gives the reader a very prominent inside view of the real people behind the mathematics. The book should be an enjoyable read to anyone with an interest in the history of mathematics. For the non-mathematician the book makes a good, and mostly successful, attempt at being non-technical. Technical mathematical jargon is replaced with more heuristic, intuitive terminology, making the mathematical descriptions in the book fairly easy going. A glossary\\hspace{0.25pc} of\\hspace{0.25pc} terminology for noindent the more scientifically inclined is included in various footnotes throughout the book and in a comprehensive listing at the end of the book. Some more technical material is also included in the form of appendices at the end of the book. Some aspects of physics are also explained in a simple, intuitive way. The author further attempts at various places to give the non-specialist a glimpse into what mathematical proof is all about, and explains the difficulties and technicalities involved in this very nicely (for instance, he mentions the various 100+ page articles that appeared in the hey-day of finite group theory, indicating the enormous technical nature of the subject). The book nicely paints a dramatic landscape leading up to the discovery of the Monster group, and the problems that remain to this day in trying to understand its significance. One can really take from this book a feel of the mathematics leading up to its appearance, and the importance of the classification problem which was responsible for this. One also really gets an appreciation of the efforts and commitments of the mathematicians who contributed to the subject. All in all, this book achieves a nice balance between providing a beautiful historical account of group theory, and explaining the classification problem for finite groups in a way that is accessible to non-scientists. This should prove to be a good read for both the layperson interested in mathematics or mathematical physics, and also both mathematicians and physicists alike.

Mathematical methods of studying physical phenomena

NASA Astrophysics Data System (ADS)

Man'ko, Margarita A.

2013-03-01

In recent decades, substantial theoretical and experimental progress was achieved in understanding the quantum nature of physical phenomena that serves as the foundation of present and future quantum technologies. Quantum correlations like the entanglement of the states of composite systems, the phenomenon of quantum discord, which captures other aspects of quantum correlations, quantum contextuality and, connected with these phenomena, uncertainty relations for conjugate variables and entropies, like Shannon and Rényi entropies, and the inequalities for spin states, like Bell inequalities, reflect the recently understood quantum properties of micro and macro systems. The mathematical methods needed to describe all quantum phenomena mentioned above were also the subject of intense studies in the end of the last, and beginning of the new, century. In this section of CAMOP 'Mathematical Methods of Studying Physical Phenomena' new results and new trends in the rapidly developing domain of quantum (and classical) physics are presented. Among the particular topics under discussion there are some reviews on the problems of dynamical invariants and their relations with symmetries of the physical systems. In fact, this is a very old problem of both classical and quantum systems, e.g. the systems of parametric oscillators with time-dependent parameters, like Ermakov systems, which have specific constants of motion depending linearly or quadratically on the oscillator positions and momenta. Such dynamical invariants play an important role in studying the dynamical Casimir effect, the essence of the effect being the creation of photons from the vacuum in a cavity with moving boundaries due to the presence of purely quantum fluctuations of the electromagnetic field in the vacuum. It is remarkable that this effect was recently observed experimentally. The other new direction in developing the mathematical approach in physics is quantum tomography that provides a new vision of quantum states. In the tomographic picture of quantum mechanics, the states are identified with fair conditional probability distributions, which contain the same information on the states as the wave function or the density matrix. The mathematical methods of the tomographic approach are based on studying the star-product (associative product) quantization scheme. The tomographic star-product technique provides an additional understanding of the associative product, which is connected with the existence of specific pairs of operators called quantizers and dequantizers. These operators code information on the kernels of all the star-product schemes, including the traditional phase-space Weyl-Wigner-Moyal picture describing the quantum-system evolution. The new equation to find quantizers, if the kernel of the star product of functions is given, is presented in this CAMOP section. For studying classical systems, the mathematical methods developed in quantum mechanics can also be used. The case of paraxial-radiation beams propagating in waveguides is a known example of describing a purely classical phenomenon by means of quantum-like equations. Thus, some quantum phenomenon like the entanglement can be mimicked by the properties of classical beams, for example, Gaussian modes. The mathematical structures and relations to the symplectic symmetry group are analogous for both classical and quantum phenomena. Such analogies of the mathematical classical and quantum methods used in research on quantum-like communication channels provide new tools for constructing a theoretical basis of the new information-transmission technologies. The conventional quantum mechanics and its relation to classical mechanics contain mathematical recipes of the correspondence principle and quantization rules. Attempts to find rules for deriving the quantum-mechanical formalism starting from the classical field theory, taking into account the influence of classical fluctuations of the field, is considered in these papers. The methods to solve quantum equations and formulate the boundary conditions in the problems with singular potentials are connected with the mathematical problems of self-adjointness of the Hamiltonians. The progress and some new results in this direction are reflected in this CAMOP section. The Gaussian states of the photons play an important role in quantum optics. The multimode electromagnetic field and quantum correlations in the Gaussian states are considered in this section. The new results in the statistical properties of the laser radiation discussed here are based on applications of mathematical methods in this traditional domain of physics. It is worth stressing that the universality of the mathematical procedures permitted to consider the physical phenomena in the ocean is on the same footing as the phenomena in the microworld. In this CAMOP section, there are also papers devoted to traditional problems of solving the Schrödinger equation for interesting quantum systems. Recently obtained results related to different domains of theoretical physics are united by applying mathematical methods and tools, that provide new possibilities to better understand the theoretical foundations needed to develop new quantum technologies like quantum computing and quantum communications. The papers are arranged alphabetically by the name of the first author. We are grateful to all authors who accepted our invitation to contribute to this CAMOP section.

Helping Students Come to Grips with the Meaning of Division

ERIC Educational Resources Information Center

Aubrecht, Gordon J., II

2004-01-01

Many years ago, Arons pointed out the incomprehension science students exhibit of the basic mathematical operations multiplication and division and the need to address the problem in physics classes to assure student understanding of the physical world. McDermott et al.'s Physics by Inquiry program does address this need directly and in detail (by…

ESPN2 Sports Figures Makes Math and Physics a Ball! 1996-97 Educator's Curriculum.

ERIC Educational Resources Information Center

Rusczyk, Richard; Lehoczky, Sandor

This guide is designed to accompany ESPN's SportsFigures video segments which were created to enhance the interest and learning progress of high school students in mathematics, physics, and physical science. Using actual, re-enacted, or staged events, the problems presented in each of the 16 Sports Figures segments illustrate the relationship…

An Integrated, Problem-Based Learning Material: The "Satellite" Module

ERIC Educational Resources Information Center

Selcuk, Gamze Sezgin; Emiroglu, Handan Byacioglu; Tarakci, Mehmet; Ozel, Mustafa

2011-01-01

The purpose of this study is to introduce a problem-based learning material, the Satellite Module, that has integrated some of the subjects included in the disciplines of physics and mathematics at an introductory level in undergraduate education. The reason why this modular and problem-based material has been developed is to enable students to…

Bush Physics for the 21st Century, A Distance Delivery Physics Course to Bridge the Gap in Rural Alaska and Across the North

NASA Astrophysics Data System (ADS)

Solie, D. J.; Spencer, V.

2009-12-01

Bush Physics for the 21st Century brings physics that is culturally connected, engaging to modern youth, and mathematically rigorous, to high school and college students in the remote and often road-less villages of Alaska. The primary goal of the course is to prepare rural (predominantly Alaska Native) students for success in university science and engineering degree programs and ultimately STEM careers. The course is currently delivered via video conference and web based electronic blackboard tailored to the needs of remote students. Practical, culturally relevant kinetic examples from traditional and modern northern life are used to engage students, and a rigorous and mathematical focus is stressed to strengthen problem solving skills. Simple hands-on-lab experiments are delivered to the students with the exercises completed on-line. In addition, students are teamed and required to perform a much more involved experimental study with the results presented by teams at the conclusion of the course. Connecting abstract mathematical symbols and equations to real physical objects and problems is one of the most difficult things to master in physics. Greek symbols are traditionally used in equations, however, to strengthen the visual/conceptual connection with symbol and encourage an indigenous connection to the concepts we have introduced Inuktitut symbols to complement the traditional Greek symbols. Results and observations from the first two pilot semesters (spring 2008 and 2009) will be presented.

Computer Systems for Teaching Complex Concepts.

ERIC Educational Resources Information Center

Feurzeig, Wallace

Four Programing systems--Mentor, Stringcomp, Simon, and Logo--were designed and implemented as integral parts of research into the various ways computers may be used for teaching problem-solving concepts and skills. Various instructional contexts, among them medicine, mathematics, physics, and basic problem-solving for elementary school children,…

Assessing student written problem solutions: A problem-solving rubric with application to introductory physics

NASA Astrophysics Data System (ADS)

Docktor, Jennifer L.; Dornfeld, Jay; Frodermann, Evan; Heller, Kenneth; Hsu, Leonardo; Jackson, Koblar Alan; Mason, Andrew; Ryan, Qing X.; Yang, Jie

2016-06-01

Problem solving is a complex process valuable in everyday life and crucial for learning in the STEM fields. To support the development of problem-solving skills it is important for researchers and curriculum developers to have practical tools that can measure the difference between novice and expert problem-solving performance in authentic classroom work. It is also useful if such tools can be employed by instructors to guide their pedagogy. We describe the design, development, and testing of a simple rubric to assess written solutions to problems given in undergraduate introductory physics courses. In particular, we present evidence for the validity, reliability, and utility of the instrument. The rubric identifies five general problem-solving processes and defines the criteria to attain a score in each: organizing problem information into a Useful Description, selecting appropriate principles (Physics Approach), applying those principles to the specific conditions in the problem (Specific Application of Physics), using Mathematical Procedures appropriately, and displaying evidence of an organized reasoning pattern (Logical Progression).

Relating the Learned Knowledge and Acquired Skills to Real Life: Function Sample

ERIC Educational Resources Information Center

Albayrak, Mustafa; Yazici, Nurullah; Simsek, Mertkan

2017-01-01

Considering that Mathematics is a multidimensional problem-solving method that can be effective in all areas of cultural life, it is of great importance because of its contribution to other sciences such as physical and social sciences. It is known that the basic concepts of mathematics, which can also be expressed as a way of life, have helped to…

How Do Elementary Textbooks Address Fractions? A Review of Mathematics Textbooks in the USA, Japan, and Kuwait

ERIC Educational Resources Information Center

Alajmi, Amal Hussain

2012-01-01

Textbooks play an important part in the design of instruction. This study analyzed the presentation of fractions in textbooks designed for the elementary grades in Kuwait, Japan, and the USA. The analysis focused on the physical characteristics of the books, the structure of the lessons, and the nature of the mathematical problems presented.…

Role of multiple representations in physics problem solving

NASA Astrophysics Data System (ADS)

Maries, Alexandru

This thesis explores the role of multiple representations in introductory physics students' problem solving performance through several investigations. Representations can help students focus on the conceptual aspects of physics and play a major role in effective problem solving. Diagrammatic representations can play a particularly important role in the initial stages of conceptual analysis and planning of the problem solution. Findings suggest that students who draw productive diagrams are more successful problem solvers even if their approach is primarily mathematical. Furthermore, students provided with a diagram of the physical situation presented in a problem sometimes exhibited deteriorated performance. Think-aloud interviews suggest that this deteriorated performance is in part due to reduced conceptual planning time which caused students to jump to the implementation stage without fully understanding the problem and planning problem solution. Another study investigated two interventions aimed at improving introductory students' representational consistency between mathematical and graphical representations and revealed that excessive scaffolding can have a detrimental effect. The detrimental effect was partly due to increased cognitive load brought on by the additional steps and instructions. Moreover, students who exhibited representational consistency also showed improved problem solving performance. The final investigation is centered on a problem solving task designed to provide information about the pedagogical content knowledge (PCK) of graduate student teaching assistants (TAs). In particular, the TAs identified what they considered to be the most common difficulties of introductory physics students related to graphical representations of kinematics concepts as they occur in the Test of Understanding Graphs in Kinematics (TUG-K). As an extension, the Force Concept Inventory (FCI) was also used to assess this aspect of PCK related to knowledge of student difficulties of both physics instructors and TAs. We find that teaching an independent course and recent teaching experience do not correlate with improved PCK. In addition, the performance of American TAs, Chinese TAs and other foreign TAs in identifying common student difficulties both in the context of the TUG-K and in the context of the FCI is similar. Moreover, there were many common difficulties of introductory physics students that were not identified by many instructors and TAs.

[Development of New Mathematical Methodology in Air Traffic Control for the Analysis of Hybrid Systems

NASA Technical Reports Server (NTRS)

Hermann, Robert

1997-01-01

The aim of this research is to develop new mathematical methodology for the analysis of hybrid systems of the type involved in Air Traffic Control (ATC) problems. Two directions of investigation were initiated. The first used the methodology of nonlinear generalized functions, whose mathematical foundations were initiated by Colombeau and developed further by Oberguggenberger; it has been extended to apply to ordinary differential. Systems of the type encountered in control in joint work with the PI and M. Oberguggenberger. This involved a 'mixture' of 'continuous' and 'discrete' methodology. ATC clearly involves mixtures of two sorts of mathematical problems: (1) The 'continuous' dynamics of a standard control type described by ordinary differential equations (ODE) of the form: {dx/dt = f(x, u)} and (2) the discrete lattice dynamics involved of cellular automata. Most of the CA literature involves a discretization of a partial differential equation system of the type encountered in physics problems (e.g. fluid and gas problems). Both of these directions requires much thinking and new development of mathematical fundamentals before they may be utilized in the ATC work. Rather than consider CA as 'discretization' of PDE systems, I believe that the ATC applications will require a completely different and new mathematical methodology, a sort of discrete analogue of jet bundles and/or the sheaf-theoretic techniques to topologists. Here too, I have begun work on virtually 'virgin' mathematical ground (at least from an 'applied' point of view) which will require considerable preliminary work.

Student Difficulties Regarding Symbolic and Graphical Representations of Vector Fields

ERIC Educational Resources Information Center

Bollen, Laurens; van Kampen, Paul; Baily, Charles; Kelly, Mossy; De Cock, Mieke

2017-01-01

The ability to switch between various representations is an invaluable problem-solving skill in physics. In addition, research has shown that using multiple representations can greatly enhance a person's understanding of mathematical and physical concepts. This paper describes a study of student difficulties regarding interpreting, constructing,…

Modelling by Differential Equations

ERIC Educational Resources Information Center

Chaachoua, Hamid; Saglam, Ayse

2006-01-01

This paper aims to show the close relation between physics and mathematics taking into account especially the theory of differential equations. By analysing the problems posed by scientists in the seventeenth century, we note that physics is very important for the emergence of this theory. Taking into account this analysis, we show the…

XXIV International Conference on Integrable Systems and Quantum symmetries (ISQS-24)

NASA Astrophysics Data System (ADS)

Burdík, Čestmír; Navrátil, Ondřej; Posta, Severin

2017-01-01

The XXIV International Conference on Integrable Systems and Quantum Symmetries (ISQS-24), organized by the Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University Prague and the Bogoliubov Laboratory of Theoretical Physics of the Joint Institute for Nuclear Research, belongs to the successful series of conferences held at the Czech Technical University which began in 1992 and is devoted to problems of mathematical physics related to the theory of integrable systems, quantum groups and quantum symmetries. During the last 5 years, each of the conferences gathered around 110 scientists from all over the world. 43 papers of plenary lectures and contributions presented at ISQS-24 are published in the present issue of Journal of Physics: Conference Series.

An overview of the mathematical and statistical analysis component of RICIS

NASA Technical Reports Server (NTRS)

Hallum, Cecil R.

1987-01-01

Mathematical and statistical analysis components of RICIS (Research Institute for Computing and Information Systems) can be used in the following problem areas: (1) quantification and measurement of software reliability; (2) assessment of changes in software reliability over time (reliability growth); (3) analysis of software-failure data; and (4) decision logic for whether to continue or stop testing software. Other areas of interest to NASA/JSC where mathematical and statistical analysis can be successfully employed include: math modeling of physical systems, simulation, statistical data reduction, evaluation methods, optimization, algorithm development, and mathematical methods in signal processing.

Expanding the Space of Plausible Solutions in a Medical Tutoring System for Problem-Based Learning

ERIC Educational Resources Information Center

Kazi, Hameedullah; Haddawy, Peter; Suebnukarn, Siriwan

2009-01-01

In well-defined domains such as Physics, Mathematics, and Chemistry, solutions to a posed problem can objectively be classified as correct or incorrect. In ill-defined domains such as medicine, the classification of solutions to a patient problem as correct or incorrect is much more complex. Typical tutoring systems accept only a small set of…

Cellular Automata

NASA Astrophysics Data System (ADS)

Gutowitz, Howard

1991-08-01

Cellular automata, dynamic systems in which space and time are discrete, are yielding interesting applications in both the physical and natural sciences. The thirty four contributions in this book cover many aspects of contemporary studies on cellular automata and include reviews, research reports, and guides to recent literature and available software. Chapters cover mathematical analysis, the structure of the space of cellular automata, learning rules with specified properties: cellular automata in biology, physics, chemistry, and computation theory; and generalizations of cellular automata in neural nets, Boolean nets, and coupled map lattices. Current work on cellular automata may be viewed as revolving around two central and closely related problems: the forward problem and the inverse problem. The forward problem concerns the description of properties of given cellular automata. Properties considered include reversibility, invariants, criticality, fractal dimension, and computational power. The role of cellular automata in computation theory is seen as a particularly exciting venue for exploring parallel computers as theoretical and practical tools in mathematical physics. The inverse problem, an area of study gaining prominence particularly in the natural sciences, involves designing rules that possess specified properties or perform specified task. A long-term goal is to develop a set of techniques that can find a rule or set of rules that can reproduce quantitative observations of a physical system. Studies of the inverse problem take up the organization and structure of the set of automata, in particular the parameterization of the space of cellular automata. Optimization and learning techniques, like the genetic algorithm and adaptive stochastic cellular automata are applied to find cellular automaton rules that model such physical phenomena as crystal growth or perform such adaptive-learning tasks as balancing an inverted pole. Howard Gutowitz is Collaborateur in the Service de Physique du Solide et Résonance Magnetique, Commissariat a I'Energie Atomique, Saclay, France.

Identity: a complex structure for researching students' academic behavior in science and mathematics

NASA Astrophysics Data System (ADS)

Aydeniz, Mehmet; Hodge, Lynn Liao

2011-06-01

This article is a response to Pike and Dunne's research. The focus of their analysis is on reflections of studying science post-16. Pike and Dunne draw attention to under enrollments in science, technology, engineering, and mathematics (STEM) fields, in particular, in the field of physics, chemistry and biology in the United Kingdom. We provide an analysis of how the authors conceptualize the problem of scientific career choices, the theoretical framework through which they study the problem, and the methodology they use to collect and analyze data. In addition, we examine the perspective they provide in light of new developments in the field of students' attitudes towards science and mathematics. More precisely, we draw attention to and explicate the authors' use of identity from the perspective of emerging theories that explore the relationships between the learner and culture in the context of science and mathematics.

Mathematical modeling of ignition of woodlands resulted from accident on the pipeline

NASA Astrophysics Data System (ADS)

Perminov, V. A.; Loboda, E. L.; Reyno, V. V.

2014-11-01

Accidents occurring at the sites of pipelines, accompanied by environmental damage, economic loss, and sometimes loss of life. In this paper we calculated the sizes of the possible ignition zones in emergency situations on pipelines located close to the forest, accompanied by the appearance of fireballs. In this paper, using the method of mathematical modeling calculates the maximum size of the ignition zones of vegetation as a result of accidental releases of flammable substances. The paper suggested in the context of the general mathematical model of forest fires give a new mathematical setting and method of numerical solution of a problem of a forest fire modeling. The boundary-value problem is solved numerically using the method of splitting according to physical processes. The dependences of the size of the forest fuel for different amounts of leaked flammable substances and moisture content of vegetation.

Enhanced Verification Test Suite for Physics Simulation Codes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kamm, J R; Brock, J S; Brandon, S T

2008-10-10

This document discusses problems with which to augment, in quantity and in quality, the existing tri-laboratory suite of verification problems used by Los Alamos National Laboratory (LANL), Lawrence Livermore National Laboratory (LLNL), and Sandia National Laboratories (SNL). The purpose of verification analysis is demonstrate whether the numerical results of the discretization algorithms in physics and engineering simulation codes provide correct solutions of the corresponding continuum equations. The key points of this document are: (1) Verification deals with mathematical correctness of the numerical algorithms in a code, while validation deals with physical correctness of a simulation in a regime of interest.more » This document is about verification. (2) The current seven-problem Tri-Laboratory Verification Test Suite, which has been used for approximately five years at the DOE WP laboratories, is limited. (3) Both the methodology for and technology used in verification analysis have evolved and been improved since the original test suite was proposed. (4) The proposed test problems are in three basic areas: (a) Hydrodynamics; (b) Transport processes; and (c) Dynamic strength-of-materials. (5) For several of the proposed problems we provide a 'strong sense verification benchmark', consisting of (i) a clear mathematical statement of the problem with sufficient information to run a computer simulation, (ii) an explanation of how the code result and benchmark solution are to be evaluated, and (iii) a description of the acceptance criterion for simulation code results. (6) It is proposed that the set of verification test problems with which any particular code be evaluated include some of the problems described in this document. Analysis of the proposed verification test problems constitutes part of a necessary--but not sufficient--step that builds confidence in physics and engineering simulation codes. More complicated test cases, including physics models of greater sophistication or other physics regimes (e.g., energetic material response, magneto-hydrodynamics), would represent a scientifically desirable complement to the fundamental test cases discussed in this report. The authors believe that this document can be used to enhance the verification analyses undertaken at the DOE WP Laboratories and, thus, to improve the quality, credibility, and usefulness of the simulation codes that are analyzed with these problems.« less

Mathematical, Constitutive and Numerical Modelling of Catastrophic Landslides and Related Phenomena

NASA Astrophysics Data System (ADS)

Pastor, M.; Fernández Merodo, J. A.; Herreros, M. I.; Mira, P.; González, E.; Haddad, B.; Quecedo, M.; Tonni, L.; Drempetic, V.

2008-02-01

Mathematical and numerical models are a fundamental tool for predicting the behaviour of geostructures and their interaction with the environment. The term “mathematical model” refers to a mathematical description of the more relevant physical phenomena which take place in the problem being analyzed. It is indeed a wide area including models ranging from the very simple ones for which analytical solutions can be obtained to those more complicated requiring the use of numerical approximations such as the finite element method. During the last decades, mathematical, constitutive and numerical models have been very much improved and today their use is widespread both in industry and in research. One special case is that of fast catastrophic landslides, for which simplified methods are not able to provide accurate solutions in many occasions. Moreover, many finite element codes cannot be applied for propagation of the mobilized mass. The purpose of this work is to present an overview of the different alternative mathematical and numerical models which can be applied to both the initiation and propagation mechanisms of fast catastrophic landslides and other related problems such as waves caused by landslides.

The Circle of Apollonius and Its Applications in Introductory Physics

ERIC Educational Resources Information Center

Partensky, Michael B.

2008-01-01

The circle of Apollonius is named after the ancient geometrician Apollonius of Perga. This beautiful geometric construct can be helpful when solving some general problems of geometry and mathematical physics, optics, and electricity. Here we discuss two of its applications: localizing an object in space and calculating electric fields. First, we…

Problemi e di Fisica e Astronomia ed il metodo di Gerberto docente

NASA Astrophysics Data System (ADS)

Sigismondi, Costantino

2015-04-01

Teaching Physics and Astronomy to pupils of 14-19 years old requires nowadays a continuous upgrade of knowledge as well as a capacity of selecting topics. The art of presenting arguments made Gerbert the teacher Rogatus a Pluribus in the end of X century and it is still actual; the proposed series of problems wants to link everyday experiences with the mathematical models of the phenomena, to allow the prediction and explanation of the experimental data. These problems of Physics and Astronomy are “observation oriented”, as the method of Gerbert was to start from the experience to get the theory, and not viceversa. Physics is much more than an “applied Algebra”. In the dispute of Ravenna (980) between Gerbert and Otric from Magdeburg, the primacy of Physics with respect to Mathematics was discussed. In the Italian secondary technical schools there are laboratory activities, while there is nothing similar for Lyceums and for the Astronomy teaching which is limited to a series of notions to be learned without any kind of observation; considered too difficult in polluted skyes.

Mathematical Manipulative Models: In Defense of “Beanbag Biology”

PubMed Central

Gaff, Holly; Weisstein, Anton E.

2010-01-01

Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process—1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets—we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education. PMID:20810952

Mathematical manipulative models: in defense of "beanbag biology".

PubMed

Jungck, John R; Gaff, Holly; Weisstein, Anton E

2010-01-01

Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process-1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets-we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project (http://bioquest.org/esteem) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education.

Topics in geophysical fluid dynamics: Atmospheric dynamics, dynamo theory, and climate dynamics

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ghil, M.; Childress, S.

1987-01-01

This text is the first study to apply systematically the successive bifurcations approach to complex time-dependent processes in large scale atmospheric dynamics, geomagnetism, and theoretical climate dynamics. The presentation of recent results on planetary-scale phenomena in the earth's atmosphere, ocean, cryosphere, mantle and core provides an integral account of mathematical theory and methods together with physical phenomena and processes. The authors address a number of problems in rapidly developing areas of geophysics, bringing into closer contact the modern tools of nonlinear mathematics and the novel problems of global change in the environment.

Integrating Effective Pedagogies in Science Education with a Design of Alternative Experiments on Electromagnetics

ERIC Educational Resources Information Center

Zhou, Shaona; Yeung, Yau-Yuen; Wang, Yanlin; Wang, Xiaojun; Xiao, Hua

2014-01-01

Learning electromagnetics often involves dealing with problems with strong mathematical skills or thinking about problems in abstract and multiple spaces. Moreover, many students are often unable to explain some related physical phenomena using the appropriate electromagnetic principles. In this paper, we report on integrating two effective…

Forced Convection Heat Transfer in Circular Pipes

ERIC Educational Resources Information Center

Tosun, Ismail

2007-01-01

One of the pitfalls of engineering education is to lose the physical insight of the problem while tackling the mathematical part. Forced convection heat transfer (the Graetz-Nusselt problem) certainly falls into this category. The equation of energy together with the equation of motion leads to a partial differential equation subject to various…

A Posteriori Error Analysis and Uncertainty Quantification for Adaptive Multiscale Operator Decomposition Methods for Multiphysics Problems

DTIC Science & Technology

2014-04-01

Barrier methods for critical exponent problems in geometric analysis and mathematical physics, J. Erway and M. Holst, Submitted for publication ...TR-14-33 A Posteriori Error Analysis and Uncertainty Quantification for Adaptive Multiscale Operator Decomposition Methods for Multiphysics...Problems Approved for public release, distribution is unlimited. April 2014 HDTRA1-09-1-0036 Donald Estep and Michael

Effects of a Problem-Based Learning Program on Engineering Students' Academic Achievements, Skills Development and Attitudes in a Mexican University.

ERIC Educational Resources Information Center

Polanco, Rodrigo; Calderon, Patricia; Delgado, Franciso

A 3-year follow-up evaluation was conducted of an experimental problem-based learning (PBL) integrated curriculum directed to students of the first 2 years of engineering. The PBL curriculum brought together the contents of physics, mathematics, and computer science courses in a single course in which students worked on real-life problems. In…

Is physics worth teaching?

NASA Astrophysics Data System (ADS)

Machold, Dolf K.

1992-09-01

The paper points out that many students and adults are accustomed to solving problems in physics on the basis of everyday concepts; believing that these concepts are very successful, those students are not interested in concepts offered by science teaching. Furthermore, the teaching physics in terms of mathematical descriptions of problems is too early — students don't see the original problem, so they are not interested in solutions. One way to avoid these difficulties is M. Wagenschein's proposal of the ‘Exemplary-genetic Method’. This method and its principles are presented and illustrated with examples taken from history. On the basis of this method educational and pedagogical functions of teaching physics are developed. P.S.: Martin Wagenschein (1896 1989), Professor of physics education at the University of Tübingen, was concerned with finding new methods for successfully teaching science.

Multi-representation ability of students on the problem solving physics

NASA Astrophysics Data System (ADS)

Theasy, Y.; Wiyanto; Sujarwata

2018-03-01

Accuracy in representing knowledge possessed by students will show how the level of student understanding. The multi-representation ability of students on the problem solving of physics has been done through qualitative method of grounded theory model and implemented on physics education student of Unnes academic year 2016/2017. Multiforms of representation used are verbal (V), images/diagrams (D), graph (G), and mathematically (M). High and low category students have an accurate use of graphical representation (G) of 83% and 77.78%, and medium category has accurate use of image representation (D) equal to 66%.

Applications of Massive Mathematical Computations

DTIC Science & Technology

1990-04-01

particles from the first principles of QCD . This problem is under intensive numerical study 11-6 using special purpose parallel supercomputers in...several places around the world. The method used here is the Monte Carlo integration for a fixed 3-D plus time lattices . Reliable results are still years...mathematical and theoretical physics, but its most promising applications are in the numerical realization of QCD computations. Our programs for the solution

Molecular Mechanics and Dynamics Characterization of an "in silico" Mutated Protein: A Stand-Alone Lab Module or Support Activity for "in vivo" and "in vitro" Analyses of Targeted Proteins

ERIC Educational Resources Information Center

Chiang, Harry; Robinson, Lucy C.; Brame, Cynthia J.; Messina, Troy C.

2013-01-01

Over the past 20 years, the biological sciences have increasingly incorporated chemistry, physics, computer science, and mathematics to aid in the development and use of mathematical models. Such combined approaches have been used to address problems from protein structure-function relationships to the workings of complex biological systems.…

Theoretical Mathematics

NASA Astrophysics Data System (ADS)

Stöltzner, Michael

Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.

The Place of Learning Quantum Theory in Physics Teacher Education: Motivational Elements Arising from the Context

ERIC Educational Resources Information Center

Körhasan, Nilüfer Didis

2015-01-01

Quantum theory is one of the most successful theories in physics. Because of its abstract, mathematical, and counter-intuitive nature, many students have problems learning the theory, just as teachers experience difficulty in teaching it. Pedagogical research on quantum theory has mainly focused on cognitive issues. However, affective issues about…

Challenges in Designing Appropriate Scaffolding to Improve Students' Representational Consistency: The Case of a Gauss's Law Problem

ERIC Educational Resources Information Center

Maries, Alexandru; Lin, Shih-Yin; Singh, Chandralekha

2017-01-01

Prior research suggests that introductory physics students have difficulty with graphing and interpreting graphs. Here, we discuss an investigation of student difficulties in translating between mathematical and graphical representations for a problem in electrostatics and the effect of increasing levels of scaffolding on students'…

"No Child Left Untested [sic]" Battle or Battle Cry Guiding Research and Practice? Making Research User-Friendly.

ERIC Educational Resources Information Center

Hough, David L.

2003-01-01

Critiques five articles from an online research journal in middle-level education on mathematical problem solving, social inclusion of students with disabilities in physical education, school and dispositional aggression among middle school boys, problem-based learning, and students' views of futuristics. Asserts that embracing the view that all…

Pre-service teachers' metaphorical perceptions of "physics" as a concept

NASA Astrophysics Data System (ADS)

Aykutlu, Isil; Bayrak, Celal; Bezen, Sevim

2018-02-01

In this study, the aim is to reveal pre-service biology, chemistry and mathematics teachers' metaphorical perceptions for physics. This study was patterned by employing phenomenology, which is one of the qualitative research methods. Sampling of the study consists of 90 pre-service teachers enrolled at the departments of biology, chemistry, and mathematics education at the faculty of education of a state university in Ankara. A metaphor form was prepared to determine pre-service teachers' mental metaphors for the physics concept. Then, it was determined that a total of 80 pre-service teachers generated 34 different metaphors for physics concept. As a result of the study, 34 metaphors generated by pre-service teachers for "physics" concept were gathered under seven different categories. Also, it was determined that pre-service teachers express most frequently "life" (26,25%) and "a difficult to solve problem"(21,25%) which take place in conceptual categories.

Design of multiple representations e-learning resources based on a contextual approach for the basic physics course

NASA Astrophysics Data System (ADS)

Bakri, F.; Muliyati, D.

2018-05-01

This research aims to design e-learning resources with multiple representations based on a contextual approach for the Basic Physics Course. The research uses the research and development methods accordance Dick & Carey strategy. The development carried out in the digital laboratory of Physics Education Department, Mathematics and Science Faculty, Universitas Negeri Jakarta. The result of the process of product development with Dick & Carey strategy, have produced e-learning design of the Basic Physics Course is presented in multiple representations in contextual learning syntax. The appropriate of representation used in the design of learning basic physics include: concept map, video, figures, data tables of experiment results, charts of data tables, the verbal explanations, mathematical equations, problem and solutions example, and exercise. Multiple representations are presented in the form of contextual learning by stages: relating, experiencing, applying, transferring, and cooperating.

Conceptual problem solving in high school physics

NASA Astrophysics Data System (ADS)

Docktor, Jennifer L.; Strand, Natalie E.; Mestre, José P.; Ross, Brian H.

2015-12-01

Problem solving is a critical element of learning physics. However, traditional instruction often emphasizes the quantitative aspects of problem solving such as equations and mathematical procedures rather than qualitative analysis for selecting appropriate concepts and principles. This study describes the development and evaluation of an instructional approach called Conceptual Problem Solving (CPS) which guides students to identify principles, justify their use, and plan their solution in writing before solving a problem. The CPS approach was implemented by high school physics teachers at three schools for major theorems and conservation laws in mechanics and CPS-taught classes were compared to control classes taught using traditional problem solving methods. Information about the teachers' implementation of the approach was gathered from classroom observations and interviews, and the effectiveness of the approach was evaluated from a series of written assessments. Results indicated that teachers found CPS easy to integrate into their curricula, students engaged in classroom discussions and produced problem solutions of a higher quality than before, and students scored higher on conceptual and problem solving measures.

Searching fundamental information in ordinary differential equations. Nondimensionalization technique.

PubMed

Sánchez Pérez, J F; Conesa, M; Alhama, I; Alhama, F; Cánovas, M

2017-01-01

Classical dimensional analysis and nondimensionalization are assumed to be two similar approaches in the search for dimensionless groups. Both techniques, simplify the study of many problems. The first approach does not need to know the mathematical model, being sufficient a deep understanding of the physical phenomenon involved, while the second one begins with the governing equations and reduces them to their dimensionless form by simple mathematical manipulations. In this work, a formal protocol is proposed for applying the nondimensionalization process to ordinary differential equations, linear or not, leading to dimensionless normalized equations from which the resulting dimensionless groups have two inherent properties: In one hand, they are physically interpreted as balances between counteracting quantities in the problem, and on the other hand, they are of the order of magnitude unity. The solutions provided by nondimensionalization are more precise in every case than those from dimensional analysis, as it is illustrated by the applications studied in this work.

Applying physical science techniques and CERN technology to an unsolved problem in radiation treatment for cancer: the multidisciplinary ‘VoxTox’ research programme

PubMed Central

Burnet, Neil G; Scaife, Jessica E; Romanchikova, Marina; Thomas, Simon J; Bates, Amy M; Wong, Emma; Noble, David J; Shelley, Leila EA; Bond, Simon J; Forman, Julia R; Hoole, Andrew CF; Barnett, Gillian C; Brochu, Frederic M; Simmons, Michael PD; Jena, Raj; Harrison, Karl; Yeap, Ping Lin; Drew, Amelia; Silvester, Emma; Elwood, Patrick; Pullen, Hannah; Sultana, Andrew; Seah, Shannon YK; Wilson, Megan Z; Russell, Simon G; Benson, Richard J; Rimmer, Yvonne L; Jefferies, Sarah J; Taku, Nicolette; Gurnell, Mark; Powlson, Andrew S; Schönlieb, Carola-Bibiane; Cai, Xiaohao; Sutcliffe, Michael PF; Parker, Michael A

2017-01-01

The VoxTox research programme has applied expertise from the physical sciences to the problem of radiotherapy toxicity, bringing together expertise from engineering, mathematics, high energy physics (including the Large Hadron Collider), medical physics and radiation oncology. In our initial cohort of 109 men treated with curative radiotherapy for prostate cancer, daily image guidance computed tomography (CT) scans have been used to calculate delivered dose to the rectum, as distinct from planned dose, using an automated approach. Clinical toxicity data have been collected, allowing us to address the hypothesis that delivered dose provides a better predictor of toxicity than planned dose. PMID:29177202

Applying physical science techniques and CERN technology to an unsolved problem in radiation treatment for cancer: the multidisciplinary 'VoxTox' research programme.

PubMed

Burnet, Neil G; Scaife, Jessica E; Romanchikova, Marina; Thomas, Simon J; Bates, Amy M; Wong, Emma; Noble, David J; Shelley, Leila Ea; Bond, Simon J; Forman, Julia R; Hoole, Andrew Cf; Barnett, Gillian C; Brochu, Frederic M; Simmons, Michael Pd; Jena, Raj; Harrison, Karl; Yeap, Ping Lin; Drew, Amelia; Silvester, Emma; Elwood, Patrick; Pullen, Hannah; Sultana, Andrew; Seah, Shannon Yk; Wilson, Megan Z; Russell, Simon G; Benson, Richard J; Rimmer, Yvonne L; Jefferies, Sarah J; Taku, Nicolette; Gurnell, Mark; Powlson, Andrew S; Schönlieb, Carola-Bibiane; Cai, Xiaohao; Sutcliffe, Michael Pf; Parker, Michael A

2017-06-01

The VoxTox research programme has applied expertise from the physical sciences to the problem of radiotherapy toxicity, bringing together expertise from engineering, mathematics, high energy physics (including the Large Hadron Collider), medical physics and radiation oncology. In our initial cohort of 109 men treated with curative radiotherapy for prostate cancer, daily image guidance computed tomography (CT) scans have been used to calculate delivered dose to the rectum, as distinct from planned dose, using an automated approach. Clinical toxicity data have been collected, allowing us to address the hypothesis that delivered dose provides a better predictor of toxicity than planned dose.

Understanding student use of mathematics in IPLS with the Math Epistemic Games Survey

NASA Astrophysics Data System (ADS)

Eichenlaub, Mark; Hemingway, Deborah; Redish, Edward F.

2017-01-01

We present the Math Epistemic Games Survey (MEGS), a new concept inventory on the use of mathematics in introductory physics for the life sciences. The survey asks questions that are often best-answered via techniques commonly-valued in physics instruction, including dimensional analysis, checking special or extreme cases, understanding scaling relationships, interpreting graphical representations, estimation, and mapping symbols onto physical meaning. MEGS questions are often rooted in quantitative biology. We present preliminary data on the validation and administration of the MEGS in a large, introductory physics for the life sciences course at the University of Maryland, as well as preliminary results on the clustering of questions and responses as a guide to student resource activation in problem solving. This material is based upon work supported by the US National Science Foundation under Award No. 15-04366.

Solution of some types of differential equations: operational calculus and inverse differential operators.

PubMed

Zhukovsky, K

2014-01-01

We present a general method of operational nature to analyze and obtain solutions for a variety of equations of mathematical physics and related mathematical problems. We construct inverse differential operators and produce operational identities, involving inverse derivatives and families of generalised orthogonal polynomials, such as Hermite and Laguerre polynomial families. We develop the methodology of inverse and exponential operators, employing them for the study of partial differential equations. Advantages of the operational technique, combined with the use of integral transforms, generating functions with exponentials and their integrals, for solving a wide class of partial derivative equations, related to heat, wave, and transport problems, are demonstrated.

Influence of Learning Strategy of Cognitive Conflict on Student Misconception in Computational Physics Course

NASA Astrophysics Data System (ADS)

Akmam, A.; Anshari, R.; Amir, H.; Jalinus, N.; Amran, A.

2018-04-01

Misconception is one of the factors causing students are not suitable in to choose a method for problem solving. Computational Physics course is a major subject in the Department of Physics FMIPA UNP Padang. The problem in Computational Physics learning lately is that students have difficulties in constructing knowledge. The indication of this problem was the student learning outcomes do not achieve mastery learning. The root of the problem is the ability of students to think critically weak. Student critical thinking can be improved using cognitive by conflict learning strategies. The research aims to determine the effect of cognitive conflict learning strategy to student misconception on the subject of Computational Physics Course at the Department of Physics, Faculty of Mathematics and Science, Universitas Negeri Padang. The experimental research design conducted after-before design cycles with a sample of 60 students by cluster random sampling. Data were analyzed using repeated Anova measurements. The cognitive conflict learning strategy has a significant effect on student misconception in the subject of Computational Physics Course.

Wheatley Award 2017 Winner: How Physics Can Help Africa Transform, from a Problem to an Opportunity

NASA Astrophysics Data System (ADS)

Turok, Neil

2017-01-01

Africa represents the world's greatest untapped pool of scientific and technical talent. The African Institute for Mathematical Sciences (AIMS) is providing outstanding postgraduate training and research opportunities to gifted students across the continent. Its alumni proceed to employment in fields ranging from epidemiology to natural resource management, information technology and mathematical finance, to engineering and pure research in physics and mathematics. Many have already had a major impact in revitalising Africa's universities, in tackling major epidemics, and in raising skills levels in industry and government. AIMS has opened six centres of excellence so far, in South Africa, Senegal, Ghana, Cameroon, Tanzania, and, most recently, Rwanda, and plans to grow to a network of fifteen centres over the next decade. Its 1200 alumni are at the leading edge of Africa's transformation into a knowledge-based society.

Computational and mathematical methods in brain atlasing.

PubMed

Nowinski, Wieslaw L

2017-12-01

Brain atlases have a wide range of use from education to research to clinical applications. Mathematical methods as well as computational methods and tools play a major role in the process of brain atlas building and developing atlas-based applications. Computational methods and tools cover three areas: dedicated editors for brain model creation, brain navigators supporting multiple platforms, and atlas-assisted specific applications. Mathematical methods in atlas building and developing atlas-aided applications deal with problems in image segmentation, geometric body modelling, physical modelling, atlas-to-scan registration, visualisation, interaction and virtual reality. Here I overview computational and mathematical methods in atlas building and developing atlas-assisted applications, and share my contribution to and experience in this field.

Loop Quantum Gravity.

PubMed

Rovelli, Carlo

2008-01-01

The problem of describing the quantum behavior of gravity, and thus understanding quantum spacetime , is still open. Loop quantum gravity is a well-developed approach to this problem. It is a mathematically well-defined background-independent quantization of general relativity, with its conventional matter couplings. Today research in loop quantum gravity forms a vast area, ranging from mathematical foundations to physical applications. Among the most significant results obtained so far are: (i) The computation of the spectra of geometrical quantities such as area and volume, which yield tentative quantitative predictions for Planck-scale physics. (ii) A physical picture of the microstructure of quantum spacetime, characterized by Planck-scale discreteness. Discreteness emerges as a standard quantum effect from the discrete spectra, and provides a mathematical realization of Wheeler's "spacetime foam" intuition. (iii) Control of spacetime singularities, such as those in the interior of black holes and the cosmological one. This, in particular, has opened up the possibility of a theoretical investigation into the very early universe and the spacetime regions beyond the Big Bang. (iv) A derivation of the Bekenstein-Hawking black-hole entropy. (v) Low-energy calculations, yielding n -point functions well defined in a background-independent context. The theory is at the roots of, or strictly related to, a number of formalisms that have been developed for describing background-independent quantum field theory, such as spin foams, group field theory, causal spin networks, and others. I give here a general overview of ideas, techniques, results and open problems of this candidate theory of quantum gravity, and a guide to the relevant literature.

Gesellschaft fuer angewandte Mathematik und Mechanik, Annual Scientific Meeting, Universitaet Regensburg, Regensburg, West Germany, April 16-19, 1984, Proceedings

NASA Astrophysics Data System (ADS)

Problems in applied mathematics and mechanics are addressed in reviews and reports. Areas covered are vibration and stability, elastic and plastic mechanics, fluid mechanics, the numerical treatment of differential equations (general theory and finite-element methods in particular), optimization, decision theory, stochastics, actuarial mathematics, applied analysis and mathematical physics, and numerical analysis. Included are major lectures on separated flows, the transition regime of rarefied-gas dynamics, recent results in nonlinear elasticity, fluid-elastic vibration, the new computer arithmetic, and unsteady wave propagation in layered elastic bodies.

Introduction to the special issue Hermann Weyl and the philosophy of the 'New Physics'

NASA Astrophysics Data System (ADS)

De Bianchi, Silvia; Catren, Gabriel

2018-02-01

This Special Issue Hermann Weyl and the Philosophy of the 'New Physics' has two main objectives: first, to shed fresh light on the relevance of Weyl's work for modern physics and, second, to evaluate the importance of Weyl's work and ideas for contemporary philosophy of physics. Regarding the first objective, this Special Issue emphasizes aspects of Weyl's work (e.g. his work on spinors in n dimensions) whose importance has recently been emerging in research fields across both mathematical and experimental physics, as well as in the history and philosophy of physics. Regarding the second objective, this Special Issue addresses the relevance of Weyl's ideas regarding important open problems in the philosophy of physics, such as the problem of characterizing scientific objectivity and the problem of providing a satisfactory interpretation of fundamental symmetries in gauge theories and quantum mechanics. In this Introduction, we sketch the state of the art in Weyl studies and we summarize the content of the contributions to the present volume.

Operational method of solution of linear non-integer ordinary and partial differential equations.

PubMed

Zhukovsky, K V

2016-01-01

We propose operational method with recourse to generalized forms of orthogonal polynomials for solution of a variety of differential equations of mathematical physics. Operational definitions of generalized families of orthogonal polynomials are used in this context. Integral transforms and the operational exponent together with some special functions are also employed in the solutions. The examples of solution of physical problems, related to such problems as the heat propagation in various models, evolutional processes, Black-Scholes-like equations etc. are demonstrated by the operational technique.

Development of 3-D Mechanical Models of Electric Circuits and Their Effect on Students' Understanding of Electric Potential Difference

ERIC Educational Resources Information Center

Balta, Nuri

2015-01-01

Visualizing physical concepts through models is an essential method in many sciences. While students are mostly proficient in handling mathematical aspects of problems, they frequently lack the ability to visualize and interpret abstract physical concepts in a meaningful way. In this paper, initially the electric circuits and related concepts were…

Hidden physics models: Machine learning of nonlinear partial differential equations

NASA Astrophysics Data System (ADS)

Raissi, Maziar; Karniadakis, George Em

2018-03-01

While there is currently a lot of enthusiasm about "big data", useful data is usually "small" and expensive to acquire. In this paper, we present a new paradigm of learning partial differential equations from small data. In particular, we introduce hidden physics models, which are essentially data-efficient learning machines capable of leveraging the underlying laws of physics, expressed by time dependent and nonlinear partial differential equations, to extract patterns from high-dimensional data generated from experiments. The proposed methodology may be applied to the problem of learning, system identification, or data-driven discovery of partial differential equations. Our framework relies on Gaussian processes, a powerful tool for probabilistic inference over functions, that enables us to strike a balance between model complexity and data fitting. The effectiveness of the proposed approach is demonstrated through a variety of canonical problems, spanning a number of scientific domains, including the Navier-Stokes, Schrödinger, Kuramoto-Sivashinsky, and time dependent linear fractional equations. The methodology provides a promising new direction for harnessing the long-standing developments of classical methods in applied mathematics and mathematical physics to design learning machines with the ability to operate in complex domains without requiring large quantities of data.

Problem-Based Learning and Assessment in Hydrology Courses: Can Non-Traditional Assessment Better Reflect Intended Learning Outcomes?

ERIC Educational Resources Information Center

Lyon, Steve W.; Teutschbein, Claudia

2011-01-01

Hydrology has at its core a focus on real-world applications and problems stemming from the importance of water for society and natural systems. While hydrology is firmly founded in traditional "hard" sciences like physics and mathematics, much of the innovation and excitement in current and future research-oriented hydrology comes…

The Development of Physics Learning Instrument Based on Hypermedia and Its Influence on the Student Problem Solving Skill

ERIC Educational Resources Information Center

Amin, Bunga Dara; Mahmud, Alimuddin; Muris

2016-01-01

This research aims to produce a learning instrument based on hypermedia which is valid, interesting, practical, and effective as well as to know its influence on the problem based skill of students Mathematical and Science Faculty, Makassar State University. This research is a research and development at (R&D) type. The development procedure…

An Exploration of Developing Active Exploring and Problem Solving Skill Lego Robot Course by the Application of Anchored Instruction Theory

ERIC Educational Resources Information Center

Chen, Chen-Yuan

2013-01-01

In recent years, researches had shown that the development of problem solving skill became important for education, and the educational robots are capable for promoting students not only understand the physical and mathematical concepts, but also have active and constructive learning. Meanwhile, the importance of situation in education is rising,…

Summary of research in applied mathematics, numerical analysis, and computer sciences

NASA Technical Reports Server (NTRS)

1986-01-01

The major categories of current ICASE research programs addressed include: numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; control and parameter identification problems, with emphasis on effective numerical methods; computational problems in engineering and physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and computer systems and software, especially vector and parallel computers.

Combinatorial solutions to integrable hierarchies

NASA Astrophysics Data System (ADS)

Kazarian, M. E.; Lando, S. K.

2015-06-01

This paper reviews modern approaches to the construction of formal solutions to integrable hierarchies of mathematical physics whose coefficients are answers to various enumerative problems. The relationship between these approaches and the combinatorics of symmetric groups and their representations is explained. Applications of the results to the construction of efficient computations in problems related to models of quantum field theories are described. Bibliography: 34 titles.

Compressed modes for variational problems in mathematical physics and compactly supported multiresolution basis for the Laplace operator

NASA Astrophysics Data System (ADS)

Ozolins, Vidvuds; Lai, Rongjie; Caflisch, Russel; Osher, Stanley

2014-03-01

We will describe a general formalism for obtaining spatially localized (``sparse'') solutions to a class of problems in mathematical physics, which can be recast as variational optimization problems, such as the important case of Schrödinger's equation in quantum mechanics. Sparsity is achieved by adding an L1 regularization term to the variational principle, which is shown to yield solutions with compact support (``compressed modes''). Linear combinations of these modes approximate the eigenvalue spectrum and eigenfunctions in a systematically improvable manner, and the localization properties of compressed modes make them an attractive choice for use with efficient numerical algorithms that scale linearly with the problem size. In addition, we introduce an L1 regularized variational framework for developing a spatially localized basis, compressed plane waves (CPWs), that spans the eigenspace of a differential operator, for instance, the Laplace operator. Our approach generalizes the concept of plane waves to an orthogonal real-space basis with multiresolution capabilities. Supported by NSF Award DMR-1106024 (VO), DOE Contract No. DE-FG02-05ER25710 (RC) and ONR Grant No. N00014-11-1-719 (SO).

Inverse problems in the design, modeling and testing of engineering systems

NASA Technical Reports Server (NTRS)

Alifanov, Oleg M.

1991-01-01

Formulations, classification, areas of application, and approaches to solving different inverse problems are considered for the design of structures, modeling, and experimental data processing. Problems in the practical implementation of theoretical-experimental methods based on solving inverse problems are analyzed in order to identify mathematical models of physical processes, aid in input data preparation for design parameter optimization, help in design parameter optimization itself, and to model experiments, large-scale tests, and real tests of engineering systems.

Student difficulties in translating between mathematical and graphical representations in introductory physics

NASA Astrophysics Data System (ADS)

Lin, Shih-Yin; Maries, Alexandru; Singh, Chandralekha

2013-01-01

We investigate introductory physics students' difficulties in translating between mathematical and graphical representations and the effect of scaffolding on students' performance. We gave a typical problem that can be solved using Gauss's law involving a spherically symmetric charge distribution (a conducting sphere concentric with a conducting spherical shell) to 95 calculus-based introductory physics students. We asked students to write a mathematical expression for the electric field in various regions and asked them to graph the electric field. We knew from previous experience that students have great difficulty in graphing the electric field. Therefore, we implemented two scaffolding interventions to help them. Students who received the scaffolding support were either (1) asked to plot the electric field in each region first (before having to plot it as a function of distance from the center of the sphere) or (2) asked to plot the electric field in each region after explicitly evaluating the electric field at the beginning, mid and end points of each region. The comparison group was only asked to plot the electric field at the end of the problem. We found that students benefited the most from intervention (1) and that intervention (2), although intended to aid students, had an adverse effect. Also, recorded interviews were conducted with a few students in order to understand how students were impacted by the aforementioned interventions.

Mathematical and Numerical Techniques in Energy and Environmental Modeling

NASA Astrophysics Data System (ADS)

Chen, Z.; Ewing, R. E.

Mathematical models have been widely used to predict, understand, and optimize many complex physical processes, from semiconductor or pharmaceutical design to large-scale applications such as global weather models to astrophysics. In particular, simulation of environmental effects of air pollution is extensive. Here we address the need for using similar models to understand the fate and transport of groundwater contaminants and to design in situ remediation strategies. Three basic problem areas need to be addressed in the modeling and simulation of the flow of groundwater contamination. First, one obtains an effective model to describe the complex fluid/fluid and fluid/rock interactions that control the transport of contaminants in groundwater. This includes the problem of obtaining accurate reservoir descriptions at various length scales and modeling the effects of this heterogeneity in the reservoir simulators. Next, one develops accurate discretization techniques that retain the important physical properties of the continuous models. Finally, one develops efficient numerical solution algorithms that utilize the potential of the emerging computing architectures. We will discuss recent advances and describe the contribution of each of the papers in this book in these three areas. Keywords: reservoir simulation, mathematical models, partial differential equations, numerical algorithms

Qualitative investigation into students' use of divergence and curl in electromagnetism

NASA Astrophysics Data System (ADS)

Bollen, Laurens; van Kampen, Paul; Baily, Charles; De Cock, Mieke

2016-12-01

Many students struggle with the use of mathematics in physics courses. Although typically well trained in rote mathematical calculation, they often lack the ability to apply their acquired skills to physical contexts. Such student difficulties are particularly apparent in undergraduate electrodynamics, which relies heavily on the use of vector calculus. To gain insight into student reasoning when solving problems involving divergence and curl, we conducted eight semistructured individual student interviews. During these interviews, students discussed the divergence and curl of electromagnetic fields using graphical representations, mathematical calculations, and the differential form of Maxwell's equations. We observed that while many students attempt to clarify the problem by making a sketch of the electromagnetic field, they struggle to interpret graphical representations of vector fields in terms of divergence and curl. In addition, some students confuse the characteristics of field line diagrams and field vector plots. By interpreting our results within the conceptual blending framework, we show how a lack of conceptual understanding of the vector operators and difficulties with graphical representations can account for an improper understanding of Maxwell's equations in differential form. Consequently, specific learning materials based on a multiple representation approach are required to clarify Maxwell's equations.

A new formulation for anisotropic radiative transfer problems. I - Solution with a variational technique

NASA Technical Reports Server (NTRS)

Cheyney, H., III; Arking, A.

1976-01-01

The equations of radiative transfer in anisotropically scattering media are reformulated as linear operator equations in a single independent variable. The resulting equations are suitable for solution by a variety of standard mathematical techniques. The operators appearing in the resulting equations are in general nonsymmetric; however, it is shown that every bounded linear operator equation can be embedded in a symmetric linear operator equation and a variational solution can be obtained in a straightforward way. For purposes of demonstration, a Rayleigh-Ritz variational method is applied to three problems involving simple phase functions. It is to be noted that the variational technique demonstrated is of general applicability and permits simple solutions for a wide range of otherwise difficult mathematical problems in physics.

What Would Pascal Think About Space Safety?

NASA Astrophysics Data System (ADS)

Pfitzer, Tom

2013-09-01

Blaise Pascal was a true Renaissance man being well versed in science, physics, religion, philosophy, and especially mathematics. He had a knack for simplifying complex problems into mathematical formulae. He had well-formed opinions about the scientific issues of his day, in particular about risk. There is little doubt that were he alive today, he would have opinions useful to this society. This paper addresses what he thought then as a foundation for what he would have thought now.

A Cognitive Analysis of Students’ Mathematical Problem Solving Ability on Geometry

NASA Astrophysics Data System (ADS)

Rusyda, N. A.; Kusnandi, K.; Suhendra, S.

2017-09-01

The purpose of this research is to analyze of mathematical problem solving ability of students in one of secondary school on geometry. This research was conducted by using quantitative approach with descriptive method. Population in this research was all students of that school and the sample was twenty five students that was chosen by purposive sampling technique. Data of mathematical problem solving were collected through essay test. The results showed the percentage of achievement of mathematical problem solving indicators of students were: 1) solve closed mathematical problems with context in math was 50%; 2) solve the closed mathematical problems with the context beyond mathematics was 24%; 3) solving open mathematical problems with contexts in mathematics was 35%; And 4) solving open mathematical problems with contexts outside mathematics was 44%. Based on the percentage, it can be concluded that the level of achievement of mathematical problem solving ability in geometry still low. This is because students are not used to solving problems that measure mathematical problem solving ability, weaknesses remember previous knowledge, and lack of problem solving framework. So the students’ ability of mathematical problems solving need to be improved with implement appropriate learning strategy.

The concept of physical surface in nuclear matter

NASA Astrophysics Data System (ADS)

Mazilu, Nicolae; Agop, Maricel

2015-02-01

The main point of a physical definition of surface forces in the matter in general, especially in the nuclear matter, is that the curvature of surfaces and its variation should be physically defined. The forces are therefore just the vehicles of introducing physics. The problem of mathematical definition of a surface in term of the curvature parameters thus naturally occurs. The present work addresses this problem in terms of the asymptotic directions of a surface in a point. A physical meaning of these parameters is given, first in terms of inertial forces, then in terms of a differential theory of colors, whereby the space of curvature parameters is identified with the color space. The work concludes with an image of the evolution of a local portion of a surface.

A fixed energy fixed angle inverse scattering in interior transmission problem

NASA Astrophysics Data System (ADS)

Chen, Lung-Hui

2017-06-01

We study the inverse acoustic scattering problem in mathematical physics. The problem is to recover the index of refraction in an inhomogeneous medium by measuring the scattered wave fields in the far field. We transform the problem to the interior transmission problem in the study of the Helmholtz equation. We find an inverse uniqueness on the scatterer with a knowledge of a fixed interior transmission eigenvalue. By examining the solution in a series of spherical harmonics in the far field, we can determine uniquely the perturbation source for the radially symmetric perturbations.

PREFACE: 3rd International Conference on Science & Engineering in Mathematics, Chemistry and Physics 2015 (ScieTech 2015)

NASA Astrophysics Data System (ADS)

Gaol, F. L.

2015-06-01

The 3rd International Conference on Science & Engineering in Mathematics, Chemistry and Physics 2015 (ScieTech 2015), was held at The Westin Resort Nusa Dua, Bali on 31 January - 1 February 2015. The ScieTech 2015 conference is aimed to bring together researchers, engineers and scientists from around the world. ScieTech 2015 is placed on promoting interaction between the theoretical, experimental, and applied communities, so that a high level exchange is achieved in new and emerging areas within mathematics, chemistry and physics. As we already know that science and technology have brought tremendous benefits for human civilization. People are becoming healthier, wealthier, better educated, more peaceful, increasingly connected, and living longer. Of course, science and technology provide many answers to global challenges, but we will face more complex problems in the next decade due to increasing world population, limitation of energy, and climate change. Therefore, researchers should be more active in conducting research that enables collaboration between one and the others. Interdisciplinary cooperation is absolutely necessary in order to create a smart system for solving the global problems. We need a global and general long-term view of the future with long-range goals for solving complex problems in next decade. Therefore the conference was held to be a forum for researchers from different disciplines to start collaborating and conducting research that provides a solution to the global issues. The theme of ScieTech 2015 was ''The interdisciplinary Application between Mathematics, Chemistry and Physics to enhance the Quality of Life''. We would like to express our sincere gratitude to all in the Technical Program Committee who have reviewed the papers and developed a very interesting conference program as well as the invited and plenary speakers. This year, we received 197 papers and after rigorous review, 59 papers were accepted. The participants came from 19 countries, and there were six paralell sessions and four keynote speakers. It is an honour to present this volume of Journal of Physics: Conference Series (JPCS) and we deeply thank the authors for their enthusiastic and high-grade contributions. Finally, we would like to thank the conference chairmen, members of the steering committee, the organizing committee, the organizing secretariat and the financial support from the conference sponsors that allowed the success of ScieTech 2015.

Special issue on cluster algebras in mathematical physics

NASA Astrophysics Data System (ADS)

Di Francesco, Philippe; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito

2014-02-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to cluster algebras in mathematical physics. Over the ten years since their introduction by Fomin and Zelevinsky, the theory of cluster algebras has witnessed a spectacular growth, first and foremost due to the many links that have been discovered with a wide range of subjects in mathematics and, increasingly, theoretical and mathematical physics. The main motivation of this special issue is to gather together reviews, recent developments and open problems, mainly from a mathematical physics viewpoint, into a single comprehensive issue. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will consist of invited review articles and contributed papers containing new results on the interplays of cluster algebras with mathematical physics. Editorial policy The Guest Editors for this issue are Philippe Di Francesco, Michael Gekhtman, Atsuo Kuniba and Masahito Yamazaki. The areas and topics for this issue include, but are not limited to: discrete integrable systems arising from cluster mutations cluster structure on Poisson varieties cluster algebras and soliton interactions cluster positivity conjecture Y-systems in the thermodynamic Bethe ansatz and Zamolodchikov's periodicity conjecture T-system of transfer matrices of integrable lattice models dilogarithm identities in conformal field theory wall crossing in 4d N = 2 supersymmetric gauge theories 4d N = 1 quiver gauge theories described by networks scattering amplitudes of 4d N = 4 theories 3d N = 2 gauge theories described by flat connections on 3-manifolds integrability of dimer/Ising models on graphs. All contributions will be refereed and processed according to the usual procedure of the journal. Guidelines for preparation of contributions The deadline for contributed papers is 31 March 2014. This deadline will allow the special issue to appear at the end of 2014. There is no strict regulation on article size, but as a guide the preferable size is 15-30 pages for contributed papers and 40-60 pages for reviews. Further advice on publishing your work in Journal of Physics A may be found at iopscience.iop.org/jphysa. Contributions to the special issue should be submitted by web upload via ScholarOne Manuscripts, quoting 'JPhysA special issue on cluster algebras in mathematical physics'. Submissions should ideally be in standard LaTeX form. Please see the website for further information on electronic submissions. All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. The special issue will be published in the print and online versions of the journal.

Special issue on cluster algebras in mathematical physics

NASA Astrophysics Data System (ADS)

Di Francesco, Philippe; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito

2013-12-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to cluster algebras in mathematical physics. Over the ten years since their introduction by Fomin and Zelevinsky, the theory of cluster algebras has witnessed a spectacular growth, first and foremost due to the many links that have been discovered with a wide range of subjects in mathematics and, increasingly, theoretical and mathematical physics. The main motivation of this special issue is to gather together reviews, recent developments and open problems, mainly from a mathematical physics viewpoint, into a single comprehensive issue. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will consist of invited review articles and contributed papers containing new results on the interplays of cluster algebras with mathematical physics. Editorial policy The Guest Editors for this issue are Philippe Di Francesco, Michael Gekhtman, Atsuo Kuniba and Masahito Yamazaki. The areas and topics for this issue include, but are not limited to: discrete integrable systems arising from cluster mutations cluster structure on Poisson varieties cluster algebras and soliton interactions cluster positivity conjecture Y-systems in the thermodynamic Bethe ansatz and Zamolodchikov's periodicity conjecture T-system of transfer matrices of integrable lattice models dilogarithm identities in conformal field theory wall crossing in 4d N = 2 supersymmetric gauge theories 4d N = 1 quiver gauge theories described by networks scattering amplitudes of 4d N = 4 theories 3d N = 2 gauge theories described by flat connections on 3-manifolds integrability of dimer/Ising models on graphs. All contributions will be refereed and processed according to the usual procedure of the journal. Guidelines for preparation of contributions The deadline for contributed papers is 31 March 2014. This deadline will allow the special issue to appear at the end of 2014. There is no strict regulation on article size, but as a guide the preferable size is 15-30 pages for contributed papers and 40-60 pages for reviews. Further advice on publishing your work in Journal of Physics A may be found at iopscience.iop.org/jphysa. Contributions to the special issue should be submitted by web upload via ScholarOne Manuscripts, quoting 'JPhysA special issue on cluster algebras in mathematical physics'. Submissions should ideally be in standard LaTeX form. Please see the website for further information on electronic submissions. All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. The special issue will be published in the print and online versions of the journal.

Special issue on cluster algebras in mathematical physics

NASA Astrophysics Data System (ADS)

Di Francesco, Philippe; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito

2013-11-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to cluster algebras in mathematical physics. Over the ten years since their introduction by Fomin and Zelevinsky, the theory of cluster algebras has witnessed a spectacular growth, first and foremost due to the many links that have been discovered with a wide range of subjects in mathematics and, increasingly, theoretical and mathematical physics. The main motivation of this special issue is to gather together reviews, recent developments and open problems, mainly from a mathematical physics viewpoint, into a single comprehensive issue. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will consist of invited review articles and contributed papers containing new results on the interplays of cluster algebras with mathematical physics. Editorial policy The Guest Editors for this issue are Philippe Di Francesco, Michael Gekhtman, Atsuo Kuniba and Masahito Yamazaki. The areas and topics for this issue include, but are not limited to: discrete integrable systems arising from cluster mutations cluster structure on Poisson varieties cluster algebras and soliton interactions cluster positivity conjecture Y-systems in the thermodynamic Bethe ansatz and Zamolodchikov's periodicity conjecture T-system of transfer matrices of integrable lattice models dilogarithm identities in conformal field theory wall crossing in 4d N = 2 supersymmetric gauge theories 4d N = 1 quiver gauge theories described by networks scattering amplitudes of 4d N = 4 theories 3d N = 2 gauge theories described by flat connections on 3-manifolds integrability of dimer/Ising models on graphs. All contributions will be refereed and processed according to the usual procedure of the journal. Guidelines for preparation of contributions The deadline for contributed papers is 31 March 2014. This deadline will allow the special issue to appear at the end of 2014. There is no strict regulation on article size, but as a guide the preferable size is 15-30 pages for contributed papers and 40-60 pages for reviews. Further advice on publishing your work in Journal of Physics A may be found at iopscience.iop.org/jphysa. Contributions to the special issue should be submitted by web upload via ScholarOne Manuscripts, quoting 'JPhysA special issue on cluster algebras in mathematical physics'. Submissions should ideally be in standard LaTeX form. Please see the website for further information on electronic submissions. All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. The special issue will be published in the print and online versions of the journal.

Pendulum rides, rotations and the Coriolis effect

NASA Astrophysics Data System (ADS)

Pendrill, Ann-Marie; Modig, Conny

2018-07-01

An amusement park is full of examples that can be made into challenging problems for students, combining mathematical modelling with video analysis, as well as measurements in the rides. Traditional amusement ride related textbook problems include free-fall, circular motion, pendula and energy conservation in roller coasters, where the moving bodies are typically considered point-like. However, an amusement park can offer many more examples that are useful in physics and engineering education, many of them with strong mathematical content. This paper analyses forces on riders in a large rotating pendulum ride, where the Coriolis effect is sufficiently large to be visible in accelerometer data from the rides and leads to different ride experiences in different positions.

The mathematics of virus shell assembly. Progress report 1995--1996

DOE Office of Scientific and Technical Information (OSTI.GOV)

Berger, B.

1996-08-01

This research focuses on applying computational and mathematical techniques to problems in biology, and more specifically to problems in protein folding. Significant progress has been made in the following areas relating to virus shell assembly: the local rules theory has been further developed; development has begun on a second-generation simulator which provides a more physically realistic model of assembly, collaborative efforts have continued with an experimental biologist to verify and inspire the local rules theory; an investigation has been initiated into the mechanics of virus shell assembly; laboratory experiments have been conducted on bacteriophage T4 which verify that the previouslymore » believed structure for the core may be incorrect.« less

Johannes Kepler and his contribution to Applied Mathematics

NASA Astrophysics Data System (ADS)

Pichler, Franz

The worldwide renown of Johannes Kepler is based above all on his contribution to astronomy. The 3 Kepler's Laws relating to the planets are well known and will ensure that his name is remembered by future generations. Besides his astronomical work, Kepler also made important contributions in the fields of theology, physics, phylosophy and mathematics. The actual paper discusses the advances by Kepler in the application of mathematics to the solution of "real life problems". The author made a concise account of some of the disciples by Kepler: Klug, Wieleitner, Caspar, Hammer, paying particular attention to works published by Kepler while he was living in Linz (1612-1628). The Kepler's contribution to applied mathematics is an example supremely worthy of emulation, the author concludes.

Adding Resistances and Capacitances in Introductory Electricity

NASA Astrophysics Data System (ADS)

Efthimiou, C. J.; Llewellyn, R. A.

2005-09-01

All introductory physics textbooks, with or without calculus, cover the addition of both resistances and capacitances in series and in parallel as discrete summations. However, none includes problems that involve continuous versions of resistors in parallel or capacitors in series. This paper introduces a method for solving the continuous problems that is logical, straightforward, and within the mathematical preparation of students at the introductory level.

The Concept of Proportionality as a Predictor of Success at the University of Papua and New Guinea. E.R.U. Report 6.

ERIC Educational Resources Information Center

Jones, John

A main problem encountered by science and mathematics students at secondary and tertiary institutions throughout Papua New Guinea is that of dealing with ratio and proportion. The problem is most clearly defined in science, since this is the area in which the quantitative manipulation of physical variables is most frequently carried out. An…

A Problem with STEM

ERIC Educational Resources Information Center

Marder, Michael

2013-01-01

Striking differences between physics and biology have important implications for interdisciplinary science, technology, engineering, and mathematics (STEM) education. The author is a physicist with interdisciplinary connections. The research group in which he works, the Center for Nonlinear Dynamics at the University of Texas at Austin, is…

Engineering Problem-Solving Knowledge: The Impact of Context

ERIC Educational Resources Information Center

Wolff, Karin

2017-01-01

Employer complaints of engineering graduate inability to "apply knowledge" suggests a need to interrogate the complex theory-practice relationship in twenty-first century real world contexts. Focussing specifically on the application of mathematics, physics and logic-based disciplinary knowledge, the research examines engineering…

Undergraduate Research in Quantum Information Science

ERIC Educational Resources Information Center

Lyons, David W.

2017-01-01

Quantum Information Science (QIS) is an interdisciplinary field involving mathematics, computer science, and physics. Appealing aspects include an abundance of accessible open problems, active interest and support from government and industry, and an energetic, open, and collaborative international research culture. We describe our student-faculty…

Publisher's Announcement

NASA Astrophysics Data System (ADS)

Scriven, Neil

2003-12-01

We are delighted to announce that the new Editor-in-Chief of Journal of Physics A: Mathematical and General for 2004 will be Professor Carl M Bender of Washington University, St. Louis. Carl will, with the help of his world class editorial board, maintain standards of scientific rigour whilst ensuring that research published is of the highest importance. Carl attained his first degree in physics at Cornell University before studying for his PhD at Harvard. He later worked at The Institute for Advanced Study in Princeton and at MIT before assuming his current position at Washington University, St Louis. He has been a visiting professor at Technion, Haifa, and Imperial College, London and a scientific consultant for Los Alamos National Laboratory. His main expertise is in using classical applied mathematics to solve a broad range of problems in high-energy theoretical physics and mathematical physics. Since the publication of his book Advanced Mathematical Methods for Scientists and Engineers, written with Steven Orszag, he has been regarded as an expert on the subject of asymptotic analysis and perturbative methods. `Carl publishes his own internationally-important research in the journal and has been an invaluable, energetic member of the Editorial Board for some time' said Professor Ed Corrigan, Carl's predecessor as Editor, `he will be an excellent Editor-in-Chief'. Our grateful thanks and best wishes go to Professor Corrigan who has done a magnificent job for the journal during his five-year tenure.

The role of physical digit representation and numerical magnitude representation in children's multiplication fact retrieval.

PubMed

De Visscher, Alice; Noël, Marie-Pascale; De Smedt, Bert

2016-12-01

Arithmetic facts, in particular multiplication tables, are thought to be stored in long-term memory and to be interference prone. At least two representations underpinning these arithmetic facts have been suggested: a physical representation of the digits and a numerical magnitude representation. We hypothesized that both representations are possible sources of interference that could explain individual differences in multiplication fact performance and/or in strategy use. We investigated the specificity of these interferences on arithmetic fact retrieval and explored the relation between interference and performance on the different arithmetic operations and on general mathematics achievement. Participants were 79 fourth-grade children (M age =9.6 years) who completed a products comparison and a multiplication production task with verbal strategy reports. Performances on a speeded calculation test including the four operations and on a general mathematics achievement test were also collected. Only the interference coming from physical representations was a significant predictor of the performance across multiplications. However, both the magnitude and physical representations were unique predictors of individual differences in multiplication. The frequency of the retrieval strategy across multiplication problems and across individuals was determined only by the physical representation, which therefore is suggested as being responsible for memory storage issues. Interestingly, this impact of physical representation was not observed when predicting performance on subtraction or on general mathematical achievement. In contrast, the impact of the numerical magnitude representation was more general in that it was observed across all arithmetic operations and in general mathematics achievement. Copyright © 2016 Elsevier Inc. All rights reserved.

Elementary metallography

NASA Technical Reports Server (NTRS)

Kazem, Sayyed M.

1992-01-01

Materials and Processes 1 (MET 141) is offered to freshmen by the Mechanical Engineering Department at Purdue University. The goal of MET 141 is to broaden the technical background of students who have not had any college science courses. Hence, applied physics, chemistry, and mathematics are included and quantitative problem solving is involved. In the elementary metallography experiment of this course, the objectives are: (1) introduce the vocabulary and establish outlook; (2) make qualitative observations and quantitative measurements; (3) demonstrate the proper use of equipment; and (4) review basic mathematics and science.

Determination of power distribution in the VVER-440 core on the basis of data from in-core monitors by means of a metric analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kryanev, A. V.; Udumyan, D. K.; Kurchenkov, A. Yu., E-mail: s327@vver.kiae.ru

2014-12-15

Problems associated with determining the power distribution in the VVER-440 core on the basis of a neutron-physics calculation and data from in-core monitors are considered. A new mathematical scheme is proposed for this on the basis of a metric analysis. In relation to the existing mathematical schemes, the scheme in question improves the accuracy and reliability of the resulting power distribution.

Research in applied mathematics, numerical analysis, and computer science

NASA Technical Reports Server (NTRS)

1984-01-01

Research conducted at the Institute for Computer Applications in Science and Engineering (ICASE) in applied mathematics, numerical analysis, and computer science is summarized and abstracts of published reports are presented. The major categories of the ICASE research program are: (1) numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; (2) control and parameter identification; (3) computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and (4) computer systems and software, especially vector and parallel computers.

The Construction of Mathematical Literacy Problems for Geometry

NASA Astrophysics Data System (ADS)

Malasari, P. N.; Herman, T.; Jupri, A.

2017-09-01

The students of junior high school should have mathematical literacy ability to formulate, apply, and interpret mathematics in problem solving of daily life. Teaching these students are not enough by giving them ordinary mathematics problems. Teaching activities for these students brings consequence for teacher to construct mathematical literacy problems. Therefore, the aim of this study is to construct mathematical literacy problems to assess mathematical literacy ability. The steps of this study that consists of analysing, designing, theoretical validation, revising, limited testing to students, and evaluating. The data was collected with written test to 38 students of grade IX at one of state junior high school. Mathematical literacy problems consist of three essays with three indicators and three levels at polyhedron subject. The Indicators are formulating and employing mathematics. The results show that: (1) mathematical literacy problems which are constructed have been valid and practical, (2) mathematical literacy problems have good distinguishing characteristics and adequate distinguishing characteristics, (3) difficulty levels of problems are easy and moderate. The final conclusion is mathematical literacy problems which are constructed can be used to assess mathematical literacy ability.

Examining problem solving in physics-intensive Ph.D. research

NASA Astrophysics Data System (ADS)

Leak, Anne E.; Rothwell, Susan L.; Olivera, Javier; Zwickl, Benjamin; Vosburg, Jarrett; Martin, Kelly Norris

2017-12-01

Problem-solving strategies learned by physics undergraduates should prepare them for real-world contexts as they transition from students to professionals. Yet, graduate students in physics-intensive research face problems that go beyond problem sets they experienced as undergraduates and are solved by different strategies than are typically learned in undergraduate coursework. This paper expands the notion of problem solving by characterizing the breadth of problems and problem-solving processes carried out by graduate students in physics-intensive research. We conducted semi-structured interviews with ten graduate students to determine the routine, difficult, and important problems they engage in and problem-solving strategies they found useful in their research. A qualitative typological analysis resulted in the creation of a three-dimensional framework: context, activity, and feature (that made the problem challenging). Problem contexts extended beyond theory and mathematics to include interactions with lab equipment, data, software, and people. Important and difficult contexts blended social and technical skills. Routine problem activities were typically well defined (e.g., troubleshooting), while difficult and important ones were more open ended and had multiple solution paths (e.g., evaluating options). In addition to broadening our understanding of problems faced by graduate students, our findings explore problem-solving strategies (e.g., breaking down problems, evaluating options, using test cases or approximations) and characteristics of successful problem solvers (e.g., initiative, persistence, and motivation). Our research provides evidence of the influence that problems students are exposed to have on the strategies they use and learn. Using this evidence, we have developed a preliminary framework for exploring problems from the solver's perspective. This framework will be examined and refined in future work. Understanding problems graduate students face and the strategies they use has implications for improving how we approach problem solving in undergraduate physics and physics education research.

Physics and Mathematics as Interwoven Disciplines in Science Education

NASA Astrophysics Data System (ADS)

Galili, Igal

2018-03-01

The relationship between physics and mathematics is reviewed upgrading the common in physics classes' perspective of mathematics as a toolkit for physics. The nature of the physics-mathematics relationship is considered along a certain historical path. The triadic hierarchical structure of discipline-culture helps to identify different ways in which mathematics is used in physics and to appreciate its contribution, to recognize the difference between mathematics and physics as disciplines in approaches, values, methods, and forms. We mentioned certain forms of mathematical knowledge important for physics but often missing in school curricula. The geometrical mode of codification of mathematical knowledge is compared with the analytical one in context of teaching school physics and mathematics; their complementarity is exemplified. Teaching may adopt the examples facilitating the claims of the study to reach science literacy and meaningful learning.

Computational Methods for Structural Mechanics and Dynamics, part 1

NASA Technical Reports Server (NTRS)

Stroud, W. Jefferson (Editor); Housner, Jerrold M. (Editor); Tanner, John A. (Editor); Hayduk, Robert J. (Editor)

1989-01-01

The structural analysis methods research has several goals. One goal is to develop analysis methods that are general. This goal of generality leads naturally to finite-element methods, but the research will also include other structural analysis methods. Another goal is that the methods be amenable to error analysis; that is, given a physical problem and a mathematical model of that problem, an analyst would like to know the probable error in predicting a given response quantity. The ultimate objective is to specify the error tolerances and to use automated logic to adjust the mathematical model or solution strategy to obtain that accuracy. A third goal is to develop structural analysis methods that can exploit parallel processing computers. The structural analysis methods research will focus initially on three types of problems: local/global nonlinear stress analysis, nonlinear transient dynamics, and tire modeling.

Quantum and semiclassical spin networks: from atomic and molecular physics to quantum computing and gravity

NASA Astrophysics Data System (ADS)

Aquilanti, Vincenzo; Bitencourt, Ana Carla P.; Ferreira, Cristiane da S.; Marzuoli, Annalisa; Ragni, Mirco

2008-11-01

The mathematical apparatus of quantum-mechanical angular momentum (re)coupling, developed originally to describe spectroscopic phenomena in atomic, molecular, optical and nuclear physics, is embedded in modern algebraic settings which emphasize the underlying combinatorial aspects. SU(2) recoupling theory, involving Wigner's 3nj symbols, as well as the related problems of their calculations, general properties, asymptotic limits for large entries, nowadays plays a prominent role also in quantum gravity and quantum computing applications. We refer to the ingredients of this theory—and of its extension to other Lie and quantum groups—by using the collective term of 'spin networks'. Recent progress is recorded about the already established connections with the mathematical theory of discrete orthogonal polynomials (the so-called Askey scheme), providing powerful tools based on asymptotic expansions, which correspond on the physical side to various levels of semi-classical limits. These results are useful not only in theoretical molecular physics but also in motivating algorithms for the computationally demanding problems of molecular dynamics and chemical reaction theory, where large angular momenta are typically involved. As for quantum chemistry, applications of these techniques include selection and classification of complete orthogonal basis sets in atomic and molecular problems, either in configuration space (Sturmian orbitals) or in momentum space. In this paper, we list and discuss some aspects of these developments—such as for instance the hyperquantization algorithm—as well as a few applications to quantum gravity and topology, thus providing evidence of a unifying background structure.

What's so Big about Being Small?

ERIC Educational Resources Information Center

Orgill, MaryKay; Crippen, Kent J.

2009-01-01

An interdisciplinary approach to teaching involves leveraging the different perspectives of each discipline to better understand an issue or problem. The most ideal topics for interdisciplinary study are those whose very nature is also interdisciplinary. Nanoscience--which combines biology, chemistry, physics, engineering, and mathematics--is one…

Virtual and concrete manipulatives: a comparison of approaches for solving mathematics problems for students with autism spectrum disorder.

PubMed

Bouck, Emily C; Satsangi, Rajiv; Doughty, Teresa Taber; Courtney, William T

2014-01-01

Students with autism spectrum disorder (ASD) are included in general education classes and expected to participate in general education content, such as mathematics. Yet, little research explores academically-based mathematics instruction for this population. This single subject alternating treatment design study explored the effectiveness of concrete (physical objects that can be manipulated) and virtual (3-D objects from the Internet that can be manipulated) manipulatives to teach single- and double-digit subtraction skills. Participants in this study included three elementary-aged students (ages ranging from 6 to 10) diagnosed with ASD. Students were selected from a clinic-based setting, where all participants received medically necessary intensive services provided via one-to-one, trained therapists. Both forms of manipulatives successfully assisted students in accurately and independently solving subtraction problem. However, all three students demonstrated greater accuracy and faster independence with the virtual manipulatives as compared to the concrete manipulatives. Beyond correctly solving the subtraction problems, students were also able to generalize their learning of subtraction through concrete and virtual manipulatives to more real-world applications.

An algorithm for full parametric solution of problems on the statics of orthotropic plates by the method of boundary states with perturbations

NASA Astrophysics Data System (ADS)

Penkov, V. B.; Ivanychev, D. A.; Novikova, O. S.; Levina, L. V.

2018-03-01

The article substantiates the possibility of building full parametric analytical solutions of mathematical physics problems in arbitrary regions by means of computer systems. The suggested effective means for such solutions is the method of boundary states with perturbations, which aptly incorporates all parameters of an orthotropic medium in a general solution. We performed check calculations of elastic fields of an anisotropic rectangular region (test and calculation problems) for a generalized plane stress state.

Qualitative methods in quantum theory

DOE Office of Scientific and Technical Information (OSTI.GOV)

Migdal, A.B.

The author feels that the solution of most problems in theoretical physics begins with the application of qualitative methods - dimensional estimates and estimates made from simple models, the investigation of limiting cases, the use of the analytic properties of physical quantities, etc. This book proceeds in this spirit, rather than in a formal, mathematical way with no traces of the sweat involved in the original work left to show. The chapters are entitled Dimensional and model approximations, Various types of perturbation theory, The quasi-classical approximation, Analytic properties of physical quantities, Methods in the many-body problem, and Qualitative methods inmore » quantum field theory. Each chapter begins with a detailed introduction, in which the physical meaning of the results obtained in that chapter is explained in a simple way. 61 figures. (RWR)« less

A conceptual physics class where students found meaning in calculations

NASA Astrophysics Data System (ADS)

Hull, Michael M.; Elby, Andrew

2013-01-01

Prior to taking a translated version of the Maryland Open Source Tutorials (OSTs) as a stand-alone course, most students at Tokyo Gakugei University in Japan had experienced physics as memorizing laws and equations to use as computational tools. We might expect this reformed physics class, which emphasizes common sense and conceptual reasoning and rarely invokes equations, to produce students who see a disconnect between equation use and intuitive/conceptual reasoning. Many students at Gakugei, however, somehow learned to integrate mathematics into their "constructivist" epistemologies of physics, even though OSTs do not emphasize this integration. Tadao, for example, came to see that although a common-sense solution to a problem is preferable for explaining to someone who doesn't know physics, solving the problem with a quantitative calculation (that connects to physical meaning) can bring clarity and concreteness to communication between experts. How this integration occurred remains an open question for future research.

Algorithm for Overcoming the Curse of Dimensionality for Certain Non-convex Hamilton-Jacobi Equations, Projections and Differential Games

DTIC Science & Technology

2016-05-01

Algorithm for Overcoming the Curse of Dimensionality for Certain Non-convex Hamilton-Jacobi Equations, Projections and Differential Games Yat Tin...subproblems. Our approach is expected to have wide applications in continuous dynamic games , control theory problems, and elsewhere. Mathematics...differential dynamic games , control theory problems, and dynamical systems coming from the physical world, e.g. [11]. An important application is to

Quantum-like Modeling of Cognition

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei

2015-09-01

This paper begins with a historical review of the mutual influence of physics and psychology, from Freud's invention of psychic energy inspired by von Boltzmann' thermodynamics to the enrichment quantum physics gained from the side of psychology by the notion of complementarity (the invention of Niels Bohr who was inspired by William James), besides we consider the resonance of the correspondence between Wolfgang Pauli and Carl Jung in both physics and psychology. Then we turn to the problem of development of mathematical models for laws of thought starting with Boolean logic and progressing towards foundations of classical probability theory. Interestingly, the laws of classical logic and probability are routinely violated not only by quantum statistical phenomena but by cognitive phenomena as well. This is yet another common feature between quantum physics and psychology. In particular, cognitive data can exhibit a kind of the probabilistic interference effect. This similarity with quantum physics convinced a multi-disciplinary group of scientists (physicists, psychologists, economists, sociologists) to apply the mathematical apparatus of quantum mechanics to modeling of cognition. We illustrate this activity by considering a few concrete phenomena: the order and disjunction effects, recognition of ambiguous figures, categorization-decision making. In Appendix 1 we briefly present essentials of theory of contextual probability and a method of representations of contextual probabilities by complex probability amplitudes (solution of the ``inverse Born's problem'') based on a quantum-like representation algorithm (QLRA).

Geophysics: The Earth in Space. A Guide for High School Students.

ERIC Educational Resources Information Center

American Geophysical Union, Washington, DC.

Geophysics is the application of physics, chemistry, and mathematics to the problems and processes of the earth, from its innermost core to its outermost environs in space. Fields within geophysics include the atmospheric sciences; geodesy; geomagnetism and paleomagnetism; hydrology; oceanography; planetology; seismology; solar-planetary…

Norms and Mathematical Proficiency

ERIC Educational Resources Information Center

Kastberg, Signe E.; Frye, R. Scott

2013-01-01

To challenge students' reasoning and to align with a physical fitness unit that students were studying, teachers and authors, Scott Frye and Signe Kastberg adapted a ratio comparison problem from Susan Lamon, "Ratio and Proportion: Connecting Content and Children's Thinking," (1994) to include athletes and doctors who share…

LASER APPLICATIONS AND OTHER TOPICS IN QUANTUM ELECTRONICS: Methods of computational physics in the problem of mathematical interpretation of laser investigations

NASA Astrophysics Data System (ADS)

Brodyn, M. S.; Starkov, V. N.

2007-07-01

It is shown that in laser experiments performed by using an 'imperfect' setup when instrumental distortions are considerable, sufficiently accurate results can be obtained by the modern methods of computational physics. It is found for the first time that a new instrumental function — the 'cap' function — a 'sister' of a Gaussian curve proved to be demanded namely in laser experiments. A new mathematical model of a measurement path and carefully performed computational experiment show that a light beam transmitted through a mesoporous film has actually a narrower intensity distribution than the detected beam, and the amplitude of the real intensity distribution is twice as large as that for measured intensity distributions.

Transforming a fourth year modern optics course using a deliberate practice framework

NASA Astrophysics Data System (ADS)

Jones, David J.; Madison, Kirk W.; Wieman, Carl E.

2015-12-01

[This paper is part of the Focused Collection on Upper Division Physics Courses.] We present a study of active learning pedagogies in an upper-division physics course. This work was guided by the principle of deliberate practice for the development of expertise, and this principle was used in the design of the materials and the orchestration of the classroom activities of the students. We present our process for efficiently converting a traditional lecture course based on instructor notes into activities for such a course with active learning methods. Ninety percent of the same material was covered and scores on common exam problems showed a 15% improvement with an effect size greater than 1 after the transformation. We observe that the improvement and the associated effect size is sustained after handing off the materials to a second instructor. Because the improvement on exam questions was independent of specific problem topics and because the material tested was so mathematically advanced and broad (including linear algebra, Fourier transforms, partial differential equations, and vector calculus), we expect the transformation process could be applied to most upper-division physics courses having a similar mathematical base.

Lectures on Selected Topics in Mathematical Physics: Elliptic Functions and Elliptic Integrals

NASA Astrophysics Data System (ADS)

Schwalm, William A.

2015-12-01

This volume is a basic introduction to certain aspects of elliptic functions and elliptic integrals. Primarily, the elliptic functions stand out as closed solutions to a class of physical and geometrical problems giving rise to nonlinear differential equations. While these nonlinear equations may not be the types of greatest interest currently, the fact that they are solvable exactly in terms of functions about which much is known makes up for this. The elliptic functions of Jacobi, or equivalently the Weierstrass elliptic functions, inhabit the literature on current problems in condensed matter and statistical physics, on solitons and conformal representations, and all sorts of famous problems in classical mechanics. The lectures on elliptic functions have evolved as part of the first semester of a course on theoretical and mathematical methods given to first- and second-year graduate students in physics and chemistry at the University of North Dakota. They are for graduate students or for researchers who want an elementary introduction to the subject that nevertheless leaves them with enough of the details to address real problems. The style is supposed to be informal. The intention is to introduce the subject as a moderate extension of ordinary trigonometry in which the reference circle is replaced by an ellipse. This entre depends upon fewer tools and has seemed less intimidating that other typical introductions to the subject that depend on some knowledge of complex variables. The first three lectures assume only calculus, including the chain rule and elementary knowledge of differential equations. In the later lectures, the complex analytic properties are introduced naturally so that a more complete study becomes possible.

Remembering Larkin

NASA Astrophysics Data System (ADS)

Varlamov, Andrei

2013-06-01

Knowing Anatoly Ivanovich - Tolya for his friends and colleagues - for years I can't recall him ever writing mathematical expressions on a sheet of paper as he was usually solving problems in his head. Tolya was Homo Sapiens in its true, literal sense of this word. A side observer would hardly notice his mastery and deep understanding of modern methods of theoretical physics and mathematics as there were no piles of paper speckled with math symbols on his desk. But there was a blackboard in his office, all covered with fragments of problems he was discussing with various coauthors. He was famous among his students and coauthors for "falling asleep" in the chair in his office and then writing the solution on the board immediately after awakening...

Numerical simulation of phase transition problems with explicit interface tracking

DOE PAGES

Hu, Yijing; Shi, Qiangqiang; de Almeida, Valmor F.; ...

2015-12-19

Phase change is ubiquitous in nature and industrial processes. Started from the Stefan problem, it is a topic with a long history in applied mathematics and sciences and continues to generate outstanding mathematical problems. For instance, the explicit tracking of the Gibbs dividing surface between phases is still a grand challenge. Our work has been motivated by such challenge and here we report on progress made in solving the governing equations of continuum transport in the presence of a moving interface by the front tracking method. The most pressing issue is the accounting of topological changes suffered by the interfacemore » between phases wherein break up and/or merge takes place. The underlying physics of topological changes require the incorporation of space-time subscales not at reach at the moment. Therefore we use heuristic geometrical arguments to reconnect phases in space. This heuristic approach provides new insight in various applications and it is extensible to include subscale physics and chemistry in the future. We demonstrate the method on applications such as simulating freezing, melting, dissolution, and precipitation. The later examples also include the coupling of the phase transition solution with the Navier-Stokes equations for the effect of flow convection.« less

Special issue on cluster algebras in mathematical physics

NASA Astrophysics Data System (ADS)

Di Francesco, Philippe; Gekhtman, Michael; Kuniba, Atsuo; Yamazaki, Masahito

2013-10-01

This is a call for contributions to a special issue of Journal of Physics A: Mathematical and Theoretical dedicated to cluster algebras in mathematical physics. Over the ten years since their introduction by Fomin and Zelevinsky, the theory of cluster algebras has witnessed a spectacular growth, first and foremost due to the many links that have been discovered with a wide range of subjects in mathematics and, increasingly, theoretical and mathematical physics. The main motivation of this special issue is to gather together reviews, recent developments and open problems, mainly from a mathematical physics viewpoint, into a single comprehensive issue. We expect that such a special issue will become a valuable reference for the broad scientific community working in mathematical and theoretical physics. The issue will consist of invited review articles and contributed papers containing new results on the interplays of cluster algebras with mathematical physics. Editorial policy The Guest Editors for this issue are Philippe Di Francesco, Michael Gekhtman, Atsuo Kuniba and Masahito Yamazaki. The areas and topics for this issue include, but are not limited to: discrete integrable systems arising from cluster mutations cluster structure on Poisson varieties cluster algebras and soliton interactions cluster positivity conjecture Y-systems in the thermodynamic Bethe ansatz and Zamolodchikov's periodicity conjecture T-system of transfer matrices of integrable lattice models dilogarithm identities in conformal field theory wall crossing in 4d N = 2 supersymmetric gauge theories 4d N = 1 quiver gauge theories described by networks scattering amplitudes of 4d N = 4 theories 3d N = 2 gauge theories described by flat connections on 3-manifolds integrability of dimer/Ising models on graphs. All contributions will be refereed and processed according to the usual procedure of the journal. Guidelines for preparation of contributions The deadline for contributed papers is 31 March 2014. This deadline will allow the special issue to appear at the end of 2014. There is no strict regulation on article size, but as a guide the preferable size is 15-30 pages for contributed papers and 40-60 pages for reviews. Further advice on publishing your work in Journal of Physics A may be found at iopscience.iop.org/jphysa. Contributions to the special issue should be submitted by web upload via authors.iop.org/, or by email to jphysa@iop.org, quoting 'JPhysA special issue on cluster algebras in mathematical physics'. Submissions should ideally be in standard LaTeX form. Please see the website for further information on electronic submissions. All contributions should be accompanied by a read-me file or covering letter giving the postal and e-mail addresses for correspondence. The Publishing Office should be notified of any subsequent change of address. The special issue will be published in the print and online versions of the journal.

Find the Dimensions: Students Solving a Tiling Problem

ERIC Educational Resources Information Center

Obara, Samuel

2018-01-01

Students learn mathematics by solving problems. Mathematics textbooks are full of problems, and mathematics teachers use these problems to test students' understanding of mathematical concepts. This paper discusses how problem-solving skills can be fostered with a geometric tiling problem.

What Makes a Problem Mathematically Interesting? Inviting Prospective Teachers to Pose Better Problems

ERIC Educational Resources Information Center

Crespo, Sandra; Sinclair, Nathalie

2008-01-01

School students of all ages, including those who subsequently become teachers, have limited experience posing their own mathematical problems. Yet problem posing, both as an act of mathematical inquiry and of mathematics teaching, is part of the mathematics education reform vision that seeks to promote mathematics as an worthy intellectual…

A new mathematical adjoint for the modified SAAF -SN equations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Schunert, Sebastian; Wang, Yaqi; Martineau, Richard

2015-01-01

We present a new adjoint FEM weak form, which can be directly used for evaluating the mathematical adjoint, suitable for perturbation calculations, of the self-adjoint angular flux SN equations (SAAF -SN) without construction and transposition of the underlying coefficient matrix. Stabilization schemes incorporated in the described SAAF -SN method make the mathematical adjoint distinct from the physical adjoint, i.e. the solution of the continuous adjoint equation with SAAF -SN . This weak form is implemented into RattleSnake, the MOOSE (Multiphysics Object-Oriented Simulation Environment) based transport solver. Numerical results verify the correctness of the implementation and show its utility both formore » fixed source and eigenvalue problems.« less

Dispersive traveling wave solutions of the Equal-Width and Modified Equal-Width equations via mathematical methods and its applications

NASA Astrophysics Data System (ADS)

Lu, Dianchen; Seadawy, Aly R.; Ali, Asghar

2018-06-01

The Equal-Width and Modified Equal-Width equations are used as a model in partial differential equations for the simulation of one-dimensional wave transmission in nonlinear media with dispersion processes. In this article we have employed extend simple equation method and the exp(-varphi(ξ)) expansion method to construct the exact traveling wave solutions of equal width and modified equal width equations. The obtained results are novel and have numerous applications in current areas of research in mathematical physics. It is exposed that our method, with the help of symbolic computation, provides a effective and powerful mathematical tool for solving different kind nonlinear wave problems.

The influence of wind-tunnel walls on discrete frequency noise

NASA Technical Reports Server (NTRS)

Mosher, M.

1984-01-01

This paper describes an analytical model that can be used to examine the effects of wind-tunnel walls on discrete frequency noise. First, a complete physical model of an acoustic source in a wind tunnel is described, and a simplified version is then developed. This simplified model retains the important physical processes involved, yet it is more amenable to analysis. Second, the simplified physical model is formulated as a mathematical problem. An inhomogeneous partial differential equation with mixed boundary conditions is set up and then transformed into an integral equation. The integral equation has been solved with a panel program on a computer. Preliminary results from a simple model problem will be shown and compared with the approximate analytic solution.

PT quantum mechanics.

PubMed

Bender, Carl M; DeKieviet, Maarten; Klevansky, S P

2013-04-28

PT-symmetric quantum mechanics (PTQM) has become a hot area of research and investigation. Since its beginnings in 1998, there have been over 1000 published papers and more than 15 international conferences entirely devoted to this research topic. Originally, PTQM was studied at a highly mathematical level and the techniques of complex variables, asymptotics, differential equations and perturbation theory were used to understand the subtleties associated with the analytic continuation of eigenvalue problems. However, as experiments on PT-symmetric physical systems have been performed, a simple and beautiful physical picture has emerged, and a PT-symmetric system can be understood as one that has a balanced loss and gain. Furthermore, the PT phase transition can now be understood intuitively without resorting to sophisticated mathematics. Research on PTQM is following two different paths: at a fundamental level, physicists are attempting to understand the underlying mathematical structure of these theories with the long-range objective of applying the techniques of PTQM to understanding some of the outstanding problems in physics today, such as the nature of the Higgs particle, the properties of dark matter, the matter-antimatter asymmetry in the universe, neutrino oscillations and the cosmological constant; at an applied level, new kinds of PT-synthetic materials are being developed, and the PT phase transition is being observed in many physical contexts, such as lasers, optical wave guides, microwave cavities, superconducting wires and electronic circuits. The purpose of this Theme Issue is to acquaint the reader with the latest developments in PTQM. The articles in this volume are written in the style of mini-reviews and address diverse areas of the emerging and exciting new area of PT-symmetric quantum mechanics.

The problem of the Grand Unification Theory

NASA Astrophysics Data System (ADS)

Treder, H.-J.

The evolution and fundamental questions of physical theories unifying the gravitational, electromagnetic, and quantum-mechanical interactions are explored, taking Pauli's aphorism as a motto: 'Let no man join what God has cast asunder.' The contributions of Faraday and Riemann, Lorentz, Einstein, and others are discussed, and the criterion of Pauli is applied to Grand Unification Theories (GUT) in general and to those seeking to link gravitation and electromagnetism in particular. Formal mathematical symmetry principles must be shown to have real physical relevance by predicting measurable phenomena not explainable without a GUT; these phenomena must be macroscopic because gravitational effects are to weak to be measured on the microscopic level. It is shown that empirical and theoretical studies of 'gravomagnetism', 'gravoelectricity', or possible links between gravoelectrity and the cosmic baryon assymmetry eventually lead back to basic questions which appear philosophical or purely mathematical but actually challenge physics to seek verifiable answers.

Theoretical Explanations in Mathematical Physics

NASA Astrophysics Data System (ADS)

Rivadulla, Andrés

Many physicists wonder at the usefulness of mathematics in physics. According Madrid to Einstein mathematics is admirably appropriate to the objects of reality. Wigner asserts that mathematics plays an unreasonable important role in physics. James Jeans affirms that God is a mathematician, and that the first aim of physics is to discover the laws of nature, which are written in mathematical language. Dirac suggests that God may have used very advanced mathematics in constructing the universe. And Barrow adheres himself to Wigner's claim about the unreasonable effectiveness of mathematics for the workings of the physical world.

Liquid disinfection using power impulse laser

NASA Astrophysics Data System (ADS)

Gribin, S.; Assaoul, Viktor; Markova, Elena; Gromova, Ludmila P.; Spesivtsev, Boris; Bazanov, V.

1996-05-01

The presented method is based on the bactericidal effect of micro-blast induced by various sources (laser breakdown, electrohydraulic effect...). Using elaborated conception of physical phenomena providing liquid disinfection it is possible to determine optimal conditions of water treatment. The problem of optimization is solved using methods of mathematical modeling and special experiments.

A Novel Interdisciplinary Science Experience for Undergraduates across Introductory Biology, Chemistry, and Physics Courses

ERIC Educational Resources Information Center

Murray, Joelle L.; Atkinson, Elizabeth J. O.; Gilbert, Brian D.; Kruchten, Anne E.

2014-01-01

Successfully creating and implementing interdisciplinary curricula in introductory science, technology, engineering, and mathematics (STEM) courses is challenging, but doing so is increasingly more important as current problems in science become more interdisciplinary. Opening up the silos between science disciplines and overcoming common…

A Transformative Model for Undergraduate Quantitative Biology Education

ERIC Educational Resources Information Center

Usher, David C.; Driscoll, Tobin A.; Dhurjati, Prasad; Pelesko, John A.; Rossi, Louis F.; Schleiniger, Gilberto; Pusecker, Kathleen; White, Harold B.

2010-01-01

The "BIO2010" report recommended that students in the life sciences receive a more rigorous education in mathematics and physical sciences. The University of Delaware approached this problem by (1) developing a bio-calculus section of a standard calculus course, (2) embedding quantitative activities into existing biology courses, and (3)…

Connection of Scattering Principles: A Visual and Mathematical Tour

ERIC Educational Resources Information Center

Broggini, Filippo; Snieder, Roel

2012-01-01

Inverse scattering, Green's function reconstruction, focusing, imaging and the optical theorem are subjects usually studied as separate problems in different research areas. We show a physical connection between the principles because the equations that rule these "scattering principles" have a similar functional form. We first lead the reader…

Computer program determines chemical composition of physical system at equilibrium

NASA Technical Reports Server (NTRS)

Kwong, S. S.

1966-01-01

FORTRAN 4 digital computer program calculates equilibrium composition of complex, multiphase chemical systems. This is a free energy minimization method with solution of the problem reduced to mathematical operations, without concern for the chemistry involved. Also certain thermodynamic properties are determined as byproducts of the main calculations.

Liquid disinfection using power impulse laser

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gribin, S.; Assaoul, V.; Markova, E.

1996-12-31

The presented method is based on the bactericidal effect of micro-blast induced by various sources (laser breakdown, electrohydraulic effect ... ). Using elaborated conception of physical phenomena providing liquid disinfection it is possible to determine optimal conditions of water treatment. The problem of optimization is solved using methods of mathematical modeling and special experiments.

Ground Water Flow No Longer A Mystery

ERIC Educational Resources Information Center

Lehr, Jay H.; Pettyjohn, Wayne A.

1976-01-01

Examined are the physical characteristics of ground water movement. Some potential pollution problems are identified. Models are used to explain mathematical and hydraulic principles of flow toward a pumping well and an effluent stream, flow around and through lenticular beds, and effects of pumping on the water table. (Author/MR)

Fractional phenomenology of cosmic ray anomalous diffusion

NASA Astrophysics Data System (ADS)

Uchaikin, V. V.

2013-11-01

We review the evolution of the cosmic ray diffusion concept from the ordinary (Einstein) model of Brownian motion to the fractional models that appeared in the last decade. The mathematical and physical foundations of these models are discussed, as are their consequences, related problems, and prospects for further development.

Radiative-conductive inverse problem for lumped parameter systems

NASA Astrophysics Data System (ADS)

Alifanov, O. M.; Nenarokomov, A. V.; Gonzalez, V. M.

2008-11-01

The purpose of this paper is to introduce a iterative regularization method in the research of radiative and thermal properties of materials with applications in the design of Thermal Control Systems (TCS) of spacecrafts. In this paper the radiative and thermal properties (emissivity and thermal conductance) of a multilayered thermal-insulating blanket (MLI), which is a screen-vacuum thermal insulation as a part of the (TCS) for perspective spacecrafts, are estimated. Properties of the materials under study are determined in the result of temperature and heat flux measurement data processing based on the solution of the Inverse Heat Transfer Problem (IHTP) technique. Given are physical and mathematical models of heat transfer processes in a specimen of the multilayered thermal-insulating blanket located in the experimental facility. A mathematical formulation of the inverse heat conduction problem is presented too. The practical testing were performed for specimen of the real MLI.

Study of multilayer thermal insulation by inverse problems method

NASA Astrophysics Data System (ADS)

Alifanov, O. M.; Nenarokomov, A. V.; Gonzalez, V. M.

2009-11-01

The purpose of this paper is to introduce a new method in the research of radiative and thermal properties of materials with further applications in the design of thermal control systems (TCS) of spacecrafts. In this paper the radiative and thermal properties (emissivity and thermal conductance) of a multilayered thermal-insulating blanket (MLI), which is a screen-vacuum thermal insulation as a part of the TCS for perspective spacecrafts, are estimated. Properties of the materials under study are determined in the result of temperature and heat flux measurement data processing based on the solution of the inverse heat transfer problem (IHTP) technique. Given are physical and mathematical models of heat transfer processes in a specimen of the multilayered thermal-insulating blanket located in the experimental facility. A mathematical formulation of the inverse heat conduction problem is presented as well. The practical approves were made for specimen of the real MLI.

Some unsolved problems in discrete mathematics and mathematical cybernetics

NASA Astrophysics Data System (ADS)

Korshunov, Aleksei D.

2009-10-01

There are many unsolved problems in discrete mathematics and mathematical cybernetics. Writing a comprehensive survey of such problems involves great difficulties. First, such problems are rather numerous and varied. Second, they greatly differ from each other in degree of completeness of their solution. Therefore, even a comprehensive survey should not attempt to cover the whole variety of such problems; only the most important and significant problems should be reviewed. An impersonal choice of problems to include is quite hard. This paper includes 13 unsolved problems related to combinatorial mathematics and computational complexity theory. The problems selected give an indication of the author's studies for 50 years; for this reason, the choice of the problems reviewed here is, to some extent, subjective. At the same time, these problems are very difficult and quite important for discrete mathematics and mathematical cybernetics. Bibliography: 74 items.

Use of altimetry data in a sampling-function approach to the geoid

NASA Technical Reports Server (NTRS)

Lundquist, C. A.; Giacaglia, G. E. O.

1972-01-01

Problems associated with using an altimetry sampling function approach to the geoid are examined. They include: (1) conventent mathematical representation of short-wavelength (eventually approximately 1 deg) features of the geoid or geopotential, (2) utilization of detailed data from only part of the globe (i.e., the oceans) (3) application of appropriate formalism to relate the sea-level equipotential below the atmospheric mass to the external potential above the atmosphere, (4) mathematical applicability of an adopted geopotential representation on the surface of the physical geoid.

On laminar and turbulent friction

NASA Technical Reports Server (NTRS)

Von Karman, TH

1946-01-01

Report deals, first with the theory of the laminar friction flow, where the basic concepts of Prandtl's boundary layer theory are represented from mathematical and physical points of view, and a method is indicated by means of which even more complicated cases can be treated with simple mathematical means, at least approximately. An attempt is also made to secure a basis for the computation of the turbulent friction by means of formulas through which the empirical laws of the turbulent pipe resistance can be applied to other problems on friction drag. (author)

Phenomenological and mechanics aspects of nondestructive evaluation and characterization by sound and ultrasound of material and fracture properties

NASA Technical Reports Server (NTRS)

Fu, L. S. W.

1982-01-01

Developments in fracture mechanics and elastic wave theory enhance the understanding of many physical phenomena in a mathematical context. Available literature in the material, and fracture characterization by NDT, and the related mathematical methods in mechanics that provide fundamental underlying principles for its interpretation and evaluation are reviewed. Information on the energy release mechanism of defects and the interaction of microstructures within the material is basic in the formulation of the mechanics problems that supply guidance for nondestructive evaluation (NDE).

Self-similar seismogenic structure of the crust: A review of the problem and a mathematical model

NASA Astrophysics Data System (ADS)

Stakhovsky, I. R.

2007-12-01

The paper presents a brief review of studies of the structural organization of a seismogenic medium showing that the crust of seismically active regions possesses a fractal structure. A new mathematical model of the self-similar seismogenic structure (SSS) of the crust generalizing the reviewed publications is proposed on the basis of the scaling correspondence between the fault, seismic, and seismic energy multifractal fields of the crust. Multifractal fields of other physical origin can also be incorporated in the SSS model.

A Posteriori Error Analysis and Uncertainty Quantification for Adaptive Multiscale Operator Decomposition Methods for Multiphysics Problems

DTIC Science & Technology

2013-06-24

Barrier methods for critical exponent problems in geometric analysis and mathematical physics, J. Erway and M. Hoist, Submitted for publication . • Finite...1996. [20] C. LANCZOS, Linear Differential Operators, Dover Publications , Mineola, NY, 1997. [21] G.I. MARCHUK, Adjoint Equations and Analysis of...NUMBER(S) 16. SECURITY CLASSIFICATION OF: 19b. TELEPHONE NUMBER (Include area code) The public reporting burden for this collection of information is

The quest for a new modelling framework in mathematical biology. Comment on "On the interplay between mathematics and biology: Hallmarks towards a new systems biology" by N. Bellomo et al.

NASA Astrophysics Data System (ADS)

Eftimie, Raluca

2015-03-01

One of the main unsolved problems of modern physics is finding a "theory of everything" - a theory that can explain, with the help of mathematics, all physical aspects of the universe. While the laws of physics could explain some aspects of the biology of living systems (e.g., the phenomenological interpretation of movement of cells and animals), there are other aspects specific to biology that cannot be captured by physics models. For example, it is generally accepted that the evolution of a cell-based system is influenced by the activation state of cells (e.g., only activated and functional immune cells can fight diseases); on the other hand, the evolution of an animal-based system can be influenced by the psychological state (e.g., distress) of animals. Therefore, the last 10-20 years have seen also a quest for a "theory of everything"-approach extended to biology, with researchers trying to propose mathematical modelling frameworks that can explain various biological phenomena ranging from ecology to developmental biology and medicine [1,2,6]. The basic idea behind this approach can be found in a few reviews on ecology and cell biology [6,7,9-11], where researchers suggested that due to the parallel between the micro-scale dynamics and the emerging macro-scale phenomena in both cell biology and in ecology, many mathematical methods used for ecological processes could be adapted to cancer modelling [7,9] or to modelling in immunology [11]. However, this approach generally involved the use of different models to describe different biological aspects (e.g., models for cell and animal movement, models for competition between cells or animals, etc.).

The Gibbs paradox and the physical criteria for indistinguishability of identical particles

NASA Astrophysics Data System (ADS)

Unnikrishnan, C. S.

2016-08-01

Gibbs paradox in the context of statistical mechanics addresses the issue of additivity of entropy of mixing gases. The usual discussion attributes the paradoxical situation to classical distinguishability of identical particles and credits quantum theory for enabling indistinguishability of identical particles to solve the problem. We argue that indistinguishability of identical particles is already a feature in classical mechanics and this is clearly brought out when the problem is treated in the language of information and associated entropy. We pinpoint the physical criteria for indistinguishability that is crucial for the treatment of the Gibbs’ problem and the consistency of its solution with conventional thermodynamics. Quantum mechanics provides a quantitative criterion, not possible in the classical picture, for the degree of indistinguishability in terms of visibility of quantum interference, or overlap of the states as pointed out by von Neumann, thereby endowing the entropy expression with mathematical continuity and physical reasonableness.

Additional Crime Scenes for Projectile Motion Unit

NASA Astrophysics Data System (ADS)

Fullerton, Dan; Bonner, David

2011-12-01

Building students' ability to transfer physics fundamentals to real-world applications establishes a deeper understanding of underlying concepts while enhancing student interest. Forensic science offers a great opportunity for students to apply physics to highly engaging, real-world contexts. Integrating these opportunities into inquiry-based problem solving in a team environment provides a terrific backdrop for fostering communication, analysis, and critical thinking skills. One such activity, inspired jointly by the museum exhibit "CSI: The Experience"2 and David Bonner's TPT article "Increasing Student Engagement and Enthusiasm: A Projectile Motion Crime Scene,"3 provides students with three different crime scenes, each requiring an analysis of projectile motion. In this lesson students socially engage in higher-order analysis of two-dimensional projectile motion problems by collecting information from 3-D scale models and collaborating with one another on its interpretation, in addition to diagramming and mathematical analysis typical to problem solving in physics.

From action to abstraction: Using the hands to learn math

PubMed Central

Novack, Miriam A.; Congdon, Eliza L.; Hemani-Lopez, Naureen; Goldin-Meadow, Susan

2014-01-01

Previous research has shown that children benefit from gesturing during math instruction. Here we ask whether gesturing promotes learning because it is itself a physical action, or because it uses physical action to represent abstract ideas. To address this question, we taught third-grade children a strategy for solving mathematical equivalence problems that was instantiated in one of three ways: (1) in the physical action children performed on objects, (2) in a concrete gesture miming that action, or (3) in an abstract gesture. All three types of hand movements helped children learn how to solve the problems on which they were trained. However, only gesture led to success on problems that required generalizing the knowledge gained. The results provide the first evidence that gesture promotes transfer of knowledge better than action, and suggest that the beneficial effects gesture has on learning may reside in the features that differentiate it from action. PMID:24503873

The Circle of Apollonius and Its Applications in Introductory Physics

NASA Astrophysics Data System (ADS)

Partensky, Michael B.

2008-02-01

The circle of Apollonius is named after the ancient geometrician Apollonius of Perga. This beautiful geometric construct can be helpful when solving some general problems of geometry and mathematical physics, optics, and electricity. Here we discuss two of its applications: localizing an object in space and calculating electric fields. First, we pose an entertaining localization problem to trigger students' interest in the subject. Analyzing this problem, we introduce the circle of Apollonius and show that this geometric technique helps solve the problem in an elegant and intuitive manner. Then we switch to seemingly unrelated problems of calculating the electric fields. We show that the zero equipotential line for two unlike charges is the Apollonius circle for these two charges and use this discovery to find the electric field of a charge positioned near a grounded conductive sphere. Finally, we pose some questions for further examination.

77 FR 17102 - Advisory Committee for Mathematical and Physical Sciences

Federal Register 2010, 2011, 2012, 2013, 2014

2012-03-23

... NATIONAL SCIENCE FOUNDATION Advisory Committee for Mathematical and Physical Sciences Correction... meeting information is as follows: Name: Directorate for Mathematical and Physical Sciences Advisory... Person: Dr. Morris L. Aizenman, Senior Science Associate, Directorate for Mathematical and Physical...

The problem-solving approach in the teaching of number theory

NASA Astrophysics Data System (ADS)

Toh, Pee Choon; Hoong Leong, Yew; Toh, Tin Lam; Dindyal, Jaguthsing; Quek, Khiok Seng; Guan Tay, Eng; Him Ho, Foo

2014-02-01

Mathematical problem solving is the mainstay of the mathematics curriculum for Singapore schools. In the preparation of prospective mathematics teachers, the authors, who are mathematics teacher educators, deem it important that pre-service mathematics teachers experience non-routine problem solving and acquire an attitude that predisposes them to adopt a Pólya-style approach in learning mathematics. The Practical Worksheet is an instructional scaffold we adopted to help our pre-service mathematics teachers develop problem-solving dispositions alongside the learning of the subject matter. The Worksheet was initially used in a design experiment aimed at teaching problem solving in a secondary school. In this paper, we describe an application and adaptation of the MProSE (Mathematical Problem Solving for Everyone) design experiment to a university level number theory course for pre-service mathematics teachers. The goal of the enterprise was to help the pre-service mathematics teachers develop problem-solving dispositions alongside the learning of the subject matter. Our analysis of the pre-service mathematics teachers' work shows that the MProSE design holds promise for mathematics courses at the tertiary level.

Determination of the Geometric Form of a Plane of a Tectonic Gap as the Inverse III-posed Problem of Mathematical Physics

NASA Astrophysics Data System (ADS)

Sirota, Dmitry; Ivanov, Vadim

2017-11-01

Any mining operations influence stability of natural and technogenic massifs are the reason of emergence of the sources of differences of mechanical tension. These sources generate a quasistationary electric field with a Newtonian potential. The paper reviews the method of determining the shape and size of a flat source field with this kind of potential. This common problem meets in many fields of mining: geological exploration mineral resources, ore deposits, control of mining by underground method, determining coal self-heating source, localization of the rock crack's sources and other applied problems of practical physics. This problems are ill-posed and inverse and solved by converting to Fredholm-Uryson integral equation of the first kind. This equation will be solved by A.N. Tikhonov regularization method.

The Cauchy problem for the Pavlov equation

NASA Astrophysics Data System (ADS)

Grinevich, P. G.; Santini, P. M.; Wu, D.

2015-10-01

Commutation of multidimensional vector fields leads to integrable nonlinear dispersionless PDEs that arise in various problems of mathematical physics and have been intensively studied in recent literature. This report aims to solve the scattering and inverse scattering problem for integrable dispersionless PDEs, recently introduced just at a formal level, concentrating on the prototypical example of the Pavlov equation, and to justify an existence theorem for global bounded solutions of the associated Cauchy problem with small data. An essential part of this work was made during the visit of the three authors to the Centro Internacional de Ciencias in Cuernavaca, Mexico in November-December 2012.

Problem Solving: How Do In-Service Secondary School Teachers of Mathematics Make Sense of a Non-Routine Problem Context?

ERIC Educational Resources Information Center

Mwei, Philip K.

2017-01-01

The concept of mathematical problem solving is an important mathematical process in mathematics curricula of education systems worldwide. These math curricula demand that learners are exposed to authentic problems that foster successful problem solving. To attain this very important goal, there must be mathematics teachers well versed in content…

Evaluating the Suitability of Mathematical Thinking Problems for Senior High-School Students by Including Mathematical Sense Making and Global Planning

ERIC Educational Resources Information Center

van Velzen, Joke H.

2016-01-01

The mathematics curriculum often provides for relatively few mathematical thinking problems or non-routine problems that focus on a deepening of understanding mathematical concepts and the problem-solving process. To develop such problems, methods are required to evaluate their suitability. The purpose of this preliminary study was to find such an…

Students’ Mathematical Problem-Solving Abilities Through The Application of Learning Models Problem Based Learning

NASA Astrophysics Data System (ADS)

Nasution, M. L.; Yerizon, Y.; Gusmiyanti, R.

2018-04-01

One of the purpose mathematic learning is to develop problem solving abilities. Problem solving is obtained through experience in questioning non-routine. Improving students’ mathematical problem-solving abilities required an appropriate strategy in learning activities one of them is models problem based learning (PBL). Thus, the purpose of this research is to determine whether the problem solving abilities of mathematical students’ who learn to use PBL better than on the ability of students’ mathematical problem solving by applying conventional learning. This research included quasi experiment with static group design and population is students class XI MIA SMAN 1 Lubuk Alung. Class experiment in the class XI MIA 5 and class control in the class XI MIA 6. The instrument of final test students’ mathematical problem solving used essay form. The result of data final test in analyzed with t-test. The result is students’ mathematical problem solving abilities with PBL better then on the ability of students’ mathematical problem solving by applying conventional learning. It’s seen from the high percentage achieved by the group of students who learn to use PBL for each indicator of students’ mathematical problem solving.

Mathematical Modeling Is Also Physics--Interdisciplinary Teaching between Mathematics and Physics in Danish Upper Secondary Education

ERIC Educational Resources Information Center

Michelsen, Claus

2015-01-01

Mathematics plays a crucial role in physics. This role is brought about predominantly through the building, employment, and assessment of mathematical models, and teachers and educators should capture this relationship in the classroom in an effort to improve students' achievement and attitude in both physics and mathematics. But although there…

Physics of the Mind.

PubMed

Perlovsky, Leonid I

2016-01-01

Is it possible to turn psychology into "hard science"? Physics of the mind follows the fundamental methodology of physics in all areas where physics have been developed. What is common among Newtonian mechanics, statistical physics, quantum physics, thermodynamics, theory of relativity, astrophysics… and a theory of superstrings? The common among all areas of physics is a methodology of physics discussed in the first few lines of the paper. Is physics of the mind possible? Is it possible to describe the mind based on the few first principles as physics does? The mind with its variabilities and uncertainties, the mind from perception and elementary cognition to emotions and abstract ideas, to high cognition. Is it possible to turn psychology and neuroscience into "hard" sciences? The paper discusses established first principles of the mind, their mathematical formulations, and a mathematical model of the mind derived from these first principles, mechanisms of concepts, emotions, instincts, behavior, language, cognition, intuitions, conscious and unconscious, abilities for symbols, functions of the beautiful and musical emotions in cognition and evolution. Some of the theoretical predictions have been experimentally confirmed. This research won national and international awards. In addition to summarizing existing results the paper describes new development theoretical and experimental. The paper discusses unsolved theoretical problems as well as experimental challenges for future research.

Physics of the Mind

PubMed Central

Perlovsky, Leonid I.

2016-01-01

Is it possible to turn psychology into “hard science”? Physics of the mind follows the fundamental methodology of physics in all areas where physics have been developed. What is common among Newtonian mechanics, statistical physics, quantum physics, thermodynamics, theory of relativity, astrophysics… and a theory of superstrings? The common among all areas of physics is a methodology of physics discussed in the first few lines of the paper. Is physics of the mind possible? Is it possible to describe the mind based on the few first principles as physics does? The mind with its variabilities and uncertainties, the mind from perception and elementary cognition to emotions and abstract ideas, to high cognition. Is it possible to turn psychology and neuroscience into “hard” sciences? The paper discusses established first principles of the mind, their mathematical formulations, and a mathematical model of the mind derived from these first principles, mechanisms of concepts, emotions, instincts, behavior, language, cognition, intuitions, conscious and unconscious, abilities for symbols, functions of the beautiful and musical emotions in cognition and evolution. Some of the theoretical predictions have been experimentally confirmed. This research won national and international awards. In addition to summarizing existing results the paper describes new development theoretical and experimental. The paper discusses unsolved theoretical problems as well as experimental challenges for future research. PMID:27895558

Current Results and Proposed Activities in Microgravity Fluid Dynamics

NASA Technical Reports Server (NTRS)

Polezhaev, V. I.

1996-01-01

The Institute for Problems in Mechanics' Laboratory work in mathematical and physical modelling of fluid mechanics develops models, methods, and software for analysis of fluid flow, instability analysis, direct numerical modelling and semi-empirical models of turbulence, as well as experimental research and verification of these models and their applications in technological fluid dynamics, microgravity fluid mechanics, geophysics, and a number of engineering problems. This paper presents an overview of the results in microgravity fluid dynamics research during the last two years. Nonlinear problems of weakly compressible and compressible fluid flows are discussed.

Conference on Non-linear Phenomena in Mathematical Physics: Dedicated to Cathleen Synge Morawetz on her 85th Birthday. The Fields Institute, Toronto, Canada September 18-20, 2008. Sponsors: Association for Women in Mathematics, Inc. and The Fields Institute

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lewis, Jennifer

2012-10-15

This scientific meeting focused on the legacy of Cathleen S. Morawetz and the impact that her scientific work on transonic flow and the non-linear wave equation has had in recent progress on different aspects of analysis for non-linear wave, kinetic and quantum transport problems associated to mathematical physics. These are areas where the elements of continuum, statistical and stochastic mechanics, and their interplay, have counterparts in the theory of existence, uniqueness and stability of the associated systems of equations and geometric constraints. It was a central event for the applied and computational analysis community focusing on Partial Differential Equations. Themore » goal of the proposal was to honor Cathleen Morawetz, a highly successful woman in mathematics, while encouraging beginning researchers. The conference was successful in show casing the work of successful women, enhancing the visibility of women in the profession and providing role models for those just beginning their careers. The two-day conference included seven 45-minute lectures and one day of six 45-minute lectures, and a poster session for junior participants. The conference program included 19 distinguished speakers, 10 poster presentations, about 70 junior and senior participants and, of course, the participation of Cathleen Synge Morawetz. The conference celebrated Morawetz's paramount contributions to the theory of non-linear equations in gas dynamics and their impact in the current trends of nonlinear phenomena in mathematical physics, but also served as an awareness session of current women's contribution to mathematics.« less

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2012-07-20

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Solutions for Dynamic Variants of Eshelby's Inclusion Problem

NASA Astrophysics Data System (ADS)

Michelitsch, Thomas M.; Askes, Harm; Wang, Jizeng; Levin, Valery M.

The dynamic variant of Eshelby's inclusion problem plays a crucial role in many areas of mechanics and theoretical physics. Because of its mathematical complexity, dynamic variants of the inclusion problems so far are only little touched. In this paper we derive solutions for dynamic variants of the Eshelby inclusion problem for arbitrary scalar source densities of the eigenstrain. We study a series of examples of Eshelby problems which are of interest for applications in materials sciences, such as for instance cubic and prismatic inclusions. The method which covers both the time and frequency domain is especially useful for dynamically transforming inclusions of any shape.

The Music of Mathematics: Toward a New Problem Typology

NASA Astrophysics Data System (ADS)

Quarfoot, David

Halmos (1980) once described problems and their solutions as "the heart of mathematics". Following this line of thinking, one might naturally ask: "What, then, is the heart of problems?". In this work, I attempt to answer this question using techniques from statistics, information visualization, and machine learning. I begin the journey by cataloging the features of problems delineated by the mathematics and mathematics education communities. These dimensions are explored in a large data set of students working thousands of problems at the Art of Problem Solving, an online company that provides adaptive mathematical training for students around the world. This analysis is able to concretely show how the fabric of mathematical problems changes across different subjects, difficulty levels, and students. Furthermore, it locates problems that stand out in the crowd -- those that synergize cognitive engagement, learning, and difficulty. This quantitatively-heavy side of the dissertation is partnered with a qualitatively-inspired portion that involves human scoring of 105 problems and their solutions. In this setting, I am able to capture elusive features of mathematical problems and derive a fuller picture of the space of mathematical problems. Using correlation matrices, principal components analysis, and clustering techniques, I explore the relationships among those features frequently discussed in mathematics problems (e.g., difficulty, creativity, novelty, affective engagement, authenticity). Along the way, I define a new set of uncorrelated features in problems and use these as the basis for a New Mathematical Problem Typology (NMPT). Grounded in the terminology of classical music, the NMPT works to quickly convey the essence and value of a problem, just as terms like "etude" and "mazurka" do for musicians. Taken together, these quantitative and qualitative analyses seek to terraform the landscape of mathematical problems and, concomitantly, the current thinking about that world. Most importantly, this work highlights and names the panoply of problems that exist, expanding the myopic vision of contemporary mathematical problem solving.

Mapping university students' epistemic framing of computational physics using network analysis

NASA Astrophysics Data System (ADS)

Bodin, Madelen

2012-06-01

Solving physics problem in university physics education using a computational approach requires knowledge and skills in several domains, for example, physics, mathematics, programming, and modeling. These competences are in turn related to students’ beliefs about the domains as well as about learning. These knowledge and beliefs components are referred to here as epistemic elements, which together represent the students’ epistemic framing of the situation. The purpose of this study was to investigate university physics students’ epistemic framing when solving and visualizing a physics problem using a particle-spring model system. Students’ epistemic framings are analyzed before and after the task using a network analysis approach on interview transcripts, producing visual representations as epistemic networks. The results show that students change their epistemic framing from a modeling task, with expectancies about learning programming, to a physics task, in which they are challenged to use physics principles and conservation laws in order to troubleshoot and understand their simulations. This implies that the task, even though it is not introducing any new physics, helps the students to develop a more coherent view of the importance of using physics principles in problem solving. The network analysis method used in this study is shown to give intelligible representations of the students’ epistemic framing and is proposed as a useful method of analysis of textual data.

Will the digital computer transform classical mathematics?

PubMed

Rotman, Brian

2003-08-15

Mathematics and machines have influenced each other for millennia. The advent of the digital computer introduced a powerfully new element that promises to transform the relation between them. This paper outlines the thesis that the effect of the digital computer on mathematics, already widespread, is likely to be radical and far-reaching. To articulate this claim, an abstract model of doing mathematics is introduced based on a triad of actors of which one, the 'agent', corresponds to the function performed by the computer. The model is used to frame two sorts of transformation. The first is pragmatic and involves the alterations and progressive colonization of the content and methods of enquiry of various mathematical fields brought about by digital methods. The second is conceptual and concerns a fundamental antagonism between the infinity enshrined in classical mathematics and physics (continuity, real numbers, asymptotic definitions) and the inherently real and material limit of processes associated with digital computation. An example which lies in the intersection of classical mathematics and computer science, the P=NP problem, is analysed in the light of this latter issue.

Mathematization in introductory physics

NASA Astrophysics Data System (ADS)

Brahmia, Suzanne M.

Mathematization is central to STEM disciplines as a cornerstone of the quantitative reasoning that characterizes these fields. Introductory physics is required for most STEM majors in part so that students develop expert-like mathematization. This dissertation describes coordinated research and curriculum development for strengthening mathematization in introductory physics; it blends scholarship in physics and mathematics education in the form of three papers. The first paper explores mathematization in the context of physics, and makes an original contribution to the measurement of physics students' struggle to mathematize. Instructors naturally assume students have a conceptual mastery of algebra before embarking on a college physics course because these students are enrolled in math courses beyond algebra. This paper provides evidence that refutes the validity of this assumption and categorizes some of the barriers students commonly encounter with quantification and representing ideas symbolically. The second paper develops a model of instruction that can help students progress from their starting points to their instructor's desired endpoints. Instructors recognize that the introductory physics course introduces new ideas at an astonishing rate. More than most physicists realize, however, the way that mathematics is used in the course is foreign to a large portion of class. This paper puts forth an instructional model that can move all students toward better quantitative and physical reasoning, despite the substantial variability of those students' initial states. The third paper describes the design and testing of curricular materials that foster mathematical creativity to prepare students to better understand physics reasoning. Few students enter introductory physics with experience generating equations in response to specific challenges involving unfamiliar quantities and units, yet this generative use of mathematics is typical of the thinking involved in doing physics. It contrasts with their more common experience with mathematics as the practice of specified procedures to improve efficiency. This paper describes new curricular materials based on invention instruction provide students with opportunities to generate mathematical relationships in physics, and the paper presents preliminary evidence of the effectiveness of this method with mathematically underprepared engineering students.

On the possibility of control restoration in some inverse problems of heat and mass transfer

NASA Astrophysics Data System (ADS)

Bilchenko, G. G.; Bilchenko, N. G.

2016-11-01

The hypersonic aircraft permeable surfaces effective heat protection problems are considered. The physic-chemical processes (the dissociation and the ionization) in laminar boundary layer of compressible gas are appreciated in mathematical model. The statements of direct problems of heat and mass transfer are given: according to preset given controls it is necessary to compute the boundary layer mathematical model parameters and determinate the local and total heat flows and friction forces and the power of blowing system. The A.A.Dorodnicyn's generalized integral relations method has been used as calculation basis. The optimal control - the blowing into boundary layer (for continuous functions) was constructed as the solution of direct problem in extreme statement with the use of this approach. The statement of inverse problems are given: the control laws ensuring the preset given local heat flow and local tangent friction are restored. The differences between the interpolation and the approximation statements are discussed. The possibility of unique control restoration is established and proved (in the stagnation point). The computational experiments results are presented.

Mathematics applied to the climate system: outstanding challenges and recent progress

PubMed Central

Williams, Paul D.; Cullen, Michael J. P.; Davey, Michael K.; Huthnance, John M.

2013-01-01

The societal need for reliable climate predictions and a proper assessment of their uncertainties is pressing. Uncertainties arise not only from initial conditions and forcing scenarios, but also from model formulation. Here, we identify and document three broad classes of problems, each representing what we regard to be an outstanding challenge in the area of mathematics applied to the climate system. First, there is the problem of the development and evaluation of simple physically based models of the global climate. Second, there is the problem of the development and evaluation of the components of complex models such as general circulation models. Third, there is the problem of the development and evaluation of appropriate statistical frameworks. We discuss these problems in turn, emphasizing the recent progress made by the papers presented in this Theme Issue. Many pressing challenges in climate science require closer collaboration between climate scientists, mathematicians and statisticians. We hope the papers contained in this Theme Issue will act as inspiration for such collaborations and for setting future research directions. PMID:23588054

Epistemic game for answer making in learning about hydrostatics

NASA Astrophysics Data System (ADS)

Chen, Ying; Irving, Paul W.; Sayre, Eleanor C.

2013-06-01

Previous research into problem solving in physics resulted in researchers introducing six epistemic games to describe the organizational structures of locally coherent resources. We present a new epistemic game—the “answer-making epistemic game”—which was identified in this paper through the analysis of interviews carried out to validate a survey focusing on students’ understanding of Archimedes’ principle and Pascal’s law. In the game, the ultimate goal is a solution to a problem posed by the survey. Students may remember or intuit an answer, then use conceptual and/or mathematical reasoning to justify it. Alternately, they may use conceptual and/or mathematical reasoning to generate an answer. We demonstrate how students generate their solutions using these two different paths and discuss some implications for instruction.

Challenges in designing appropriate scaffolding to improve students' representational consistency: The case of a Gauss's law problem

NASA Astrophysics Data System (ADS)

Maries, Alexandru; Lin, Shih-Yin; Singh, Chandralekha

2017-12-01

Prior research suggests that introductory physics students have difficulty with graphing and interpreting graphs. Here, we discuss an investigation of student difficulties in translating between mathematical and graphical representations for a problem in electrostatics and the effect of increasing levels of scaffolding on students' representational consistency. Students in calculus-based introductory physics were given a typical problem that can be solved using Gauss's law involving a spherically symmetric charge distribution in which they were asked to write a mathematical expression for the electric field in various regions and then plot the electric field. In study 1, we found that students had great difficulty in plotting the electric field as a function of the distance from the center of the sphere consistent with the mathematical expressions in various regions, and interviews with students suggested possible reasons which may account for this difficulty. Therefore, in study 2, we designed two scaffolding interventions with levels of support which built on each other (i.e., the second scaffolding level built on the first) in order to help students plot their expressions consistently and compared the performance of students provided with scaffolding with a comparison group which was not given any scaffolding support. Analysis of student performance with different levels of scaffolding reveals that scaffolding from an expert perspective beyond a certain level may sometimes hinder student performance and students may not even discern the relevance of the additional support. We provide possible interpretations for these findings based on in-depth, think-aloud student interviews.

Method for the simulation of blood platelet shape and its evolution during activation

PubMed Central

Muliukov, Artem R.; Litvinenko, Alena L.; Nekrasov, Vyacheslav M.; Chernyshev, Andrei V.; Maltsev, Valeri P.

2018-01-01

We present a simple physically based quantitative model of blood platelet shape and its evolution during agonist-induced activation. The model is based on the consideration of two major cytoskeletal elements: the marginal band of microtubules and the submembrane cortex. Mathematically, we consider the problem of minimization of surface area constrained to confine the marginal band and a certain cellular volume. For resting platelets, the marginal band appears as a peripheral ring, allowing for the analytical solution of the minimization problem. Upon activation, the marginal band coils out of plane and forms 3D convoluted structure. We show that its shape is well approximated by an overcurved circle, a mathematical concept of closed curve with constant excessive curvature. Possible mechanisms leading to such marginal band coiling are discussed, resulting in simple parametric expression for the marginal band shape during platelet activation. The excessive curvature of marginal band is a convenient state variable which tracks the progress of activation. The cell surface is determined using numerical optimization. The shapes are strictly mathematically defined by only three parameters and show good agreement with literature data. They can be utilized in simulation of platelets interaction with different physical fields, e.g. for the description of hydrodynamic and mechanical properties of platelets, leading to better understanding of platelets margination and adhesion and thrombus formation in blood flow. It would also facilitate precise characterization of platelets in clinical diagnosis, where a novel optical model is needed for the correct solution of inverse light-scattering problem. PMID:29518073

The metamorphoses of relativity

NASA Astrophysics Data System (ADS)

Staley, Richard

This talk will explore the ways that problems shifted and disciplinary boundaries changed around physicists' engagement with relational physics and relativistic thought, first in research dealing with physiology, psychology and geometry in the late nineteenth century and then (a better-known story) moving between physics, mathematics and geometry in the twentieth century. I hope to develop a richer approach for understanding the disciplinary and political significance of relativity, especially by considering in one framework the work of Engels, Mach, Einstein and Planck.

Make your trappings count: The mathematics of pest insect monitoring. Comment on “Multiscale approach to pest insect monitoring: Random walks, pattern formation, synchronization, and networks” by Petrovskii et al.

NASA Astrophysics Data System (ADS)

Blasius, Bernd

2014-09-01

Since the beginnings of agriculture the production of crops is characterized by an ongoing battle between farmers and pests [1]. Already during biblical times swarms of the desert locust, Schistocerca gregaria, were known as major pest that can devour a field of corn within an hour. Even today, harmful organisms have the potential to threaten food production worldwide. It is estimated that about 37% of all potential crops are destroyed by pests. Harmful insects alone destroy 13%, causing financial losses in the agricultural industry of millions of dollars each year [2-4]. These numbers emphasize the importance of pest insect monitoring as a crucial step of integrated pest management [1]. The main approach to gain information about infestation levels is based on trapping, which leads to the question of how to extrapolate the sparse population counts at singularly disposed traps to a spatial representation of the pest species distribution. In their review Petrovskii et al. provide a mathematical framework to tackle this problem [5]. Their analysis reveals that this seemingly inconspicuous problem gives rise to surprisingly deep mathematical challenges that touch several modern contemporary concepts of statistical physics and complex systems theory. The review does not aim for a collection of numerical recipes to support crop growers in the analysis of their trapping data. Instead the review identifies the relevant biological and physical processes that are involved in pest insect monitoring and it presents the mathematical techniques that are required to capture these processes.

Mind map learning for advanced engineering study: case study in system dynamics

NASA Astrophysics Data System (ADS)

Woradechjumroen, Denchai

2018-01-01

System Dynamics (SD) is one of the subjects that were use in learning Automatic Control Systems in dynamic and control field. Mathematical modelling and solving skills of students for engineering systems are expecting outcomes of the course which can be further used to efficiently study control systems and mechanical vibration; however, the fundamental of the SD includes strong backgrounds in Dynamics and Differential Equations, which are appropriate to the students in governmental universities that have strong skills in Mathematics and Scientifics. For private universities, students are weak in the above subjects since they obtained high vocational certificate from Technical College or Polytechnic School, which emphasize the learning contents in practice. To enhance their learning for improving their backgrounds, this paper applies mind maps based problem based learning to relate the essential relations of mathematical and physical equations. With the advantages of mind maps, each student is assigned to design individual mind maps for self-leaning development after they attend the class and learn overall picture of each chapter from the class instructor. Four problems based mind maps learning are assigned to each student. Each assignment is evaluated via mid-term and final examinations, which are issued in terms of learning concepts and applications. In the method testing, thirty students are tested and evaluated via student learning backgrounds in the past. The result shows that well-design mind maps can improve learning performance based on outcome evaluation. Especially, mind maps can reduce time-consuming and reviewing for Mathematics and Physics in SD significantly.

Problem Posing with the Multiplication Table

ERIC Educational Resources Information Center

Dickman, Benjamin

2014-01-01

Mathematical problem posing is an important skill for teachers of mathematics, and relates readily to mathematical creativity. This article gives a bit of background information on mathematical problem posing, lists further references to connect problem posing and creativity, and then provides 20 problems based on the multiplication table to be…

Use of the Moodle Platform to Promote an Ongoing Learning When Lecturing General Physics in the Physics, Mathematics and Electronic Engineering Programmes at the University of the Basque Country UPV/EHU

NASA Astrophysics Data System (ADS)

López, Gabriel A.; Sáenz, Jon; Leonardo, Aritz; Gurtubay, Idoia G.

2016-08-01

The Moodle platform has been used to put into practice an ongoing evaluation of the students' Physics learning process. The evaluation has been done on the frame of the course General Physics, which is lectured during the first year of the Physics, Mathematics and Electronic Engineering Programmes at the Faculty of Science and Technology of the University of the Basque Country (UPV/EHU). A test bank with more than 1000 multiple-choice questions, including conceptual and numerical problems, has been prepared. Throughout the course, the students have to answer a 10-question multiple-choice test for every one of the blocks the course is divided in and which were previously treated and worked in the theoretical lectures and problem-solving sessions. The tests are automatically corrected by Moodle, and under certain criteria, the corresponding mark is taken into account for the final mark of the course. According to the results obtained from a statistical study of the data on the student performances during the last four academic years, it has been observed that there exists an actual correlation between the marks obtained in the Moodle tests and the final mark of the course. In addition, it could be deduced that students who have passed the Moodle tests increase their possibilities of passing the course by an odds ratio close to 3.

Unraveling the Mystery of the Origin of Mathematical Problems: Using a Problem-Posing Framework with Prospective Mathematics Teachers

ERIC Educational Resources Information Center

Contreras, Jose

2007-01-01

In this article, I model how a problem-posing framework can be used to enhance our abilities to systematically generate mathematical problems by modifying the attributes of a given problem. The problem-posing model calls for the application of the following fundamental mathematical processes: proving, reversing, specializing, generalizing, and…

Imagery, intuition and imagination in quantum physics education

NASA Astrophysics Data System (ADS)

Stapleton, Andrew J.

2018-03-01

In response to the authors, I demonstrate how threshold concepts offer a means to both contextualise teaching and learning of quantum physics and help transform students into the culture of physics, and as a way to identify particularly troublesome concepts within quantum physics. By drawing parallels from my own doctoral research in another area of contemporary physics—special relativity—I highlight concepts that require an ontological change, namely a shift beyond the reality of everyday Newtonian experience such as time dilation and length contraction, as being troublesome concepts that can present barriers to learning with students often asking "is it real?". Similarly, the domain of quantum physics requires students to move beyond "common sense" perception as it brings into sharp focus the difference between what is experienced via the sense perceptions and the mental abstraction of phenomena. And it's this issue that highlights the important role imagery and creativity have both in quantum physics and in the evolution of physics more generally, and lies in stark contrast to the apparent mathematical focus and lack of opportunity for students to explore ontological issues evident in the authors' research. By reflecting on the authors' observations of a focus on mathematical formalisms and problem solving at the expense of alternative approaches, I explore the dialectic between Heisenberg's highly mathematical approach and Schrödinger's mechanical wave view of the atom, together with its conceptual imagery, at the heart of the evolution of quantum mechanics. In turn, I highlight the significance of imagery, imagination and intuition in quantum physics, together with the importance of adopting an epistemological pluralism—multiple ways of knowing and thinking—in physics education. Again drawing parallels with the authors' work and my own, I identify the role thought experiments have in both quantum physics education and in physics more generally. By introducing the notion of play, I advocate adopting and celebrating multiple approaches of teaching and learning, including thought experiments, play, dialogue and a more conceptual approach inclusive of multiple forms of representation, that complements the current instructional, mathematical approach so as to provide better balance to learning, teaching and the curriculum.

Physics for Occupational Therapy Majors Program

NASA Astrophysics Data System (ADS)

Singh Aurora, Tarlok

1998-03-01

In Spring 1996, a one semester course - "Survey of Physics" - was taught for students majoring in Occupational Therapy (O. T.), in contrast to the two semester physics sequence for all other health science majors. The course was designed to expose the students to the concept of physics, develop problem solving skills and to emphasize the importance of physics to O.T. In developing the course content, students' preparedness in mathematics and the perceived future applications of physics in O. T. was taken in to consideration, and steps were taken to remedy the deficiencies in students' background. The course was comprised of lecture, laboratory, and considerable self study due to the time constraints, and these will be described.

Connecting Physics Bachelors to Their Dream Jobs

NASA Astrophysics Data System (ADS)

Bhattacharya, Shouvik

2013-01-01

People who earn bachelor’s degrees in physics are highly employable. Employers value the skills that physics bachelor’s recipients acquire and develop over their four years of a college education, such as complex problem solving, advanced mathematics, teamwork and programming. The Career Pathways Project of the American Institute of Physics (AIP) aims to better prepare physics undergraduates for the science, technology, engineering, and math (STEM) workforce. This presentation will include a discussion of common features among departments visited by the AIP’s Career Pathways team, ideas for a career workshop for physics undergraduates, and advice on how to make the most out of a job fair and how to start effective online professional networking.

Introduction

NASA Astrophysics Data System (ADS)

2016-11-01

A year has passed since Raymond left us, but for many of us it seems like it was yesterday. Indeed, since his departure last July, not a week or even a day has gone by without his former collaborators, students, colleagues having a thought for him. Some initiatives have already been taken in order to celebrate Raymond's memory. The special day for Raymond organized at CERN last December was an opportunity to celebrate this exceptional man. In Annecy, with the implication of CERN and Marseille and thanks to a spontaneous and generous gift of Raymond's wife Marie-Françoise and their children Olivier and Thierry, the opening of a special room containing a huge collection of scientific books of Raymond is almost completed. It is in the same spirit that the present editors decided to dedicate a special issue of Nuclear Physics in memory of Raymond. In the following pages, some important problems Raymond was interested in are presented, discussed and sometimes solved. The diversity of topics in this issue reflects well the extent of Raymond's interests in Physics and Mathematics. Raymond was not only a gifted man for the so-called theoretical sciences, mathematics and physics, but he was also passionate about arts, music, drawing and of course literature, just as he was a leader always ready to bring his help and share his deep knowledge in physics and mathematics with others. Many people were deeply touched by Paul Sorba's tribute during Raymond's funeral. This is why we asked Paul to translate his speech, originally given in French, which seemed to us a perfect Prolegomena for this special volume of Nuclear Physics. The volume "Mathematical Foundations of Quantum Field Theory" is organized as follows: General and historical contributions

Constellation-X Observatory

NASA Technical Reports Server (NTRS)

2006-01-01

Women in Science Conferences are designed to allow young women in grades 7 through 12 to learn first-hand about careers in science, mathematics, and technology from accomplished professional women. Results of an international science and mathematics study conducted in 2000 indicated that "children in the United States were among the leaders in the 4th grade assessment, but by high school graduation, they were almost last." Part of the problem is that many girls and young women in junior and senior high school lose interest in science and technological careers. The goal of the WIS-Conferences held at the University of Wyoming in Laramie, and at Central Wyoming College in Riverton, are to directly address this problem. The conferences will be a cooperative effort supported by local agencies, schools, and businesses, in addition to several state agencies. By presenting positive role models in the science, mathematics, and technological fields, we hope to encourage all students (especially young women and minorities) to pursue higher education and careers in mathematics and science. The workshop topics include: 1) Engineering; 2) Robotics; 3) Physics/Astronomy; 4) Geology; 5) Paleontology; 6) Remote Sensing (GPS/GIS); 7) Molecular Biology; 8) Veterinary Medicine; 9) Optometry; 10) Data Encryption; and 11) Wildlife Biology.

Early Experiences and Integration in the Persistence of First-Generation College Students in STEM and Non-STEM Majors

ERIC Educational Resources Information Center

Dika, Sandra L.; D'Amico, Mark M.

2016-01-01

Representation of diverse groups in science, technology, engineering, and mathematics (STEM) fields is a persistent concern in the United States. Although there have been some strides toward more diverse representation, significant problems of underrepresentation remain in particular STEM fields: physical sciences, engineering, math, and computer…

Probability & Perception: The Representativeness Heuristic in Action

ERIC Educational Resources Information Center

Lu, Yun; Vasko, Francis J.; Drummond, Trevor J.; Vasko, Lisa E.

2014-01-01

If the prospective students of probability lack a background in mathematical proofs, hands-on classroom activities may work well to help them to learn to analyze problems correctly. For example, students may physically roll a die twice to count and compare the frequency of the sequences. Tools such as graphing calculators or Microsoft Excel®…

Light-Emitting Diodes: Solving Complex Problems

ERIC Educational Resources Information Center

Planinšic, Gorazd; Etkina, Eugenia

2015-01-01

This is the fourth paper in our Light-Emitting Diodes series. The series aims to create a systematic library of LED-based materials and to provide readers with the description of experiments and the pedagogical treatment that would help their students construct, test, and apply physics concepts and mathematical relations. The first paper provided…

Recruitment to Physics and Mathematics Teaching: A Personality Problem?

ERIC Educational Resources Information Center

Smithers, Alan; Hill, Susan

1989-01-01

Results of a British study indicate that, among potential applicants (N=177), a small demand exists for a proposed science education degree program. Findings suggest that recruitment of science and math teachers may be hampered because the satisfactions provided by teaching are unlike those sought by science and math specialists. (IAH)

Overview of Aro Program on Network Science for Human Decision Making

NASA Astrophysics Data System (ADS)

West, Bruce J.

This program brings together researchers from disparate disciplines to work on a complex research problem that defies confinement within any single discipline. Consequently, not only are new and rewarding solutions sought and obtained for a problem of importance to society and the Army, that is, the human dimension of complex networks, but, in addition, collaborations are established that would not otherwise have formed given the traditional disciplinary compartmentalization of research. This program develops the basic research foundation of a science of networks supporting the linkage between the physical and human (cognitive and social) domains as they relate to human decision making. The strategy is to extend the recent methods of non-equilibrium statistical physics to non-stationary, renewal stochastic processes that appear to be characteristic of the interactions among nodes in complex networks. We also pursue understanding of the phenomenon of synchronization, whose mathematical formulation has recently provided insight into how complex networks reach accommodation and cooperation. The theoretical analyses of complex networks, although mathematically rigorous, often elude analytic solutions and require computer simulation and computation to analyze the underlying dynamic process.

What your mother never told you about ... physics teaching

NASA Astrophysics Data System (ADS)

Roudebush, Deborah

2010-03-01

When I entered high school teaching after working in industry for several years, I was sure I knew exactly what to do. I was convinced that I would be the sage on the stage and would wow the students with my clear explanations, amazing problem-solving techniques, and perfect lab instructions. I was convinced that the students would soak up the wisdom and insight that I was offering and that, if the students just followed my directions exactly, they would be able to solve new and exciting problems. Instead, I found that the students became amazingly adept at applied mathematics and understood few of the underlying physics concepts. In fact, some of my star students who headed off to become physics majors were unprepared for the thought required and changed majors within two years.

Evolution of solar magnetic fields - A new approach to MHD initial-boundary value problems by the method of nearcharacteristics

NASA Technical Reports Server (NTRS)

Nakagawa, Y.

1980-01-01

A method of analysis for the MHD initial-boundary problem is presented in which the model's formulation is based on the method of nearcharacteristics developed by Werner (1968) and modified by Shin and Kot (1978). With this method, the physical causality relationship can be traced from the perturbation to the response as in the method of characteristics, while achieving the advantage of a considerable reduction in mathematical procedures. The method offers the advantage of examining not only the evolution of nonforce free fields, but also the changes of physical conditions in the atmosphere accompanying the evolution of magnetic fields. The physical validity of the method is demonstrated with examples, and their significance in interpreting observations is discussed.

78 FR 42111 - Advisory Committee for Mathematical and Physical Sciences #66; Notice of Meeting; Correction

Federal Register 2010, 2011, 2012, 2013, 2014

2013-07-15

... NATIONAL SCIENCE FOUNDATION Advisory Committee for Mathematical and Physical Sciences 66; Notice... July 18 Advisory Committee for Mathematical and Physical Sciences in the Federal Register on June 21..., Directorate for Mathematical and Physical Sciences, National Science Foundation, 4201 Wilson Blvd., Arlington...

Should I Take Further Mathematics? Physics Undergraduates' Experiences of Post-Compulsory Mathematics

ERIC Educational Resources Information Center

Bowyer, Jessica; Darlington, Ellie

2017-01-01

It is essential that physics undergraduates are appropriately prepared for the mathematical demands of their course. This study investigated physics students' perceptions of post-compulsory mathematics as preparation for their degree course. 494 physics undergraduates responded to an online questionnaire about their experiences of A-level…

Mathematical Problem Solving Ability of Junior High School Students through Ang’s Framework for Mathematical Modelling Instruction

NASA Astrophysics Data System (ADS)

Fasni, N.; Turmudi, T.; Kusnandi, K.

2017-09-01

This research background of this research is the importance of student problem solving abilities. The purpose of this study is to find out whether there are differences in the ability to solve mathematical problems between students who have learned mathematics using Ang’s Framework for Mathematical Modelling Instruction (AFFMMI) and students who have learned using scientific approach (SA). The method used in this research is a quasi-experimental method with pretest-postest control group design. Data analysis of mathematical problem solving ability using Indepent Sample Test. The results showed that there was a difference in the ability to solve mathematical problems between students who received learning with Ang’s Framework for Mathematical Modelling Instruction and students who received learning with a scientific approach. AFFMMI focuses on mathematical modeling. This modeling allows students to solve problems. The use of AFFMMI is able to improve the solving ability.

Soil physics: a Moroccan perspective

NASA Astrophysics Data System (ADS)

Lahlou, Sabah; Mrabet, Rachid; Ouadia, Mohamed

2004-06-01

Research on environmental pollution and degradation of soil and water resources is now of highest priority worldwide. To address these problems, soil physics should be conceived as a central core to this research. This paper objectives are to: (1) address the role and importance of soil physics, (2) demonstrate progress in this discipline, and (3) present various uses of soil physics in research, environment and industry. The study of dynamic processes at and within the soil vadose zone (flow, dispersion, transport, sedimentation, etc.), and ephemeral phenomena (deformation, compaction, etc.), form an area of particular interest in soil physics. Soil physics has changed considerably over time. These changes are due to needed precision in data collection for accurate interpretation of space and time variation of soil properties. Soil physics interacts with other disciplines and sciences such as hydro(geo)logy, agronomy, environment, micro-meteorology, pedology, mathematics, physics, water sciences, etc. These interactions prompted the emergence of advanced theories and comprehensive mechanisms of most natural processes, development of new mathematical tools (modeling and computer simulation, fractals, geostatistics, transformations), creation of high precision instrumentation (computer assisted, less time constraint, increased number of measured parameters) and the scale sharpening of physical measurements which ranges from micro to watershed. The environment industry has contributed to an enlargement of many facets of soil physics. In other words, research demand in soil physics has increased considerably to satisfy specific and environmental problems (contamination of water resources, global warming, etc.). Soil physics research is still at an embryonic stage in Morocco. Consequently, soil physicists can take advantage of developments occurring overseas, and need to build up a database of soil static and dynamic properties and to revise developed models to meet our conditions. Large, but special, investment is required to promote research programs in soil physics, which consider developments in this discipline and respect Moroccan needs. These programs will be highlighted herein.

Framing the Structural Role of Mathematics in Physics Lectures: A Case Study on Electromagnetism

ERIC Educational Resources Information Center

Karam, Ricardo

2014-01-01

Physics education research has shown that students tend to struggle when trying to use mathematics in a meaningful way in physics (e.g., mathematizing a physical situation or making sense of equations). Concerning the possible reasons for these difficulties, little attention has been paid to the way mathematics is treated in physics instruction.…

The Use of Graphing Technology to Promote Transfer of Learning: the Interpretation of Graphs in Physics.

NASA Astrophysics Data System (ADS)

Nichols, Jeri Ann

This study examined the relationship between mathematics background and performance on graph-related problems in physics before and after instruction on the graphical analysis of motion and several microcomputer-based laboratory experiences. Students identified as either having or not having a graphing technology enhanced precalculus mathematics background were further categorized into one of four groups according to mathematics placement at the university. The performances of these groups were compared to identity differences. Pre- and Post-test data were collected from 589 students and 312 students during Autumn Quarter 1990 and Winter Quarter 1991 respectively. Background information was collected from each student. Significant differences were found between students with the technology enhanced mathematics background and those without when considering the entire populations both quarters. The students with the technology background were favored Autumn quarter and students without the technology background were favored Winter quarter. However, the entire population included an underrepresentation of students at the highest and lowest placements; hence, these were eliminated from the analyses. No significant differences were found between the technology/no technology groups after the elimination of the underrepresented groups. All categories of students increased their mean scores from pretest to post-test; the average increase was 8.23 points Autumn Quarter and 11.41 points Winter Quarter. Males consistently outperformed females on both the pretest and the post-test Autumn 1990. All students found questions involving the concept of acceleration more difficult than questions involving velocity or distance. Questions requiring students to create graphs were more difficult than questions requiring students to interpret graphs. Further research involving a qualitative component is recommended to identify the specific skills students use when solving graph-related physics problems. In addition, it is recommended that a similar study be conducted to include a control group not participating in the microcomputer -based laboratory experiments.

Writing in Groups as a Tool for Non-Routine Problem Solving in First Year University Mathematics

ERIC Educational Resources Information Center

Taylor, J. A.; McDonald, C.

2007-01-01

Development of mathematical problem solving skills is an age old problem in mathematics. This paper details the design of a component of a first year university mathematics course in which group work and mathematical communication skills, especially writing skills, are used as a tool to develop non-routine problem solving skills. In this design…

Coherent states: a contemporary panorama Coherent states: a contemporary panorama

NASA Astrophysics Data System (ADS)

Twareque Ali, S.; Antoine, Jean-Pierre; Bagarello, Fabio; Gazeau, Jean-Pierre

2012-06-01

Coherent states (CS) of the harmonic oscillator (also called canonical CS) were introduced in 1926 by Schrödinger in answer to a remark by Lorentz on the classical interpretation of the wave function. They were rediscovered in the early 1960s, first (somewhat implicitly) by Klauder in the context of a novel representation of quantum states, then by Glauber and Sudarshan for the description of coherence in lasers. Since then, CS have grown into an extremely rich domain that pervades almost every corner of physics and have also led to the development of several flourishing topics in mathematics. Along the way, a number of review articles have appeared in the literature, devoted to CS, notably the 1985 reprint volume of Klauder and Skagerstam [1], the 1990 review paper by Zhang et al [2], the 1993 Oak Ridge Conference [3] and the 1995 review paper by Ali et al [4]. Textbooks also have been published, among which one might mention the ground breaking text of Perelomov [5] focusing on the group-theoretical aspects, that of Ali et al [6]1 analyzing systematically the mathematical structure beyond the group-theoretical approach and also the relation to wavelet analysis, that of Dodonov and Man'ko [7] mostly devoted to quantum optics, that of Gazeau [8] more oriented towards the physical, probabilistic and quantization aspects, and finally the very recent one by Combescure and Robert [9]. In retrospect, one can see that the development of CS has gone through a two-phase transition. First, the (simultaneous) discovery in 1972 by Gilmore and Perelomov that CS were rooted in group theory, then the realization that CS can be defined in a purely algebraic way, as an eigenvalue problem or by a series expansion (Malkin and Man'ko 1969, Barut and Girardello 1971, Gazeau and Klauder 1999; references to the original articles may be found in the textbooks quoted above). Both facts resulted in an explosive expansion of the CS literature. We thought, therefore, that the time was ripe to devote a special issue of Journal of Physics A: Mathematical and Theoretical to CS. However, because of limitations of space and time, it would have been impossible to get a fully representative cross-section of papers, covering all the different facets of the subject. Consequently, we have selected 37 articles, including some by a few of the originators of the field. We thank all the authors for submitting their up-to-date thoughts on this fascinating subject. The contents of this special issue are subdivided into five categories: (1) review papers; (2) physics-oriented CS; (3) physics and quantum information; (4) mathematics, general topics; and (5) mathematics, particular problems. (1) Review papers We start with five review papers. The first paper, by Klauder, surveys the many possible applications of affine variables, both in classical and quantum physics. The second, by Sanders, proposes a grand tour of entangled CS, which are present in many fields, such as quantum optics, quantum information processing, etc. The next paper, by Rowe, surveys the field of vector CS and the attendant group representation problems (including induced representations). Then Oriti et al describe a particular class of CS relevant to (loop) quantum gravity. Finally, Combescure and Robert present a comprehensive review of fermionic CS, including all mathematical details. (2) Physics-oriented CS The six contributions in this section deal with specific physical problems: (i) Dajka-Luczka study Gazeau-Klauder cat states associated with a nonlinear Kerr oscillator, instead of the usual canonical CS leading to Schrödinger cat states; (ii) Angelova et al discuss squeezed CS associated with a 1D Morse potential, used in molecular physics; (iii) Bagrov et al study CS in a magnetic solenoid field and prove their completeness; (iv) Blasone-Jizba treat Nambu-Goldstone dynamics in spontaneously broken symmetries, using CS functional integrals; (v) Calixto et al describe accelerated relativistic particles in the context of spontaneous breakdown of conformal SU(2,2) symmetry, using SU(2,2) CS; and (vi) Mortazavi-Tavassoly study f-deformed charge CS and their physical properties (nonclassical features, sub-Poissonian statistical behavior, etc). (3) Physics and quantum information The second group of physically related CS contains four contributions with a distinct quantum information theoretic flavor. First, Thilagam describes the dynamical behavior of entanglement of a pair of qubits (excitons), using a CS basis. Next, Lavoie-de Guise study SU(3) intelligent states (i.e., minimal uncertainty states), of interest in the quantum information community. Then Muñoz constructs discrete CS for n qubits. Finally, Wagner-Kendon explore the continuous variable Deutsch-Jozsa algorithm known in quantum computing in a discrete formulation. (4) Mathematics, general topics In this subgroup, there are eight papers dealing with general properties of CS, independently of any particular system or application. A whole series discusses the interaction between CS and various mathematical objects: pseudodifferential operators and Weyl calculus (Unterberger); induced representations of the affine group and intertwining operators (Elmabrok-Hutnik) measure-free CS and reproducing kernels (Horzela-Szafraniec) extremal POV measures (Heinosaari-Pellonpää) Hilbert W*-modules (Bhattacharyya-Roy) Toeplitz operators (Hutníková-Hutník) and operator localization and homogeneous structure of nilpotent Lie groups (Kisil). In addition, Balazs et al consider multipliers for continuous frames, including CS or wavelet frames. (5) Mathematics, particular problems The second group of mathematically oriented papers contains 14 contributions, devoted to CS in particular systems. We start with a paper by Gilmore, which explores the (sometimes chaotic) evolution of atomic CS under a time-periodic driving field, using sphere maps S2 → S2. Next, we include a paper on CS on the 2-sphere in a magnetic field (Hall-Mitchell) a paper on CS for a quantum particle on a Möbius strip (Cirilo-Lombardo) a discussion of quantization on the circle (Chadzitaskos et al); SUSY CS for Pöschl-Teller potentials (Bergeron et al); generalized Bargmann functions and von Neumann lattices (Vourdas et al); partial reconstruction for a finite CS system, using the Fock-Bargmann representation (Calixto et al); phase operators for SU(3) irreps, thus for finite quantum systems (de Guise); semiclassical CS in periodic potentials (Carles-Sparber) complexified CS with non-Hermitian Hamiltonians (Graefe-Schubert) minimal uncertainty states in the context of (semisimple) group representation theory (Oszmaniec); localization operators in the time-frequency domain, i.e., in Gabor analysis (Muzhikyan-Avanesyan) and, finally, two papers about fermionic CS (Daoud-Kibler and Trifonov). This brief description illustrates perfectly the extreme versatility of the CS concept. As already stressed, coherent states constitute nowadays a flourishing research topic, with applications to a wide spectrum of domains. Indeed, CS are everywhere in physics: condensed matter physics, atomic physics, nuclear and particle physics, quantum optics, dynamics—both quantum and classical potentials—quantum gravity, quantization and quantum information theory. On the other hand, CS have grown into a fully-fledged domain in mathematics, incorporating many tools such as group representations, POV measures, frames, holomorphic functions, orthogonal polynomials and so on. Interestingly enough, the majority of contributions to this special issue (22 out of 37) are mathematically minded, demonstrating the widespread interest CS have generated in various areas of mathematics. A third field related to CS (but almost not represented in the present collection) is signal processing. Indeed both Gabor analysis and wavelet analysis derive in the first place from CS theory, namely, CS associated to the Weyl-Heisenberg and the ax + b group, respectively. Here too, a tremendous development has taken place in recent years, another testimony to the richness of the notion of CS. We leave it to the jury of public opinion to judge whether the call for a special issue of the journal, devoted to coherent states, has been justified. References [1] Klauder J R and Skagerstam B S 1985 Coherent States—Applications in Physics and Mathematical Physics (Singapore: World Scientific) [2] Zhang W-M, Feng D H and Gilmore R 1990 Coherent states: theory and some applications Rev. Mod. Phys. 62 867-927 [3] Feng D H, Klauder J R and Strayer M (ed) 1994 Coherent States: Past, Present and Future (Singapore: World Scientific) [4] Ali S T, Antoine J-P, Gazeau J-P and Mueller U A 1995 Coherent states and their generalizations: a mathematical overview Rev. Math. Phys. 7 1013-104 [5] Perelomov A M 1986 Generalized Coherent States and Their Applications (New York: Springer) [6] Ali S T, Antoine J-P and Gazeau J-P 2000 Coherent States, Wavelets and Their Generalizations (New York: Springer) [7] Dodonov V V and Man'ko V I (ed) 2003 Theory of Nonclassical States of Light (London: Taylor & Francis) [8] Gazeau J-P 2009 Coherent States in Quantum Physics (Berlin: Wiley) [9] Combescure M and Robert D 2012 Coherent States and Applications in Mathematical Physics (New York: Springer) 1 A second edition of that volume is in preparation.

Engineering physics and mathematics division

NASA Astrophysics Data System (ADS)

Sincovec, R. F.

1995-07-01

This report provides a record of the research activities of the Engineering Physics and Mathematics Division for the period 1 Jan. 1993 - 31 Dec. 1994. This report is the final archival record of the EPM Division. On 1 Oct. 1994, ORELA was transferred to Physics Division and on 1 Jan. 1995, the Engineering Physics and Mathematics Division and the Computer Applications Division reorganized to form the Computer Science and Mathematics Division and the Computational Physics and Engineering Division. Earlier reports in this series are identified on the previous pages, along with the progress reports describing ORNL's research in the mathematical sciences prior to 1984 when those activities moved into the Engineering Physics and Mathematics Division.

Curved spaces before Einstein: Karl Schwarzschild's cosmological speculations and the beginnings of relativistic cosmology (German Title: Gekrümmte Universen vor Einstein: Karl Schwarzschilds kosmologische Spekulationen und die Anfänge der relativistischen Kosmologie)

NASA Astrophysics Data System (ADS)

Schemmel, Matthias

In contrast to most of his collegues in astronomy and physics, the German astronomer Karl Schwarzschild immediately recognized the significance of general relativity for physics and astronomy, and played a pioneering role in its early development. In this contribution, it is argued that the clue for understanding Schwarzschild's exceptional reaction to general relativity lies in the study of his prerelativistic work. Long before the rise of general relativity, Schwarzschild occupied himself with foundational problems on the borderline of physics, astronomy, and mathematics that, from today's perspective, belong to the field of problems of that theory. In this contribution, the example of Schwarzschild's early speculations about the non-Euclidean nature of physical space on cosmological scales is presented and their reflection in his reception of general relativity is discussed.

Secondary Teachers’ Mathematics-related Beliefs and Knowledge about Mathematical Problem-solving

NASA Astrophysics Data System (ADS)

E Siswono, T. Y.; Kohar, A. W.; Hartono, S.

2017-02-01

This study investigates secondary teachers’ belief about the three mathematics-related beliefs, i.e. nature of mathematics, teaching mathematics, learning mathematics, and knowledge about mathematical problem solving. Data were gathered through a set of task-based semi-structured interviews of three selected teachers with different philosophical views of teaching mathematics, i.e. instrumental, platonist, and problem solving. Those teachers were selected from an interview using a belief-related task from purposively selected teachers in Surabaya and Sidoarjo. While the interviews about knowledge examine teachers’ problem solving content and pedagogical knowledge, the interviews about beliefs examine their views on several cases extracted from each of such mathematics-related beliefs. Analysis included the categorization and comparison on each of beliefs and knowledge as well as their interaction. Results indicate that all the teachers did not show a high consistency in responding views of their mathematics-related beliefs, while they showed weaknesses primarily on problem solving content knowledge. Findings also point out that teachers’ beliefs have a strong relationship with teachers’ knowledge about problem solving. In particular, the instrumental teacher’s beliefs were consistent with his insufficient knowledge about problem-solving, while both platonist and problem-solving teacher’s beliefs were consistent with their sufficient knowledge of either content or pedagogical problem solving.

Impact of Maple(TM) on the design, instruction and performance in an undergraduate physics mathematical methods course

NASA Astrophysics Data System (ADS)

Runge, Alan Paul

1997-10-01

A traditional undergraduate physics course on mathematical methods has been redesigned to incorporate the use of Maplesp{sc {TM}}, a computer algebra program, during all aspects of the course. Topics covered were: complex number theory; series approximations; matrix theory; partial differentiation; vector algebra; and vector calculus. Five undergraduate students were enrolled, from sophomore to senior in academic class standing. A qualitative case study methodology was used to describe the changes in the course design resulting from the incorporation of Maplesp{sc {TM}} and their impact on the instruction of the course, and to determine the effects on the students' learning and development of problem solving skills in physics using Maplesp{sc {TM}} as a problem solving tool. The impact of using Maplesp{sc {TM}} on the number and types of interactions is presented. The entire semester long course was included in this study. Each class session is described in detail. Examples of the Maplesp{sc {TM}} materials used are given. The use of the Maplesp{sc {TM}} program was allowed on all homework and exams with each student having their own computer during class. Constraints were made so that the assessment emphasis remained on the mathematics and the conceptual understanding of the problem solving methods. All of the students demonstrated some level of proficiency in using Maplesp{TM} to solve the assigned problems. Strategies for effectively using Maplesp{TM} were presented and were individualized by the students. The students reported positive and negative impacts of using Maplesp{sc {TM}}. All of the students satisfactorily completed the course requirements, receiving final course grades from B to A+. All of them continued to voluntarily use Maplesp{sc {TM}} during the following semester. Instructional methods used included various lecture techniques without Maplesp{sc {TM}} assistance, lectures and demonstrations using only Maplesp{sc {TM}}, and student tasks assigned in class worked with the aid of Maplesp{sc {TM}}. Maplesp{sc {TM}} was used in one of these aspects in all but 3, out of 45, class periods. The use of Maplesp{sc {TM}} constituted about half of the overall class time.

Pre-service mathematics teachers’ ability in solving well-structured problem

NASA Astrophysics Data System (ADS)

Paradesa, R.

2018-01-01

This study aimed to describe the mathematical problem-solving ability of undergraduate students of mathematics education in solving the well-structured problem. The type of this study was qualitative descriptive. The subjects in this study were 100 undergraduate students of Mathematics Education at one of the private universities in Palembang city. The data in this study was collected through two test items with essay form. The results of this study showed that, from the first problem, only 8% students can solve it, but do not check back again to validate the process. Based on a scoring rubric that follows Polya strategy, their answer satisfied 2 4 2 0 patterns. But, from the second problem, 45% students satisfied it. This is because the second problem imitated from the example that was given in learning process. The average score of undergraduate students mathematical problem-solving ability in solving well-structured problems showed 56.00 with standard deviation was 13.22. It means that, from 0 - 100 scale, undergraduate students mathematical problem-solving ability can be categorized low. From this result, the conclusion was undergraduate students of mathematics education in Palembang still have a problem in solving mathematics well-structured problem.

Framing the structural role of mathematics in physics lectures: A case study on electromagnetism

NASA Astrophysics Data System (ADS)

Karam, Ricardo

2014-06-01

Physics education research has shown that students tend to struggle when trying to use mathematics in a meaningful way in physics (e.g., mathematizing a physical situation or making sense of equations). Concerning the possible reasons for these difficulties, little attention has been paid to the way mathematics is treated in physics instruction. Starting from an overall distinction between a technical approach, which involves an instrumental (tool-like) use of mathematics, and a structural one, focused on reasoning about the physical world mathematically, the goal of this study is to characterize the development of the latter in didactic contexts. For this purpose, a case study was conducted on the electromagnetism course given by a distinguished physics professor. The analysis of selected teaching episodes with the software Videograph led to the identification of a set of categories that describe different strategies used by the professor to emphasize the structural role of mathematics in his lectures. As a consequence of this research, an analytic tool to enable future comparative studies between didactic approaches regarding the way mathematics is treated in physics teaching is provided.

Method for simulating discontinuous physical systems

DOEpatents

Baty, Roy S.; Vaughn, Mark R.

2001-01-01

The mathematical foundations of conventional numerical simulation of physical systems provide no consistent description of the behavior of such systems when subjected to discontinuous physical influences. As a result, the numerical simulation of such problems requires ad hoc encoding of specific experimental results in order to address the behavior of such discontinuous physical systems. In the present invention, these foundations are replaced by a new combination of generalized function theory and nonstandard analysis. The result is a class of new approaches to the numerical simulation of physical systems which allows the accurate and well-behaved simulation of discontinuous and other difficult physical systems, as well as simpler physical systems. Applications of this new class of numerical simulation techniques to process control, robotics, and apparatus design are outlined.

Book Review: Book review

NASA Astrophysics Data System (ADS)

Wüthrich, Christian

Symmetry considerations stand at the core of classical and quantum physics. No modern-and few older-physical theories forgo the immense services that these considerations offer. It is therefore only natural that philosophers of physics have increasingly started to study the motivations for, as well as the technical implementations and the interpretative implications of, symmetries in fundamental physics. Apart from the extraordinary foundational interest of symmetries, they provide a vehicle to study more general philosophical issues such as the relation between the physical world and its representations and between physics and mathematics. Moreover, traditional problems in metaphysics and philosophy of science such as the nature and status of laws of nature, scientific realism, and determinism naturally arise in, and enjoy substantial fertilisation from, the context of symmetries in physics.

Research Mathematicians' Practices in Selecting Mathematical Problems

ERIC Educational Resources Information Center

Misfeldt, Morten; Johansen, Mikkel Willum

2015-01-01

Developing abilities to create, inquire into, qualify, and choose among mathematical problems is an important educational goal. In this paper, we elucidate how mathematicians work with mathematical problems in order to understand this mathematical process. More specifically, we investigate how mathematicians select and pose problems and discuss to…

Reevaluating the two-representation model of numerical magnitude processing.

PubMed

Jiang, Ting; Zhang, Wenfeng; Wen, Wen; Zhu, Haiting; Du, Han; Zhu, Xiangru; Gao, Xuefei; Zhang, Hongchuan; Dong, Qi; Chen, Chuansheng

2016-01-01

One debate in mathematical cognition centers on the single-representation model versus the two-representation model. Using an improved number Stroop paradigm (i.e., systematically manipulating physical size distance), in the present study we tested the predictions of the two models for number magnitude processing. The results supported the single-representation model and, more importantly, explained how a design problem (failure to manipulate physical size distance) and an analytical problem (failure to consider the interaction between congruity and task-irrelevant numerical distance) might have contributed to the evidence used to support the two-representation model. This study, therefore, can help settle the debate between the single-representation and two-representation models.

Optimization of controlled processes in combined-cycle plant (new developments and researches)

NASA Astrophysics Data System (ADS)

Tverskoy, Yu S.; Muravev, I. K.

2017-11-01

All modern complex technical systems, including power units of TPP and nuclear power plants, work in the system-forming structure of multifunctional APCS. The development of the modern APCS mathematical support allows bringing the automation degree to the solution of complex optimization problems of equipment heat-mass-exchange processes in real time. The difficulty of efficient management of a binary power unit is related to the need to solve jointly at least three problems. The first problem is related to the physical issues of combined-cycle technologies. The second problem is determined by the criticality of the CCGT operation to changes in the regime and climatic factors. The third problem is related to a precise description of a vector of controlled coordinates of a complex technological object. To obtain a joint solution of this complex of interconnected problems, the methodology of generalized thermodynamic analysis, methods of the theory of automatic control and mathematical modeling are used. In the present report, results of new developments and studies are shown. These results allow improving the principles of process control and the automatic control systems structural synthesis of power units with combined-cycle plants that provide attainable technical and economic efficiency and operational reliability of equipment.

Infrared band absorptance correlations and applications to nongray radiation. [mathematical models of absorption spectra for nongray atmospheres in order to study air pollution

NASA Technical Reports Server (NTRS)

Tiwari, S. N.; Manian, S. V. S.

1976-01-01

Various mathematical models for infrared radiation absorption spectra for atmospheric gases are reviewed, and continuous correlations for the total absorptance of a wide band are presented. Different band absorptance correlations were employed in two physically realistic problems (radiative transfer in gases with internal heat source, and heat transfer in laminar flow of absorbing-emitting gases between parallel plates) to study their influence on final radiative transfer results. This information will be applied to the study of atmospheric pollutants by infrared radiation measurement.

Instructional computing in space physics moves ahead

NASA Astrophysics Data System (ADS)

Russell, C. T.; Omidi, N.

As the number of spacecraft stationed in the Earth's magnetosphere exponentiates and society becomes more technologically sophisticated and dependent on these spacebased resources, both the importance of space physics and the need to train people in this field will increase.Space physics is a very difficult subject for students to master. Both mechanical and electromagnetic forces are important. The treatment of problems can be very mathematical, and the scale sizes of phenomena are usually such that laboratory studies become impossible, and experimentation, when possible at all, must be carried out in deep space. Fortunately, computers have evolved to the point that they are able to greatly facilitate instruction in space physics.

A useful demonstration of calculus in a physics high school laboratory

NASA Astrophysics Data System (ADS)

Alvarez, Gustavo; Schulte, Jurgen; Stockton, Geoffrey; Wheeler, David

2018-01-01

The real power of calculus is revealed when it is applied to actual physical problems. In this paper, we present a calculus inspired physics experiment suitable for high school and undergraduate programs. A model for the theory of the terminal velocity of a falling body subject to a resistive force is developed and its validity tested in an experiment of a falling magnet in a column of self-induced eddy currents. The presented method combines multiple physics concepts such as 1D kinematics, classical mechanics, electromagnetism and non-trivial mathematics. It offers the opportunity for lateral as well as project-based learning.

Pre-Service Teachers' Free and Structured Mathematical Problem Posing

ERIC Educational Resources Information Center

Silber, Steven; Cai, Jinfa

2017-01-01

This exploratory study examined how pre-service teachers (PSTs) pose mathematical problems for free and structured mathematical problem-posing conditions. It was hypothesized that PSTs would pose more complex mathematical problems under structured posing conditions, with increasing levels of complexity, than PSTs would pose under free posing…

The Role of Expository Writing in Mathematical Problem Solving

ERIC Educational Resources Information Center

Craig, Tracy S.

2016-01-01

Mathematical problem-solving is notoriously difficult to teach in a standard university mathematics classroom. The project on which this article reports aimed to investigate the effect of the writing of explanatory strategies in the context of mathematical problem solving on problem-solving behaviour. This article serves to describe the…

Using Diagrams as Tools for the Solution of Non-Routine Mathematical Problems

ERIC Educational Resources Information Center

Pantziara, Marilena; Gagatsis, Athanasios; Elia, Iliada

2009-01-01

The Mathematics education community has long recognized the importance of diagrams in the solution of mathematical problems. Particularly, it is stated that diagrams facilitate the solution of mathematical problems because they represent problems' structure and information (Novick & Hurley, 2001; Diezmann, 2005). Novick and Hurley were the first…

The Problem-Solving Approach in the Teaching of Number Theory

ERIC Educational Resources Information Center

Toh, Pee Choon; Leong, Yew Hoong; Toh, Tin Lam; Dindyal, Jaguthsing; Quek, Khiok Seng; Tay, Eng Guan; Ho, Foo Him

2014-01-01

Mathematical problem solving is the mainstay of the mathematics curriculum for Singapore schools. In the preparation of prospective mathematics teachers, the authors, who are mathematics teacher educators, deem it important that pre-service mathematics teachers experience non-routine problem solving and acquire an attitude that predisposes them to…

How Students Process Equations in Solving Quantitative Synthesis Problems? Role of Mathematical Complexity in Students' Mathematical Performance

ERIC Educational Resources Information Center

Ibrahim, Bashirah; Ding, Lin; Heckler, Andrew F.; White, Daniel R.; Badeau, Ryan

2017-01-01

We examine students' mathematical performance on quantitative "synthesis problems" with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking,…

Quod erat demonstrandum: Understanding and Explaining Equations in Physics Teacher Education

NASA Astrophysics Data System (ADS)

Karam, Ricardo; Krey, Olaf

2015-07-01

In physics education, equations are commonly seen as calculation tools to solve problems or as concise descriptions of experimental regularities. In physical science, however, equations often play a much more important role associated with the formulation of theories to provide explanations for physical phenomena. In order to overcome this inconsistency, one crucial step is to improve physics teacher education. In this work, we describe the structure of a course that was given to physics teacher students at the end of their master's degree in two European universities. The course had two main goals: (1) To investigate the complex interplay between physics and mathematics from a historical and philosophical perspective and (2) To expand students' repertoire of explanations regarding possible ways to derive certain school-relevant equations. A qualitative analysis on a case study basis was conducted to investigate the learning outcomes of the course. Here, we focus on the comparative analysis of two students who had considerably different views of the math-physics interplay in the beginning of the course. Our general results point to important changes on some of the students' views on the role of mathematics in physics, an increase in the participants' awareness of the difficulties faced by learners to understand physics equations and a broadening in the students' repertoire to answer "Why?" questions formulated to equations. Based on this analysis, further implications for physics teacher education are derived.

On Riemann boundary value problems for null solutions of the two dimensional Helmholtz equation

NASA Astrophysics Data System (ADS)

Bory Reyes, Juan; Abreu Blaya, Ricardo; Rodríguez Dagnino, Ramón Martin; Kats, Boris Aleksandrovich

2018-01-01

The Riemann boundary value problem (RBVP to shorten notation) in the complex plane, for different classes of functions and curves, is still widely used in mathematical physics and engineering. For instance, in elasticity theory, hydro and aerodynamics, shell theory, quantum mechanics, theory of orthogonal polynomials, and so on. In this paper, we present an appropriate hyperholomorphic approach to the RBVP associated to the two dimensional Helmholtz equation in R^2 . Our analysis is based on a suitable operator calculus.

Aerodynamics of an airfoil with a jet issuing from its surface

NASA Technical Reports Server (NTRS)

Tavella, D. A.; Karamcheti, K.

1982-01-01

A simple, two dimensional, incompressible and inviscid model for the problem posed by a two dimensional wing with a jet issuing from its lower surface is considered and a parametric analysis is carried out to observe how the aerodynamic characteristics depend on the different parameters. The mathematical problem constitutes a boundary value problem where the position of part of the boundary is not known a priori. A nonlinear optimization approach was used to solve the problem, and the analysis reveals interesting characteristics that may help to better understand the physics involved in more complex situations in connection with high lift systems.

FOREWORD: Imaging from coupled physics Imaging from coupled physics

NASA Astrophysics Data System (ADS)

Arridge, S. R.; Scherzer, O.

2012-08-01

Due to the increased demand for tomographic imaging in applied sciences, such as medicine, biology and nondestructive testing, the field has expanded enormously in the past few decades. The common task of tomography is to image the interior of three-dimensional objects from indirect measurement data. In practical realizations, the specimen to be investigated is exposed to probing fields. A variety of these, such as acoustic, electromagnetic or thermal radiation, amongst others, have been advocated in the literature. In all cases, the field is measured after interaction with internal mechanisms of attenuation and/or scattering and images are reconstructed using inverse problems techniques, representing spatial maps of the parameters of these perturbation mechanisms. In the majority of these imaging modalities, either the useful contrast is of low resolution, or high resolution images are obtained with limited contrast or quantitative discriminatory ability. In the last decade, an alternative phenomenon has become of increasing interest, although its origins can be traced much further back; see Widlak and Scherzer [1], Kuchment and Steinhaur [2], and Seo et al [3] in this issue for references to this historical context. Rather than using the same physical field for probing and measurement, with a contrast caused by perturbation, these methods exploit the generation of a secondary physical field which can be measured in addition to, or without, the often dominating effect of the primary probe field. These techniques are variously called 'hybrid imaging' or 'multimodality imaging'. However, in this article and special section we suggest the term 'imaging from coupled physics' (ICP) to more clearly distinguish this methodology from those that simply measure several types of data simultaneously. The key idea is that contrast induced by one type of radiation is read by another kind, so that both high resolution and high contrast are obtained simultaneously. As with all new imaging techniques, the discovery of physical principles which can be exploited to yield information about internal physical parameters has led, hand in hand, to the development of new mathematical methods for solving the corresponding inverse problems. In many cases, the coupled physics imaging problems are expected to be much better posed than conventional tomographical imaging problems. However, still, at the current state of research, there exist a variety of open mathematical questions regarding uniqueness, existence and stability. In this special section we have invited contributions from many of the leading researchers in the mathematics, physics and engineering of these techniques to survey and to elaborate on these novel methodologies, and to present recent research directions. Historically, one of the best studied strongly ill-posed problems in the mathematical literature is the Calderón problem occuring in conductivity imaging, and one of the first examples of ICP is the use of magnetic resonance imaging (MRI) to detect internal current distributions. This topic, known as current density imaging (CDI) or magnetic resonance elecrical impedance tomography (MREIT), and its related technique of magnetic resonance electrical property tomography (MREPT), is reviewed by Wildak and Scherzer [1], and also by Seo et al [3], where experimental studies are documented. Mathematically, several of the ICP problems can be analyzed in terms of the 'p-Laplacian' which raises interesting research questions of non-linear partial differential equations. One approach for analyzing and for the solution of the CDI problem, using characteristics of the 1-Laplacian, is discussed by Tamasan and Veras [4]. Moreover, Moradifam et al [5] present a novel iterative algorithm based on Bregman splitting for solving the CDI problem. Probably the most active research areas in ICP are related to acoustic detection, because most of these techniques rely on the photoacoustic effect wherein absorption of an ultrashort pulse of light, having propagated by multiple scattering some distance into a diffusing medium, generates a source of acoustic waves that are propagated with hyperbolic stability to a surface detector. A complementary problem is that of 'acousto-optics' which uses focussed acoustic waves as the primary field to induce perturbations in optical or electrical properties, which are thus spatially localized. Similar physical principles apply to implement ultrasound modulated electrical impedance tomography (UMEIT). These topics are included in the review of Wildak and Scherzer [1], and Kuchment and Steinhauer [2] offer a general analysis of their structure in terms of pseudo-differential operators. 'Acousto-electrical' imaging is analyzed as a particular case by Ammari et al [6]. In the paper by Tarvainen et al [7], the photo-acoustic problem is studied with respect to different models of the light propagation step. In the paper by Monard and Bal [8], a more general problem for the reconstruction of an anisotropic diffusion parameter from power density measurements is considered; here, issues of uniqueness with respect to the number of measurements is of great importance. A distinctive, and highly important, example of ICP is that of elastography, in which the primary field is low-frequency ultrasound giving rise to mechanical displacement that reveals information on the local elasticity tensor. As in all the methods discussed in this section, this contrast mechanism is measured internally, with a secondary technique, which in this case can be either MRI or ultrasound. McLaughlin et al [9] give a comprehensive analysis of this problem. Our intention for this special section was to provide both an overview and a snapshot of current work in this exciting area. The increasing interest, and the involvement of cross-disciplinary groups of scientists, will continue to lead to the rapid expansion and important new results in this novel area of imaging science. References [1] Widlak T and Scherzer O 2012 Inverse Problems 28 084008 [2] Kuchment P and Steinhauer D 2012 Inverse Problems 28 084007 [3] Seo J K, Kim D-H, Lee J, Kwon O I, Sajib S Z K and Woo E J 2012 Inverse Problems 28 084002 [4] Tamasan A and Veras J 2012 Inverse Problems 28 084006 [5] Moradifam A, Nachman A and Timonov A 2012 Inverse Problems 28 084003 [6] Ammari H, Garnier J and Jing W 2012 Inverse Problems 28 084005 [7] Tarvainen T, Cox B T, Kaipio J P and Arridge S R 2012 Inverse Problems 28 084009 [8] Monard F and Bal G 2012 Inverse Problems 28 084001 [9] McLaughlin J, Oberai A and Yoon J R 2012 Inverse Problems 28 084004

How do open-ended problems promote mathematical creativity? A reflection of bare mathematics problem and contextual problem

NASA Astrophysics Data System (ADS)

Wijaya, A.

2018-03-01

Creativity is often seen as one of the fundamental aspects of character education. As one of the 21st century skills, creativity has also been considered as an important goal of education across the world. This paper reports a study on promoting mathematical creativity through the use of open-ended mathematics problems. A total of 53 undergraduate students participated in the study. These students worked on open-ended problems in two types, i.e. bare mathematics problem and contextual problem. The contextual problem was presented in the form of paper-based and Geogebra-based. The students’ works were analysed qualitatively in order to describe how students’ mathematical creativity developed. It was found that the open-ended problems successfully promote students’ creativity as indicated by various solutions or strategies that were used by students to solve the problems. The analysis of students’ works show that students’ creativity developed through three kinds of exploration, i. e. (1) exploration of contexts, (2) exploration of software features, and (3) exploration of mathematics concepts. The use of metacognitive questioning was found to be helpful to develop the first two explorations into mathematical exploration.

Teachers' Beliefs about Improving Transfer of Algebraic Skills from Mathematics into Physics in Senior Pre-University Education

ERIC Educational Resources Information Center

Tursucu, Süleyman; Spandaw, Jeroen; Flipse, Steven; de Vries, Marc J.

2017-01-01

Students in senior pre-university education encounter difficulties in the application of mathematics into physics. This paper presents the outcome of an explorative qualitative study of teachers' beliefs about improving the transfer of algebraic skills from mathematics into physics. We interviewed 10 mathematics and 10 physics teachers using a…

Reality-Theoretical Models-Mathematics: A Ternary Perspective on Physics Lessons in Upper-Secondary School

ERIC Educational Resources Information Center

Hansson, Lena; Hansson, Örjan; Juter, Kristina; Redfors, Andreas

2015-01-01

This article discusses the role of mathematics during physics lessons in upper-secondary school. Mathematics is an inherent part of theoretical models in physics and makes powerful predictions of natural phenomena possible. Ability to use both theoretical models and mathematics is central in physics. This paper takes as a starting point that the…

Mathematical models in simulation process in rehabilitation of persons with disabilities

NASA Astrophysics Data System (ADS)

Gorie, Nina; Dolga, Valer; Mondoc, Alina

2012-11-01

The problems of people with disability are varied. A disability may be physical, cognitive, mental, sensory, emotional, developmental or some combination of these. The major disabilities which can appear in people's lives are: the blindness, the deafness, the limb-girdle muscular dystrophy, the orthopedic impairment, the visual impairment. A disability is an umbrella term, covering impairments, activity limitations and participation restrictions. A disability may occur during a person's lifetime or may be present from birth. The authors conclude that some of these disabilities like physical, cognitive, mental, sensory, emotional, developmental can be rehabilitated. Starting from this state of affairs the authors present briefly the possibility of using certain mechatronic systems for rehabilitation of persons with different disabilities. The authors focus their presentation on alternative calling the Stewart platform in order to achieve the proposed goal. The authors present a mathematical model of systems theory approach under the parallel system and described its contents can. The authors analyze in a meaningful mathematical model describing the procedure of rehabilitation process. From the affected function biomechanics and taking into account medical recommendations the authors illustrate the mathematical models of rehabilitation work. The authors assemble a whole mathematical model of parallel structure and the rehabilitation process and making simulation and highlighting the results estimated. The authors present in the end work the results envisaged in the end analysis work, conclusions and steps for future work program..

Both Perelmans Thrown Down Gauntlets Versus Would-Be ``Science'' But Alas Sadly Mere ``SEANCES'' Put Jargonial-Obfuscation Sociological-Dysfunctionality(S-D) Ridden/Dominated Would-Be ``Sciences'' But Alas Sadly Mere SEANCES in ``Peril, Man''!!!

NASA Astrophysics Data System (ADS)

Carlson, J.; Young, F.; Clay, London; Siegel, Edward Carl-Ludwig (Physical-Mathematicist/Mathsicist)

2011-03-01

Both Perelman (Grigory[Poincare-conjecture: partial(with Richard Hamilton!!!)-"sole"-prover: by turning down first the Fields Medal at International Congress of [S-D right there: not mathematICS, but mathematicIANS!!!] Mathematicians (2007: Madrid); then the million-dollar Clay-Institute of Mathemat"ICS" (but really mathematicIANS POLITICIANS: Carlson, Yau,...et. al.) millennium-problem prize, revealing that it and its INSIDER POLITICS/POLITICIANS has/have "Feet of Clay"!!!], as sumarized by Naser-Gruber[Manfold-Destiny, The New Yorker, (August, 2007)] and separately Carlos Castro[with Corredoira: Against the Tid (2008)] put, by revealing the Jargonial-Obfuscation(J.-O.) (Bradshaw[Healing the SHAME that BINDS You, Hazelden(1980s)]-Martin[Brian, Wollongong University]-...ad INFINITUM (i.e. most if not all scientists), ad NAUSEUM!!! (disgusted with "games people play!!!)) S-D ridden/ dominated "games people play" would-be "sciences" (maths, physics,...: ad infinitum; ad NAUSEUM!!!) but alas sadly only mere Bradshaw-Martin S-D DOMINATED "SEANCES"!!!, in "peril, man"!!!

Modelling of Molecular Structures and Properties. Proceedings of the International Meeting of Physical Chemistry on Modeling of Molecular Structures and Properties in Physical Chemistry and Biophysics Organized by the Division de Chimie Physique of the Societe Francaise de Chimie Held in Nancy, France on 11-15 September 1989

DTIC Science & Technology

1990-01-01

expert systems, "intelligent" computer-aided instruction , symbolic learning . These aspects will be discussed, focusing on the specific problems the...VLSI chips) according to preliminary specifications. Finally ES are also used in computer-aided instruction (CAI) due to their ability of... instructions to process controllers), academic teaching (for mathematics , physics, foreign language, etc.). Domains of application The different

The Emergence of Mathematical Physics at the University of Leipzig

NASA Astrophysics Data System (ADS)

Schlote, Karl-Heinz

Except for the well-known blossoming of theoretical physics with the group around Werner Heisenberg at the University of Leipzig at the end of the 1920s, the tradition of mathematical physics had been analyzed in only a few aspects, in particular the work of Carl Neumann and his contributions to the shaping of mathematical physics in general and the theory of electrodynamics in particular. However, the establishment of mathematical physics and its strong position at the University of Leipzig, with Neumann as its leading figure in the last third of the nineteenth century, formed important preconditions for the later upswing. That process is analyzed in this article, focusing on the work of Neumann. It includes a discussion of his ideas on the structure of a physical theory and the role of mathematics in physics as well as his impact on the interaction of mathematics and physics.

The semantic system is involved in mathematical problem solving.

PubMed

Zhou, Xinlin; Li, Mengyi; Li, Leinian; Zhang, Yiyun; Cui, Jiaxin; Liu, Jie; Chen, Chuansheng

2018-02-01

Numerous studies have shown that the brain regions around bilateral intraparietal cortex are critical for number processing and arithmetical computation. However, the neural circuits for more advanced mathematics such as mathematical problem solving (with little routine arithmetical computation) remain unclear. Using functional magnetic resonance imaging (fMRI), this study (N = 24 undergraduate students) compared neural bases of mathematical problem solving (i.e., number series completion, mathematical word problem solving, and geometric problem solving) and arithmetical computation. Direct subject- and item-wise comparisons revealed that mathematical problem solving typically had greater activation than arithmetical computation in all 7 regions of the semantic system (which was based on a meta-analysis of 120 functional neuroimaging studies on semantic processing). Arithmetical computation typically had greater activation in the supplementary motor area and left precentral gyrus. The results suggest that the semantic system in the brain supports mathematical problem solving. Copyright © 2017 Elsevier Inc. All rights reserved.

On the solving of one type of problems of mathematical physics

NASA Astrophysics Data System (ADS)

Chebakova, V. J.; Gerasimov, A. V.; Kirpichnikov, A. P.

2016-11-01

A relationship between generalized hypergeometric functions of a special type and modified Bessel functions has been established. Using this relationship the solution of inhomogeneous differential equations of Bessel type containing even degrees of an independent variable in the right-hand part can be expressed in a form convenient for engineering and technical applications.

Solution of Poisson's Equation with Global, Local and Nonlocal Boundary Conditions

ERIC Educational Resources Information Center

Aliev, Nihan; Jahanshahi, Mohammad

2002-01-01

Boundary value problems (BVPs) for partial differential equations are common in mathematical physics. The differential equation is often considered in simple and symmetric regions, such as a circle, cube, cylinder, etc., with global and separable boundary conditions. In this paper and other works of the authors, a general method is used for the…

A Primer on Elliptic Functions with Applications in Classical Mechanics

ERIC Educational Resources Information Center

Brizard, Alain J.

2009-01-01

The Jacobi and Weierstrass elliptic functions used to be part of the standard mathematical arsenal of physics students. They appear as solutions of many important problems in classical mechanics: the motion of a planar pendulum (Jacobi), the motion of a force-free asymmetric top (Jacobi), the motion of a spherical pendulum (Weierstrass) and the…

THE STUDY OF HYDROMAGNETIC PROBLEMS BEARING ON GEOMAGNETISM. Final Report

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chandrasekhar, S.

1962-01-01

The thermal instability of fluid spheres, hydrodynamic and hydromagnetic stability of fluid flows, and configurations in gravitational equilibrium have been studied over a number of years, together with associated topics in plasma physics and mathematics. The publications arising from these studies are listed, and abstracts are presented for thirty-eight papers published. (D.C.W.)

The Pendulum: A Paradigm for the Linear Oscillator

ERIC Educational Resources Information Center

Newburgh, Ronald

2004-01-01

The simple pendulum is a model for the linear oscillator. The usual mathematical treatment of the problem begins with a differential equation that one solves with the techniques of the differential calculus, a formal process that tends to obscure the physics. In this paper we begin with a kinematic description of the motion obtained by experiment…

An Introduction to Equilibrium Thermodynamics. A Rational Approach to Its Teaching. Part 2: Internal Energy, Entropy, and Temperature.

ERIC Educational Resources Information Center

Williams, Donald F.; Glasser, David

1991-01-01

An approach that may be used to introduce the fundamental ideas of thermodynamics using a mathematical background with the knowledge of the behavior of matter is described. The physical background, conservation of energy, predicting the behavior of a system, and solving problems are topics of discussion. (KR)

Quantum correlations and dynamics from classical random fields valued in complex Hilbert spaces

DOE Office of Scientific and Technical Information (OSTI.GOV)

Khrennikov, Andrei

2010-08-15

One of the crucial differences between mathematical models of classical and quantum mechanics (QM) is the use of the tensor product of the state spaces of subsystems as the state space of the corresponding composite system. (To describe an ensemble of classical composite systems, one uses random variables taking values in the Cartesian product of the state spaces of subsystems.) We show that, nevertheless, it is possible to establish a natural correspondence between the classical and the quantum probabilistic descriptions of composite systems. Quantum averages for composite systems (including entangled) can be represented as averages with respect to classical randommore » fields. It is essentially what Albert Einstein dreamed of. QM is represented as classical statistical mechanics with infinite-dimensional phase space. While the mathematical construction is completely rigorous, its physical interpretation is a complicated problem. We present the basic physical interpretation of prequantum classical statistical field theory in Sec. II. However, this is only the first step toward real physical theory.« less

Motion of a Point Mass in a Rotating Disc: A Quantitative Analysis of the Coriolis and Centrifugal Force

NASA Astrophysics Data System (ADS)

Haddout, Soufiane

2016-06-01

In Newtonian mechanics, the non-inertial reference frames is a generalization of Newton's laws to any reference frames. While this approach simplifies some problems, there is often little physical insight into the motion, in particular into the effects of the Coriolis force. The fictitious Coriolis force can be used by anyone in that frame of reference to explain why objects follow curved paths. In this paper, a mathematical solution based on differential equations in non-inertial reference is used to study different types of motion in rotating system. In addition, the experimental data measured on a turntable device, using a video camera in a mechanics laboratory was conducted to compare with mathematical solution in case of parabolically curved, solving non-linear least-squares problems, based on Levenberg-Marquardt's and Gauss-Newton algorithms.

Tractable Experiment Design via Mathematical Surrogates

DOE Office of Scientific and Technical Information (OSTI.GOV)

Williams, Brian J.

This presentation summarizes the development and implementation of quantitative design criteria motivated by targeted inference objectives for identifying new, potentially expensive computational or physical experiments. The first application is concerned with estimating features of quantities of interest arising from complex computational models, such as quantiles or failure probabilities. A sequential strategy is proposed for iterative refinement of the importance distributions used to efficiently sample the uncertain inputs to the computational model. In the second application, effective use of mathematical surrogates is investigated to help alleviate the analytical and numerical intractability often associated with Bayesian experiment design. This approach allows formore » the incorporation of prior information into the design process without the need for gross simplification of the design criterion. Illustrative examples of both design problems will be presented as an argument for the relevance of these research problems.« less

What Is the Problem in Problem-Based Learning in Higher Education Mathematics

ERIC Educational Resources Information Center

Dahl, Bettina

2018-01-01

Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge…

Learning to Solve Story Problems--Supporting Transitions between Reality and Mathematics

ERIC Educational Resources Information Center

Große, Cornelia S.

2014-01-01

Applying mathematics to real problems is increasingly emphasized in school education; however, it is often complained that many students are not able to solve mathematical problems embedded in contexts. In order to solve story problems, a transition from a textual description to a mathematical notation has to be found, intra-mathematical…

Astrodynamics. Volume 1 - Orbit determination, space navigation, celestial mechanics.

NASA Technical Reports Server (NTRS)

Herrick, S.

1971-01-01

Essential navigational, physical, and mathematical problems of space exploration are covered. The introductory chapters dealing with conic sections, orientation, and the integration of the two-body problem are followed by an introduction to orbit determination and design. Systems of units and constants, as well as ephemerides, representations, reference systems, and data are then dealt with. A detailed attention is given to rendezvous problems and to differential processes in observational orbit correction, and in rendezvous or guidance correction. Finally, the Laplacian methods for determining preliminary orbits, and the orbit methods of Lagrange, Gauss, and Gibbs are reviewed.

Actuality of transcendental æsthetics for modern physics

NASA Astrophysics Data System (ADS)

Petitot, Jean

1. The more mathematics and physics unify themselves in the physico-mathematical modern theories, the more an objective epistemology becomes necessary. Only such a transcendental epistemology is able to thematize correctly the status of the mathematical determination of physical reality. 2. There exists a transcendental history of the synthetic a priori and of the construction of physical categories. 3. The transcendental approach allows to supersed Wittgenstein's and Carnap's antiplatonist thesis according to which pure mathematics are physically applicable only if they lack any descriptive, cognitive or objective, content and reduce to mere prescriptive and normative devices. In fact, pure mathematics are prescriptive-normative in physics because: (i) the categories of physical objectivity are prescriptive-normative, and (ii) their categorial content is mathematically “constructed” through a Transcendental Aesthetics. Only a transcendental approach make compatible, in the one hand, a grammatical conventionalism of Wittgensteinian or Carnapian type and, on the other hand, a platonist realism of Gödelian type. Mathematics are not a grammar of the world but a mathematical hermeneutics of the intuitive forms and of the categorial grammar of the world.

Mimetic finite difference method

NASA Astrophysics Data System (ADS)

Lipnikov, Konstantin; Manzini, Gianmarco; Shashkov, Mikhail

2014-01-01

The mimetic finite difference (MFD) method mimics fundamental properties of mathematical and physical systems including conservation laws, symmetry and positivity of solutions, duality and self-adjointness of differential operators, and exact mathematical identities of the vector and tensor calculus. This article is the first comprehensive review of the 50-year long history of the mimetic methodology and describes in a systematic way the major mimetic ideas and their relevance to academic and real-life problems. The supporting applications include diffusion, electromagnetics, fluid flow, and Lagrangian hydrodynamics problems. The article provides enough details to build various discrete operators on unstructured polygonal and polyhedral meshes and summarizes the major convergence results for the mimetic approximations. Most of these theoretical results, which are presented here as lemmas, propositions and theorems, are either original or an extension of existing results to a more general formulation using polyhedral meshes. Finally, flexibility and extensibility of the mimetic methodology are shown by deriving higher-order approximations, enforcing discrete maximum principles for diffusion problems, and ensuring the numerical stability for saddle-point systems.

Modeling Physical Systems Using Vensim PLE Systems Dynamics Software

NASA Astrophysics Data System (ADS)

Widmark, Stephen

2012-02-01

Many physical systems are described by time-dependent differential equations or systems of such equations. This makes it difficult for students in an introductory physics class to solve many real-world problems since these students typically have little or no experience with this kind of mathematics. In my high school physics classes, I address this problem by having my students use a variety of software solutions to model physical systems described by differential equations. These include spreadsheets, applets, software my students themselves create, and systems dynamics software. For the latter, cost is often the main issue in choosing a solution for use in a public school and so I researched no-cost software. I found Sphinx SD,2OptiSim,3 Systems Dynamics,4 Simile (Trial Edition),5 and Vensim PLE.6 In evaluating each of these solutions, I looked for the fewest restrictions in the license for educational use, ease of use by students, power, and versatility. In my opinion, Vensim PLE best fulfills these criteria.7

The place of probability in Hilbert's axiomatization of physics, ca. 1900-1928

NASA Astrophysics Data System (ADS)

Verburgt, Lukas M.

2016-02-01

Although it has become a common place to refer to the 'sixth problem' of Hilbert's (1900) Paris lecture as the starting point for modern axiomatized probability theory, his own views on probability have received comparatively little explicit attention. The central aim of this paper is to provide a detailed account of this topic in light of the central observation that the development of Hilbert's project of the axiomatization of physics went hand-in-hand with a redefinition of the status of probability theory and the meaning of probability. Where Hilbert first regarded the theory as a mathematizable physical discipline and later approached it as a 'vague' mathematical application in physics, he eventually understood probability, first, as a feature of human thought and, then, as an implicitly defined concept without a fixed physical interpretation. It thus becomes possible to suggest that Hilbert came to question, from the early 1920s on, the very possibility of achieving the goal of the axiomatization of probability as described in the 'sixth problem' of 1900.

Particle Physics, 2nd Edition

NASA Astrophysics Data System (ADS)

Martin, B. R.; Shaw, G.

1998-01-01

Particle Physics, Second Edition is a concise and lucid account of the fundamental constituents of matter. The standard model of particle physics is developed carefully and systematically, without heavy mathematical formalism, to make this stimulating subject accessible to undergraduate students. Throughout, the emphasis is on the interpretation of experimental data in terms of the basic properties of quarks and leptons, and extensive use is made of symmetry principles and Feynman diagrams, which are introduced early in the book. The Second Edition brings the book fully up to date, including the discovery of the top quark and the search for the Higgs boson. A final short chapter is devoted to the continuing search for new physics beyond the standard model. Particle Physics, Second Edition features: * A carefully structured and written text to help students understand this exciting and demanding subject. * Many worked examples and problems to aid student learning. Hints for solving the problems are given in an Appendix. * Optional "starred" sections and appendices, containing more specialised and advanced material for the more ambitious reader.

Physical Principle for Generation of Randomness

NASA Technical Reports Server (NTRS)

Zak, Michail

2009-01-01

A physical principle (more precisely, a principle that incorporates mathematical models used in physics) has been conceived as the basis of a method of generating randomness in Monte Carlo simulations. The principle eliminates the need for conventional random-number generators. The Monte Carlo simulation method is among the most powerful computational methods for solving high-dimensional problems in physics, chemistry, economics, and information processing. The Monte Carlo simulation method is especially effective for solving problems in which computational complexity increases exponentially with dimensionality. The main advantage of the Monte Carlo simulation method over other methods is that the demand on computational resources becomes independent of dimensionality. As augmented by the present principle, the Monte Carlo simulation method becomes an even more powerful computational method that is especially useful for solving problems associated with dynamics of fluids, planning, scheduling, and combinatorial optimization. The present principle is based on coupling of dynamical equations with the corresponding Liouville equation. The randomness is generated by non-Lipschitz instability of dynamics triggered and controlled by feedback from the Liouville equation. (In non-Lipschitz dynamics, the derivatives of solutions of the dynamical equations are not required to be bounded.)

Magnetohydrodynamics Carreau nanofluid flow over an inclined convective heated stretching cylinder with Joule heating

NASA Astrophysics Data System (ADS)

Khan, Imad; Shafquatullah; Malik, M. Y.; Hussain, Arif; Khan, Mair

Current work highlights the computational aspects of MHD Carreau nanofluid flow over an inclined stretching cylinder with convective boundary conditions and Joule heating. The mathematical modeling of physical problem yields nonlinear set of partial differential equations. A suitable scaling group of variables is employed on modeled equations to convert them into non-dimensional form. The integration scheme Runge-Kutta-Fehlberg on the behalf of shooting technique is utilized to solve attained set of equations. The interesting aspects of physical problem (linear momentum, energy and nanoparticles concentration) are elaborated under the different parametric conditions through graphical and tabular manners. Additionally, the quantities (local skin friction coefficient, local Nusselt number and local Sherwood number) which are responsible to dig out the physical phenomena in the vicinity of stretched surface are computed and delineated by varying controlling flow parameters.

Individualized Math Problems in Percent. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. This volume includes problems concerned with computing percents.…

Individualized Math Problems in Algebra. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic, and contains problems related to diverse vocations. Solutions are provided for all problems. Problems presented in this package concern ratios used in food…

Individualized Math Problems in Fractions. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. This package contains problems involving computation with common…

Individualized Math Problems in Geometry. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. The volume contains problems in applied geometry. Measurement of…

Individualized Math Problems in Measurement and Conversion. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. This volume includes problems involving measurement, computation of…

Individualized Math Problems in Integers. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. This volume presents problems involving operations with positive and…

Astrophysical Flows

NASA Astrophysics Data System (ADS)

Pringle, James E.; King, Andrew

2003-07-01

Almost all conventional matter in the Universe is fluid, and fluid dynamics plays a crucial role in astrophysics. This new graduate textbook provides a basic understanding of the fluid dynamical processes relevant to astrophysics. The mathematics used to describe these processes is simplified to bring out the underlying physics. The authors cover many topics, including wave propagation, shocks, spherical flows, stellar oscillations, the instabilities caused by effects such as magnetic fields, thermal driving, gravity, shear flows, and the basic concepts of compressible fluid dynamics and magnetohydrodynamics. The authors are Directors of the UK Astrophysical Fluids Facility (UKAFF) at the University of Leicester, and editors of the Cambridge Astrophysics Series. This book has been developed from a course in astrophysical fluid dynamics taught at the University of Cambridge. It is suitable for graduate students in astrophysics, physics and applied mathematics, and requires only a basic familiarity with fluid dynamics.• Provides coverage of the fundamental fluid dynamical processes an astrophysical theorist needs to know • Introduces new mathematical theory and techniques in a straightforward manner • Includes end-of-chapter problems to illustrate the course and introduce additional ideas

Engineering Education in K-12 Schools

NASA Astrophysics Data System (ADS)

Spence, Anne

2013-03-01

Engineers rely on physicists as well as other scientists and mathematicians to explain the world in which we live. Engineers take this knowledge of the world and use it to create the world that never was. The teaching of physics and other sciences as well as mathematics is critical to maintaining our national workforce. Science and mathematics education are inherently different, however, from engineering education. Engineering educators seek to enable students to develop the habits of mind critical for innovation. Through understanding of the engineering design process and how it differs from the scientific method, students can apply problem and project based learning to solve the challenges facing society today. In this talk, I will discuss the elements critical to a solid K-12 engineering education that integrates science and mathematics to solve challenges throughout the world.

Mathematical Reasoning Requirements in Swedish National Physics Tests

ERIC Educational Resources Information Center

Johansson, Helena

2016-01-01

This paper focuses on one aspect of mathematical competence, namely mathematical reasoning, and how this competency influences students' knowing of physics. This influence was studied by analysing the mathematical reasoning requirements upper secondary students meet when solving tasks in national physics tests. National tests are constructed to…

Towards a physics on fractals: Differential vector calculus in three-dimensional continuum with fractal metric

NASA Astrophysics Data System (ADS)

Balankin, Alexander S.; Bory-Reyes, Juan; Shapiro, Michael

2016-02-01

One way to deal with physical problems on nowhere differentiable fractals is the mapping of these problems into the corresponding problems for continuum with a proper fractal metric. On this way different definitions of the fractal metric were suggested to account for the essential fractal features. In this work we develop the metric differential vector calculus in a three-dimensional continuum with a non-Euclidean metric. The metric differential forms and Laplacian are introduced, fundamental identities for metric differential operators are established and integral theorems are proved by employing the metric version of the quaternionic analysis for the Moisil-Teodoresco operator, which has been introduced and partially developed in this paper. The relations between the metric and conventional operators are revealed. It should be emphasized that the metric vector calculus developed in this work provides a comprehensive mathematical formalism for the continuum with any suitable definition of fractal metric. This offers a novel tool to study physics on fractals.

Attitude Towards Physics and Additional Mathematics Achievement Towards Physics Achievement

ERIC Educational Resources Information Center

Veloo, Arsaythamby; Nor, Rahimah; Khalid, Rozalina

2015-01-01

The purpose of this research is to identify the difference in students' attitude towards Physics and Additional Mathematics achievement based on gender and relationship between attitudinal variables towards Physics and Additional Mathematics achievement with achievement in Physics. This research focused on six variables, which is attitude towards…

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

NASA Astrophysics Data System (ADS)

Shadid, J. N.; Smith, T. M.; Cyr, E. C.; Wildey, T. M.; Pawlowski, R. P.

2016-09-01

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts to apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier-Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shadid, J.N., E-mail: jnshadi@sandia.gov; Department of Mathematics and Statistics, University of New Mexico; Smith, T.M.

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts tomore » apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.« less

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

DOE Office of Scientific and Technical Information (OSTI.GOV)

Shadid, J. N.; Smith, T. M.; Cyr, E. C.

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. The understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In our study we report on initial efforts to apply integrated adjoint-basedmore » computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. We present the initial results that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.« less

Stabilized FE simulation of prototype thermal-hydraulics problems with integrated adjoint-based capabilities

DOE PAGES

Shadid, J. N.; Smith, T. M.; Cyr, E. C.; ...

2016-05-20

A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. The understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In our study we report on initial efforts to apply integrated adjoint-basedmore » computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier–Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. We present the initial results that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.« less

Improving mathematical problem solving ability through problem-based learning and authentic assessment for the students of Bali State Polytechnic

NASA Astrophysics Data System (ADS)

Darma, I. K.

2018-01-01

This research is aimed at determining: 1) the differences of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) the differences of mathematical problem solving ability between the students facilitated with authentic and conventional assessment model, and 3) interaction effect between learning and assessment model on mathematical problem solving. The research was conducted in Bali State Polytechnic, using the 2x2 experiment factorial design. The samples of this research were 110 students. The data were collected using a theoretically and empirically-validated test. Instruments were validated by using Aiken’s approach of technique content validity and item analysis, and then analyzed using anova stylistic. The result of the analysis shows that the students facilitated with problem-based learning and authentic assessment models get the highest score average compared to the other students, both in the concept understanding and mathematical problem solving. The result of hypothesis test shows that, significantly: 1) there is difference of mathematical problem solving ability between the students facilitated with problem-based learning model and conventional learning model, 2) there is difference of mathematical problem solving ability between the students facilitated with authentic assessment model and conventional assessment model, and 3) there is interaction effect between learning model and assessment model on mathematical problem solving. In order to improve the effectiveness of mathematics learning, collaboration between problem-based learning model and authentic assessment model can be considered as one of learning models in class.

What is the problem in problem-based learning in higher education mathematics

NASA Astrophysics Data System (ADS)

Dahl, Bettina

2018-01-01

Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge where the application in society is not always obvious. Does mathematics, including pure mathematics, fit into a PBL curriculum? This paper argues that it does for two reasons: (1) PBL resembles the working methods of research mathematicians. (2) The concept of society includes the society of researchers to whom theoretical mathematics is relevant. The paper describes two cases of university PBL projects in mathematics; one in pure mathematics and the other in applied mathematics. The paper also discusses that future engineers need to understand the world of mathematics as well as how engineers fit into a process of fundamental-research-turned-into-applied-science.

High School Class for Gifted Pupils in Physics and Sciences and Pupils' Skills Measured by Standard and Pisa Test

NASA Astrophysics Data System (ADS)

Djordjevic, G. S.; Pavlovic-Babic, D.

2010-01-01

The "High school class for students with special abilities in physics" was founded in Nis, Serbia (www.pmf.ni.ac.yu/f_odeljenje) in 2003. The basic aim of this project has been introducing a broadened curriculum of physics, mathematics, computer science, as well as chemistry and biology. Now, six years after establishing of this specialized class, and 3 years after the previous report, we present analyses of the pupils' skills in solving rather problem oriented test, as PISA test, and compare their results with the results of pupils who study under standard curricula. More precisely results are compared to the progress results of the pupils in a standard Grammar School and the corresponding classes of the Mathematical Gymnasiums in Nis. Analysis of achievement data should clarify what are benefits of introducing in school system track for gifted students. Additionally, item analysis helps in understanding and improvement of learning strategies' efficacy. We make some conclusions and remarks that may be useful for the future work that aims to increase pupils' intrinsic and instrumental motivation for physics and sciences, as well as to increase the efficacy of teaching physics and science.

Protocol Analysis of Group Problem Solving in Mathematics: A Cognitive-Metacognitive Framework for Assessment.

ERIC Educational Resources Information Center

Artzt, Alice F.; Armour-Thomas, Eleanor

The roles of cognition and metacognition were examined in the mathematical problem-solving behaviors of students as they worked in small groups. As an outcome, a framework that links the literature of cognitive science and mathematical problem solving was developed for protocol analysis of mathematical problem solving. Within this framework, each…

Mathematical Profiles and Problem Solving Abilities of Mathematically Promising Students

ERIC Educational Resources Information Center

Budak, Ibrahim

2012-01-01

Mathematically promising students are defined as those who have the potential to become the leaders and problem solvers of the future. The purpose of this research is to reveal what problem solving abilities mathematically promising students show in solving non-routine problems and type of profiles they present in the classroom and during problem…

Engaging Future Teachers in Problem-Based Learning with the Park City Mathematics Institute Problems

ERIC Educational Resources Information Center

Pilgrim, Mary E.

2014-01-01

Problem-based learning (PBL) is a pedagogical technique recommended for K-12 mathematics classrooms. However, the mathematics courses in future teachers' degree programs are often lecture based. Students typically learn about problem-based learning in theory, but rarely get to experience it first-hand in their mathematics courses. The premise…

Investigating and Developing Engineering Students' Mathematical Modelling and Problem-Solving Skills

ERIC Educational Resources Information Center

Wedelin, Dag; Adawi, Tom; Jahan, Tabassum; Andersson, Sven

2015-01-01

How do engineering students approach mathematical modelling problems and how can they learn to deal with such problems? In the context of a course in mathematical modelling and problem solving, and using a qualitative case study approach, we found that the students had little prior experience of mathematical modelling. They were also inexperienced…

Mathematics Student Teachers' Modelling Approaches While Solving the Designed Esme Rug Problem

ERIC Educational Resources Information Center

Hidiroglu, Çaglar Naci; Dede, Ayse Tekin; Ünver, Semiha Kula; Güzel, Esra Bukova

2017-01-01

The purpose of the study is to analyze the mathematics student teachers' solutions on the Esme Rug Problem through 7-stage mathematical modelling process. This problem was designed by the researchers by considering the modelling problems' main properties. The study was conducted with twenty one secondary mathematics student teachers. The data were…

Developing Instruction Materials Based on Joyful PBL to Improve Students Mathematical Representation Ability

ERIC Educational Resources Information Center

Minarni, Ani; Napitupulu, E. Elvis

2017-01-01

Solving problem either within mathematics or beyond is one of the ultimate goal students learn mathematics. It is since mathematics takes role tool as well as vehicle to develop problem solving ability. One of the supporting components to problem solving is mathematical representation ability (MRA). Nowadays, many teachers and researchers find out…

Using the Wonder of Inequalities between Averages for Mathematics Problems Solving

ERIC Educational Resources Information Center

Shaanan, Rachel Mogilevsky; Gordon, Moshe Stupel

2016-01-01

The study presents an introductory idea of using mathematical averages as a tool for enriching mathematical problem solving. Throughout students' activities, a research was conducted on their ability to solve mathematical problems, and how to cope with a variety of mathematical tasks, in a variety of ways, using the skills, tools and experiences…

A Critical Discourse Analysis of Practical Problems in a Foundation Mathematics Course at a South African University

ERIC Educational Resources Information Center

le Roux, Kate; Adler, Jill

2016-01-01

Mathematical problems that make links to the everyday and to disciplines other than mathematics--variously referred to as practical, realistic, real-world or applied problems in the literature--feature in school and undergraduate mathematics reforms aimed at increasing mathematics participation in contexts of inequity and diversity. In this…

An Examination of Pre-Service Mathematics Teachers' Approaches to Construct and Solve Mathematical Modelling Problems

ERIC Educational Resources Information Center

Bukova-Guzel, Esra

2011-01-01

This study examines the approaches displayed by pre-service mathematics teachers in their experiences of constructing mathematical modelling problems and the extent to which they perform the modelling process when solving the problems they construct. This case study was carried out with 35 pre-service teachers taking the Mathematical Modelling…

STEM education and Fermi problems

NASA Astrophysics Data System (ADS)

Holubova, Renata

2017-01-01

One of the research areas of Physics education is the study of the educational process. Investigations in this area are aimed for example on the teaching and learning process and its results. The conception of STEM education (Science, Technology, Engineering, and Mathematics) is discussed - it is one possible approach to the preparation of the curriculum and the focus on the educational process at basic and secondary schools. At schools in the Czech Republic STEM is much more realized by the application of interdisciplinary relations between subjects Physics-Nature-Technique. In both conceptions the aim is to support pupils' creativity, critical thinking, cross-curricular links. In this context the possibility of using Fermi problems in teaching Physics was discussed (as an interdisciplinary and constructivist activity). The aim of our research was the analysis of Fermi problems solving strategies, the ability of pupils to solve Fermi problems. The outcome of our analysis was to find out methods and teaching strategies which are important to use in teaching - how to solve qualitative and interdisciplinary tasks in physics. In this paper the theoretical basis of STEM education and Fermi problems will be presented. The outcome of our findings based on the research activities will be discussed so as our experiences from 10 years of Fermi problems competition that takes place at the Science Faculty, Palacky University in Olomouc. Changes in competencies of solving tasks by our students (from the point of view in terms of modern, activating teaching methods recommended by theory of Physics education and other science subjects) will be identified.

The limitations of mathematical modeling in high school physics education

NASA Astrophysics Data System (ADS)

Forjan, Matej

The theme of the doctoral dissertation falls within the scope of didactics of physics. Theoretical analysis of the key constraints that occur in the transmission of mathematical modeling of dynamical systems into field of physics education in secondary schools is presented. In an effort to explore the extent to which current physics education promotes understanding of models and modeling, we analyze the curriculum and the three most commonly used textbooks for high school physics. We focus primarily on the representation of the various stages of modeling in the solved tasks in textbooks and on the presentation of certain simplifications and idealizations, which are in high school physics frequently used. We show that one of the textbooks in most cases fairly and reasonably presents the simplifications, while the other two half of the analyzed simplifications do not explain. It also turns out that the vast majority of solved tasks in all the textbooks do not explicitly represent model assumptions based on what we can conclude that in high school physics the students do not develop sufficiently a sense of simplification and idealizations, which is a key part of the conceptual phase of modeling. For the introduction of modeling of dynamical systems the knowledge of students is also important, therefore we performed an empirical study on the extent to which high school students are able to understand the time evolution of some dynamical systems in the field of physics. The research results show the students have a very weak understanding of the dynamics of systems in which the feedbacks are present. This is independent of the year or final grade in physics and mathematics. When modeling dynamical systems in high school physics we also encounter the limitations which result from the lack of mathematical knowledge of students, because they don't know how analytically solve the differential equations. We show that when dealing with one-dimensional dynamical systems geometrical approach to solving differential equations is appropriate, while in dynamical systems of higher dimensions mathematical constraints are avoided by using a graphical oriented programs for modeling. Because in dealing with dynamical systems with four or more dimensions we may encounter problems in numerical solving, we also show how to overcome them. In the case of electrostatic pendulum we show the process of modeling the real dynamical system and we put a particular emphasize on the different phases of modeling and on the way of overcoming constraints on which we encounter in the development of the model.

Can Television Enhance Children's Mathematical Problem Solving?

ERIC Educational Resources Information Center

Fisch, Shalom M.; And Others

1994-01-01

A summative evaluation of "Square One TV," an educational mathematics series produced by the Children's Television Workshop, shows that children who regularly viewed the program showed significant improvement in solving unfamiliar, complex mathematical problems, and viewers showed improvement in their mathematical problem-solving ability…

A Strategy for Improving US Middle School Student Mathematics Word Problem Solving Performance

NASA Technical Reports Server (NTRS)

Thomas, Valerie L.

2004-01-01

U.S. middle school students have difficulty understanding and solving mathematics word problems. Their mathematics performance on the Third International Mathematics and Science Study (TIMMS) is far below their international peers, and minority students are less likely than high socioeconomic status (SES) White/Asian students to be exposed to higher-level mathematics concepts. Research literature also indicates that when students use both In-School and Out-of-School knowledge and experiences to create authentic mathematics word problems, student achievement improves. This researcher developed a Strategy for improving mathematics problem solving performance and a Professional Development Model (PDM) to effectively implement the Strategy.

An Investigation of Secondary Teachers’ Understanding and Belief on Mathematical Problem Solving

NASA Astrophysics Data System (ADS)

Yuli Eko Siswono, Tatag; Wachidul Kohar, Ahmad; Kurniasari, Ika; Puji Astuti, Yuliani

2016-02-01

Weaknesses on problem solving of Indonesian students as reported by recent international surveys give rise to questions on how Indonesian teachers bring out idea of problem solving in mathematics lesson. An explorative study was undertaken to investigate how secondary teachers who teach mathematics at junior high school level understand and show belief toward mathematical problem solving. Participants were teachers from four cities in East Java province comprising 45 state teachers and 25 private teachers. Data was obtained through questionnaires and written test. The results of this study point out that the teachers understand pedagogical problem solving knowledge well as indicated by high score of observed teachers‘ responses showing understanding on problem solving as instruction as well as implementation of problem solving in teaching practice. However, they less understand on problem solving content knowledge such as problem solving strategies and meaning of problem itself. Regarding teacher's difficulties, teachers admitted to most frequently fail in (1) determining a precise mathematical model or strategies when carrying out problem solving steps which is supported by data of test result that revealed transformation error as the most frequently observed errors in teachers’ work and (2) choosing suitable real situation when designing context-based problem solving task. Meanwhile, analysis of teacher's beliefs on problem solving shows that teachers tend to view both mathematics and how students should learn mathematics as body static perspective, while they tend to believe to apply idea of problem solving as dynamic approach when teaching mathematics.

Mathematical Sense-Making in Quantum Mechanics: An Initial Peek

ERIC Educational Resources Information Center

Dreyfus, Benjamin W.; Elby, Andrew; Gupta, Ayush; Sohr, Erin Ronayne

2017-01-01

Mathematical sense-making--looking for coherence between the structure of the mathematical formalism and causal or functional relations in the world--is a core component of physics expertise. Some physics education research studies have explored what mathematical sense-making looks like at the introductory physics level, while some historians and…

Individualized Math Problems in Ratio and Proportion. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. This volume contains problems involving ratio and proportion. Some…

Individualized Math Problems in Whole Numbers. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this set require computations involving whole numbers.…

Individualized Math Problems in Graphs and Tables. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems involving the construction and interpretation of graphs and…

Individualized Math Problems in Simple Equations. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this volume require solution of linear equations, systems…

Individualized Math Problems in Trigonometry. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this volume require the use of trigonometric and inverse…

Individualized Math Problems in Decimals. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

THis is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this volume concern use of decimals and are related to the…

Individualized Math Problems in Volume. Oregon Vo-Tech Mathematics Problem Sets.

ERIC Educational Resources Information Center

Cosler, Norma, Ed.

This is one of eighteen sets of individualized mathematics problems developed by the Oregon Vo-Tech Math Project. Each of these problem packages is organized around a mathematical topic and contains problems related to diverse vocations. Solutions are provided for all problems. Problems in this booklet require the computation of volumes of solids,…

Applications of Differential Operators in Geodetic Coordinates

NASA Astrophysics Data System (ADS)

Hallam, K. A. T.; Oliveira, V. C., Jr.

2016-12-01

The definition of coordinate systems and frames is an essential step to even start a problem in physical geodesy and geophysics. The commonly used coordinate systems when dealing with problems on (or close to) the surface of the Earth are the geocentric Cartesian coordinates, geocentric spherical coordinates and geodetic coordinates. Transformations between Cartesian and spherical coordinates are widely known and used for several problems. More complex, but not less important, are the transformations between Cartesian and geodetic coordinates. Although most of them utilize an ellipsoidal frame in which the three coordinates are geodetic longitude (λ), geodetic latitude (φ) and the scale factor (u), the latter being a combination of X and Y, not the geometric height (h), the data sets measured on (or close to) the surface of the Earth are given in geodetic coordinates which are usually transformed into Cartesian or spherical coordinates for mathematical developments. It would be useful, however, to preclude coordinate transformations for the subsequent operations. Thus, we derived expressions for the gradient and Laplacian operators in geodetic coordinates in order to make further use on mathematical developments. Results obtained analitically and from numerical simulations validate our expressions. We applied our operators to derive the gravitational field produced by a point mass and used it for representing the regional gravity field in geodetic coordinates. The results obtained with the numerical simulations show that our approach is potentially useful in solving a wide range of problems in physical geodesy and geophysics.

75 FR 29369 - Advisory Committee for Mathematical and Physical Sciences; Notice of Meeting

Federal Register 2010, 2011, 2012, 2013, 2014

2010-05-25

... NATIONAL SCIENCE FOUNDATION Advisory Committee for Mathematical and Physical Sciences; Notice of... Science Foundation announces the following meeting: Name: Directorate for Mathematical and Physical... Physical Sciences, Room 1005, National Science Foundation, 4201 Wilson Boulevard, Arlington, VA 22230. (703...

The implementation of multiple intelligences based teaching model to improve mathematical problem solving ability for student of junior high school

NASA Astrophysics Data System (ADS)

Fasni, Nurli; Fatimah, Siti; Yulanda, Syerli

2017-05-01

This research aims to achieve some purposes such as: to know whether mathematical problem solving ability of students who have learned mathematics using Multiple Intelligences based teaching model is higher than the student who have learned mathematics using cooperative learning; to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using Multiple Intelligences based teaching model., to know the improvement of the mathematical problem solving ability of the student who have learned mathematics using cooperative learning; to know the attitude of the students to Multiple Intelligences based teaching model. The method employed here is quasi-experiment which is controlled by pre-test and post-test. The population of this research is all of VII grade in SMP Negeri 14 Bandung even-term 2013/2014, later on two classes of it were taken for the samples of this research. A class was taught using Multiple Intelligences based teaching model and the other one was taught using cooperative learning. The data of this research were gotten from the test in mathematical problem solving, scale questionnaire of the student attitudes, and observation. The results show the mathematical problem solving of the students who have learned mathematics using Multiple Intelligences based teaching model learning is higher than the student who have learned mathematics using cooperative learning, the mathematical problem solving ability of the student who have learned mathematics using cooperative learning and Multiple Intelligences based teaching model are in intermediate level, and the students showed the positive attitude in learning mathematics using Multiple Intelligences based teaching model. As for the recommendation for next author, Multiple Intelligences based teaching model can be tested on other subject and other ability.

PREFACE: Physics-Based Mathematical Models for Nanotechnology

NASA Astrophysics Data System (ADS)

Voon, Lok C. Lew Yan; Melnik, Roderick; Willatzen, Morten

2008-03-01

In November 2007, some of the world's best nanoscientists and nanoengineers met at the Banff Centre, where the Banff International Research Station hosted a workshop on recent developments in the mathematical study of the physics of nanomaterials and nanostructures. The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located in a scenic part of Alberta, Canada and is supported by Canada's Natural Science and Engineering Research Council (NSERC), the US National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). We would like to thank the BIRS and its sponsors for the given opportunity and the BIRS staff for their excellent support during the workshop. Nanotechnology is the study and application of phenomena at or below the dimensions of 100 nm and has received a lot of public attention following popular accounts such as in the bestselling book by Michael Crichton, Prey. It is an area where fundamental questions of applied mathematics and mathematical physics, design of computational methodologies, physical insight, engineering and experimental techniques are meeting together in a quest for an adequate description of nanomaterials and nanostructures for applications in optoelectronics, medicine, energy-saving, bio- and other key technologies which will profoundly influence our life in the 21st century and beyond. There are already hundreds of applications in daily life such as in cosmetics and the hard drives in MP3 players (the 2007 Nobel prize in physics was recently awarded for the science that allowed the miniaturization of the drives), delivering drugs, high-definition DVD players and stain-resistant clothing, but with thousands more anticipated. The focus of this interdisciplinary workshop was on determining what kind of new theoretical and computational tools will be needed to advance the science and engineering of nanomaterials and nanostructures. Thanks to the stimulating environment of the BIRS, participants of the workshop had plenty of opportunity to exchange new ideas on one of the main topics of this workshop—physics-based mathematical models for the description of low-dimensional semiconductor nanostructures (LDSNs) that are becoming increasingly important in technological innovations. The main objective of the workshop was to bring together some of the world leading experts in the field from each of the key research communities working on different aspects of LDSNs in order to (a) summarize the state-of-the-art models and computational techniques for modeling LDSNs, (b) identify critical problems of major importance that require solution and prioritize them, (c) analyze feasibility of existing mathematical and computational methodologies for the solution of some such problems, and (d) use some of the workshop working sessions to explore promising approaches in addressing identified challenges. With the possibility of growing practically any shape and size of heterostructures, it becomes essential to understand the mathematical properties of quantum-confined structures including properties of bulk states, interface states, and surface states as a function of shape, size, and internal strain. This workshop put strong emphasis on discussions of the new mathematics needed in nanotechnology especially in relation to geometry and material-combination optimization of device properties such as electronic, optical, and magnetic properties. The problems that were addressed at this meeting are of immense importance in determining such quantum-mechanical properties and the group of invited participants covered very well all the relevant disciplines in the cross-disciplinary research area: low-dimensional semiconductor nanostructures. Since the main properties of two-dimensional heterostructures (such as quantum wells) are now quite well understood, there has been a consistently growing interest in the mathematical physics community to further dimensionality reduction of semiconductor structures. Experimental achievements in realizing one-dimensional and quasi-zero-dimensional heterostructures have opened new opportunities for theory and applications of such low-dimensional semiconductor nanostructures. One of the most important implications of this process has been a critical re-examining of assumptions under which traditional quantum mechanical models have been derived in this field. Indeed, the formation of LDSNs, in particular quantum dots, is a competition between the surface energy in the structure and strain energy. However, current models for bandstructure calculations use quite a simplified analysis of strain relaxation effects, although such effects are in the heart of nanostructure formation. By now, it has been understood that traditional models in this field may not be adequate for modeling realistic objects based on LDSNs due to neglecting many effects that may profoundly influence optoelectronic properties of the nanostructures. Among such effects are electromechanical effects, including strain relaxation, piezoelectric effect, spontaneous polarization, and higher order nonlinear effects. Up to date, major efforts have been concentrated on the analysis of idealized, isolated quantum dots, while a typical self-assembled semiconductor quantum dot nanostructure is an array (or a molecule) of many individual quantum dots sitting on the same `substrate' known as the wetting layer. Each such dot contains several hundred thousand atoms. In order to account for quantum effects accurately in a situation like that, attempts can be made to apply ab initio or atomistic methodologies, but then one would face a task of enormous computational complexity in solving a large-scale many-body problem. On the other hand, taking each quantum dot in isolation would lead to a manageable task for modern supercomputers, but accounting for the wetting layer even in the individual quantum dot model would increase the computational complexity of the problem in several times. As a result, the entire problem in its generality would be hardly feasible from a practical, routine-based simulation, point of view. Moreover, in calculating atomic positions the definitions of atomic forces that enter the Hamiltonian in such large scale atomic simulations are approximate by nature and a number of important coupled effects, such as piezoelectric, remain frequently outside the scope of the analysis. To attack the problem in hand, one needs to resort to some clever averaging over atomic scales. Such averaging can be achieved by empirical tight-binding, pseudopotential, and k.p approximations. These approximations are very important in further development of mathematical models for LDSNs due to the fact they are well suited for incorporating additional effects into the model, including strain, piezoelectric effects, spontaneous polarization, geometric and materials nonlinearities. These effects, despite their importance, have not been studied with vigor they deserve, in particular in the context of mathematical models for bandstructure calculations. There is a growing interest to such models as they should provide a key to better predicting optoelectromechanical properties of LDSNs. With anticipated new discoveries in theoretical and experimental analysis of LDSNs in the coming years, one of the main emphases of the workshop was on the models that would allow incorporating these effects consistently into the state-of-the-art models for LDSNs. From a mathematical point of view, many such models can be reduced to a large eigenvalue PDE problem (e.g., with the Hamiltonian accounting for the Burt-Foreman correction) coupled to strain and piezoelectric potential calculation. In its turn, in its general setting the problem of strain and piezoelectric potential calculation requires the solution of a nonlinear system of partial differential equation. A large experience in solving these two parts of the problem separately, independently of each other, has been already accumulated in the distinct communities of the researchers. This BIRS workshop effectively combined expertise of these research communities, summarized the state-of-the-art for modeling LDSNs and key challenges facing these communities, and explored ways to address those challenges in interdisciplinary team settings. The workshop brought together researchers working on different aspects of the analysis and modeling of LDSNs which require a concerted efforts of teams of researchers with close interactions between applied and pure mathematicians, physicists (theoreticians and experimentalists), computational scientists, and engineers. These scientific and engineering communities were represented in Banff by the researchers from Japan, Canada, the USA, Russia, France, Denmark, Germany, and the UK (further details can be found at http://www.m2netlab.wlu.ca/ldsn-banff/). We had four main plenary talks of one hour duration that gave state-of-the-art overviews of the subject from perspectives of applied mathematics (Professor Russel Caflisch of the University of California at Los Angeles), physics (Professor Antti-Pekka Jauho of the Danish Technical University), and computational science and engineering communities (Professor Gerhard Klimeck of Purdue University), as well as from a point of view of experimentalists (Dr Gail Brown of the Materials Lab/Air Force Research Lab at Wright-Patterson AFB). These talks helped identify the areas where joint efforts needed to be directed to, and they set up the scene for further work during the workshop, including discussions at the workshop open problem sessions. All participants had time to present their research and a specific time was allocated for on-site demonstrations of software and explanations of tools applied in the LDSN analysis. This special issue provides a flavor of the problems discussed at the workshop. It contains 12 refereed papers. Additional information, including the abstracts of all presented talks, can be found at http://www.m2netlab.wlu.ca/ldsn-banff/. Using this opportunity, we would like to thank the referees of this volume for their time and efforts. Without their timely professional comments this volume would not have been made possible. In conclusion, we note that advances in mathematics, physics and computation of LDSNs, impact such seemingly distant applications as biotechnology and medicine, quantum information processing and optoelectronics. The research into LDSNs offered exciting new challenges that are intrinsically interdisciplinary in nature and should be addressed by a multidisciplinary team of applied mathematicians, theoretical and experimental physicists, engineers and computational scientists. We hope that we are able to pass this idea to the reader. Lok C Lew Yan Voon(Wright State University, OH, USA) Roderick Melnik(M2NeT Lab, Wilfrid Laurier University, ON, Canada) Morten Willatzen(MCI, University of Southern Denmark, Denmark)

On the Role of Mathematics in Physics

ERIC Educational Resources Information Center

Quale, Andreas

2011-01-01

I examine the association between the observable physical world and the mathematical models of theoretical physics. These models will exhibit many entities that have no counterpart in the physical world, but which are still necessary for the mathematical description of physical systems. Moreover, when the model is applied to the analysis of a…

Building a Career Mathematics File: Challenging Students to Find the Importance of Mathematics in a Variety of Occupations

ERIC Educational Resources Information Center

Keleher, Lori A.

2006-01-01

The Career Mathematics file is an occupational problem-solving system, which includes a wide range of mathematical problems and solutions, collected from various resources and helps students establish connections between mathematics and their environment. The study shows that the problems given can be used as realistic examples to study and…

An Investigation of Relationships between Students' Mathematical Problem-Posing Abilities and Their Mathematical Content Knowledge

ERIC Educational Resources Information Center

Van Harpen, Xianwei Y.; Presmeg, Norma C.

2013-01-01

The importance of students' problem-posing abilities in mathematics has been emphasized in the K-12 curricula in the USA and China. There are claims that problem-posing activities are helpful in developing creative approaches to mathematics. At the same time, there are also claims that students' mathematical content knowledge could be highly…

New Existence Conditions for Order Complementarity Problems

NASA Astrophysics Data System (ADS)

Németh, S. Z.

2009-09-01

Complementarity problems are mathematical models of problems in economics, engineering and physics. A special class of complementarity problems are the order complementarity problems [2]. Order complementarity problems can be applied in lubrication theory [6] and economics [1]. The notion of exceptional family of elements for general order complementarity problems in Banach spaces will be introduced. It will be shown that for general order complementarity problems defined by completely continuous fields the problem has either a solution or an exceptional family of elements (for other notions of exceptional family of elements see [1, 2, 3, 4] and the related references therein). This solves a conjecture of [2] about the existence of exceptional family of elements for order complementarity problems. The proof can be done by using the Leray-Schauder alternative [5]. An application to integral operators will be given.

Creativity and Mathematical Problem Posing: An Analysis of High School Students' Mathematical Problem Posing in China and the USA

ERIC Educational Resources Information Center

Van Harpen, Xianwei Y.; Sriraman, Bharath

2013-01-01

In the literature, problem-posing abilities are reported to be an important aspect/indicator of creativity in mathematics. The importance of problem-posing activities in mathematics is emphasized in educational documents in many countries, including the USA and China. This study was aimed at exploring high school students' creativity in…

Recent Trends in Japanese Mathematics Textbooks for Elementary Grades: Supporting Teachers to Teach Mathematics through Problem Solving

ERIC Educational Resources Information Center

Takahashi, Akihiko

2016-01-01

Problem solving has been a major theme in Japanese mathematics curricula for nearly 50 years. Numerous teacher reference books and lesson plans using problem solving have been published since the 1960s. Government-authorized mathematics textbooks for elementary grades, published by six private companies, have had more and more problem solving over…

The way adults with orientation to mathematics teaching cope with the solution of everyday real-world problems

NASA Astrophysics Data System (ADS)

Gazit, Avikam; Patkin, Dorit

2012-03-01

The article aims to check the way adults, some who are practicing mathematics teachers at elementary school, some who are academicians making a career change to mathematics teachers at junior high school and the rest who are pre-service mathematics teachers at elementary school, cope with the solution of everyday real-world problems of buying and selling. The findings show that even adults with mathematical background tend to make mistakes in solving everyday real-world problems. Only about 70% of the adults who have an orientation to mathematics solved the sample problem correctly. The lowest percentage of success was demonstrated by the academicians making a career change to junior high school mathematics teachers whereas the highest percentage of success was manifested by pre-service elementary school mathematics teachers. Moreover, the findings illustrate that life experience of the practicing mathematics teachers and, mainly, of the academicians making a career change, who were older than the pre-service teachers, did not facilitate the solution of such a real-world problem. Perhaps the reason resides in the process of mathematics teaching at school, which does not put an emphasis on the solution of everyday real-world problems.

Workshop Physics Activity Guide, Module 4: Electricity and Magnetism

NASA Astrophysics Data System (ADS)

Laws, Priscilla W.

2004-05-01

The Workshop Physics Activity Guide is a set of student workbooks designed to serve as the foundation for a two-semester calculus-based introductory physics course. It consists of 28 units that interweave text materials with activities that include prediction, qualitative observation, explanation, equation derivation, mathematical modeling, quantitative experiments, and problem solving. Students use a powerful set of computer tools to record, display, and analyze data, as well as to develop mathematical models of physical phenomena. The design of many of the activities is based on the outcomes of physics education research. The Workshop Physics Activity Guide is supported by an Instructor's Website that: (1) describes the history and philosophy of the Workshop Physics Project; (2) provides advice on how to integrate the Guide into a variety of educational settings; (3) provides information on computer tools (hardware and software) and apparatus; and (4) includes suggested homework assignments for each unit. Log on to the Workshop Physics Project website at http://physics.dickinson.edu/ Workshop Physics is a component of the Physics Suite--a collection of materials created by a group of educational reformers known as the Activity Based Physics Group. The Physics Suite contains a broad array of curricular materials that are based on physics education research, including:

Understanding Physics, by Cummings, Laws, Redish and Cooney (an introductory textbook based on the best-selling text by Halliday/Resnick/Walker) RealTime Physics Laboratory Modules Physics by Inquiry (intended for use in a workshop setting) Interactive Lecture Demonstration Tutorials in Introductory Physics Activity Based Tutorials (designed primarily for use in recitations)

• Representations in Problem Solving: A Case Study with Optimization Problems

  ERIC Educational Resources Information Center

  Villegas, Jose L.; Castro, Enrique; Gutierrez, Jose

  2009-01-01

  Introduction: Representations play an essential role in mathematical thinking. They favor the understanding of mathematical concepts and stimulate the development of flexible and versatile thinking in problem solving. Here our focus is on their use in optimization problems, a type of problem considered important in mathematics teaching and…

• Mathematical Modelling in the Early School Years

  ERIC Educational Resources Information Center

  English, Lyn D.; Watters, James J.

  2005-01-01

  In this article we explore young children's development of mathematical knowledge and reasoning processes as they worked two modelling problems (the "Butter Beans Problem" and the "Airplane Problem"). The problems involve authentic situations that need to be interpreted and described in mathematical ways. Both problems include tables of data,…

• Learning with Multiple Representations: An Example of a Revision Lesson in Mathematics

  ERIC Educational Resources Information Center

  Wong, Darren; Poo, Sng Peng; Hock, Ng Eng; Kang, Wee Loo

  2011-01-01

  We describe an example of learning with multiple representations in an A-level revision lesson on mechanics. The context of the problem involved the motion of a ball thrown vertically upwards in air and studying how the associated physical quantities changed during its flight. Different groups of students were assigned to look at the ball's motion…

• Exploring Primary Student's Problem-Solving Ability by Doing Tasks Like PISA's Question

  ERIC Educational Resources Information Center

  Novita, Rita; Zulkardi; Hartono, Yusuf

  2012-01-01

  Problem solving plays an important role in mathematics and should have a prominent role in the mathematics education. The term "problem solving" refers to mathematics tasks that have the potential to provide intellectual challenges for enhancing students' mathematical understanding and development. In addition, the contextual problem…

• On the Relationships between (Relatively) Advanced Mathematical Knowledge and (Relatively) Advanced Problem-Solving Behaviours

  ERIC Educational Resources Information Center

  Koichu, Boris

  2010-01-01

  This article discusses an issue of inserting mathematical knowledge within the problem-solving processes. Relatively advanced mathematical knowledge is defined in terms of "three mathematical worlds"; relatively advanced problem-solving behaviours are defined in terms of taxonomies of "proof schemes" and "heuristic behaviours". The relationships…

Minimalism as a Guiding Principle: Linking Mathematical Learning to Everyday Knowledge

ERIC Educational Resources Information Center

Inoue, Noriyuki

2008-01-01

Studies report that students often fail to consider familiar aspects of reality in solving mathematical word problems. This study explored how different features of mathematical problems influence the way that undergraduate students employ realistic considerations in mathematical problem solving. Incorporating familiar contents in the word…

Pose and Solve Varignon Converse Problems

ERIC Educational Resources Information Center

Contreras, José N.

2014-01-01

The activity of posing and solving problems can enrich learners' mathematical experiences because it fosters a spirit of inquisitiveness, cultivates their mathematical curiosity, and deepens their views of what it means to do mathematics. To achieve these goals, a mathematical problem needs to be at the appropriate level of difficulty,…

Applications: Students, the Mathematics Curriculum and Mathematics Textbooks

ERIC Educational Resources Information Center

Kilic, Cigdem

2013-01-01

Problem posing is one of the most important topics in a mathematics education. Through problem posing, students gain mathematical abilities and concepts and teachers can evaluate their students and arrange adequate learning environments. The aim of the present study is to investigate Turkish primary school teachers' opinions about problem posing…

ABC Problem in Elementary Mathematics Education: Arithmetic "before" Comprehension

ERIC Educational Resources Information Center

Boote, Stacy K.; Boote, David N.

2018-01-01

Mathematical habits of prospective teachers affect problem comprehension and success and expose their beliefs about mathematics. Prospective elementary teachers (PSTs) (n = 121) engaged in a problem solving activity each week in class. Data were collected from PSTs enrolled in an undergraduate elementary mathematics methods course at a…

Students' and Teachers' Conceptual Metaphors for Mathematical Problem Solving

ERIC Educational Resources Information Center

Yee, Sean P.

2017-01-01

Metaphors are regularly used by mathematics teachers to relate difficult or complex concepts in classrooms. A complex topic of concern in mathematics education, and most STEM-based education classes, is problem solving. This study identified how students and teachers contextualize mathematical problem solving through their choice of metaphors.…

Finite-element approach to Brownian dynamics of polymers.

PubMed

Cyron, Christian J; Wall, Wolfgang A

2009-12-01

In the last decades simulation tools for Brownian dynamics of polymers have attracted more and more interest. Such simulation tools have been applied to a large variety of problems and accelerated the scientific progress significantly. However, the currently most frequently used explicit bead models exhibit severe limitations, especially with respect to time step size, the necessity of artificial constraints and the lack of a sound mathematical foundation. Here we present a framework for simulations of Brownian polymer dynamics based on the finite-element method. This approach allows simulating a wide range of physical phenomena at a highly attractive computational cost on the basis of a far-developed mathematical background.

Gesellschaft fuer angewandte Mathematik und Mechanik, Scientific Annual Meeting, Universitaet Stuttgart, Federal Republic of Germany, Apr. 13-17, 1987, Reports

NASA Astrophysics Data System (ADS)

Recent experimental, theoretical, and numerical investigations of problems in applied mechanics are discussed in reviews and reports. The fields covered include vibration and stability; the mechanics of elastic and plastic materials; fluid mechanics; the numerical treatment of differential equations; finite and boundary elements; optimization, decision theory, stochastics, and actuarial analysis; applied analysis and mathematical physics; and numerical analysis. Reviews are presented on mathematical applications of geometric-optics methods, biomechanics and implant technology, vibration theory in engineering, the stiffness and strength of damaged materials, and the existence of slow steady flows of viscoelastic fluids of integral type.

Mathematical model for the assessment of fracture risk associated with osteoporosis

NASA Astrophysics Data System (ADS)

Dinis, Jairson; Pereira, Ana I.; Fonseca, Elza M.

2012-09-01

Osteoporosis is a skeletal disease characterized by low bone mass. It is considered a worldwide public health problem that affects a large number of people, in particularly for women with more than 50 years old. The occurrence pattern of osteoporosis in a population may be related to several factors, including socio-economic factors such as income, educational attainment, and factors related to lifestyle such as diet and physical activity. These and other aspects have increasingly been identified as determining the occurrence of various diseases, including osteoporosis. This work proposes a mathematical model that provides the level of osteoporosis in the patient. Preliminary numerical results are presented.

Pre-Service Class Teacher' Ability in Solving Mathematical Problems and Skills in Solving Daily Problems

ERIC Educational Resources Information Center

Aljaberi, Nahil M.; Gheith, Eman

2016-01-01

This study aims to investigate the ability of pre-service class teacher at University of Petrain solving mathematical problems using Polya's Techniques, their level of problem solving skills in daily-life issues. The study also investigates the correlation between their ability to solve mathematical problems and their level of problem solving…

Colliding with the Speed of Light, Using Low-Energy Photon-Photon Collision Study the Nature of Matter and the universe

NASA Astrophysics Data System (ADS)

Zhang, Meggie

2013-03-01

Our research discovered logical inconsistence in physics and mathematics. Through reviewing the entire history of physics and mathematics we gained new understanding about our earlier assumptions, which led to a new interpretation of the wave function and quantum physics. We found the existing experimental data supported a 4-dimensional fractal structure of matter and the universe, we found the formation of wave, matter and the universe through the same process started from a single particle, and the process itself is a fractal that contributed to the diversity of matter. We also found physical evidence supporting a not-continuous fractal space structure. The new understanding also led to a reinterpretation of nuclear collision theories, based on this we succeeded a room-temperature low-energy photon-photon collision (RT-LE-PPC), this method allowed us to observe a topological disconnected fractal structure and succeeded a simulation of the formation of matter and the universe which provided evidences for the nature of light and matter and led to a quantum structure interpretation, and we found the formation of the universe started from two particles. However this work cannot be understood with current physics theories due to the logical problems in the current physics theories.

Physical Roots of It from Bit

NASA Astrophysics Data System (ADS)

Berezin, Alexander A.

2003-04-01

Why there is Something rather than Nothing? From Pythagoras ("everything is number") to Wheeler ("it from bit") theme of ultimate origin stresses primordiality of Ideal Platonic World (IPW) of mathematics. Even popular "quantum tunnelling out of nothing" can specify "nothing" only as (essentially) IPW. IPW exists everywhere (but nowhere in particular) and logically precedes space, time, matter or any "physics" in any conceivable universe. This leads to propositional conjecture (axiom?) that (meta)physical "Platonic Pressure" of infinitude of numbers acts as engine for self-generation of physical universe directly out of mathematics: cosmogenesis is driven by the very fact of IPW inexhaustibility. While physics in other quantum branches of inflating universe (Megaverse)can be(arbitrary) different from ours, number theory (and rest of IPW)is not (it is unique, absolute, immutable and infinitely resourceful). Let (infinite) totality of microstates ("its") of entire Megaverse form countable set. Since countable sets are hierarchically inexhaustible (Cantor's "fractal branching"), each single "it" still has infinite tail of non-overlapping IPW-based "personal labels". Thus, each "bit" ("it") is infinitely and uniquely resourceful: possible venue of elimination ergodicity basis for eternal return cosmological argument. Physics (in any subuniverse) may be limited only by inherent impossibilities residing in IPW, e.g. insolvability of Continuum Problem may be IPW foundation of quantum indeterminicity.

Analysis of forced convective modified Burgers liquid flow considering Cattaneo-Christov double diffusion

NASA Astrophysics Data System (ADS)

Waqas, M.; Hayat, T.; Shehzad, S. A.; Alsaedi, A.

2018-03-01

A mathematical model is formulated to characterize the non-Fourier and Fick's double diffusive models of heat and mass in moving flow of modified Burger's liquid. Temperature-dependent conductivity of liquid is taken into account. The concept of stratification is utilized to govern the equations of energy and mass species. The idea of boundary layer theory is employed to obtain the mathematical model of considered physical problem. The obtained partial differential system is converted into ordinary ones with the help of relevant variables. The homotopic concept lead to the convergent solutions of governing expressions. Convergence is attained and acceptable values are certified by expressing the so called ℏ -curves and numerical benchmark. Several graphs are made for different values of physical constraints to explore the mechanism of heat and mass transportation. We explored that the liquid temperature and concentration are retard for the larger thermal/concentration relaxation time constraint.

DRS: Derivational Reasoning System

NASA Technical Reports Server (NTRS)

Bose, Bhaskar

1995-01-01

The high reliability requirements for airborne systems requires fault-tolerant architectures to address failures in the presence of physical faults, and the elimination of design flaws during the specification and validation phase of the design cycle. Although much progress has been made in developing methods to address physical faults, design flaws remain a serious problem. Formal methods provides a mathematical basis for removing design flaws from digital systems. DRS (Derivational Reasoning System) is a formal design tool based on advanced research in mathematical modeling and formal synthesis. The system implements a basic design algebra for synthesizing digital circuit descriptions from high level functional specifications. DRS incorporates an executable specification language, a set of correctness preserving transformations, verification interface, and a logic synthesis interface, making it a powerful tool for realizing hardware from abstract specifications. DRS integrates recent advances in transformational reasoning, automated theorem proving and high-level CAD synthesis systems in order to provide enhanced reliability in designs with reduced time and cost.

Optimisation by hierarchical search

NASA Astrophysics Data System (ADS)

Zintchenko, Ilia; Hastings, Matthew; Troyer, Matthias

2015-03-01

Finding optimal values for a set of variables relative to a cost function gives rise to some of the hardest problems in physics, computer science and applied mathematics. Although often very simple in their formulation, these problems have a complex cost function landscape which prevents currently known algorithms from efficiently finding the global optimum. Countless techniques have been proposed to partially circumvent this problem, but an efficient method is yet to be found. We present a heuristic, general purpose approach to potentially improve the performance of conventional algorithms or special purpose hardware devices by optimising groups of variables in a hierarchical way. We apply this approach to problems in combinatorial optimisation, machine learning and other fields.

The new AP Physics exams: Integrating qualitative and quantitative reasoning

NASA Astrophysics Data System (ADS)

Elby, Andrew

2015-04-01

When physics instructors and education researchers emphasize the importance of integrating qualitative and quantitative reasoning in problem solving, they usually mean using those types of reasoning serially and separately: first students should analyze the physical situation qualitatively/conceptually to figure out the relevant equations, then they should process those equations quantitatively to generate a solution, and finally they should use qualitative reasoning to check that answer for plausibility (Heller, Keith, & Anderson, 1992). The new AP Physics 1 and 2 exams will, of course, reward this approach to problem solving. But one kind of free response question will demand and reward a further integration of qualitative and quantitative reasoning, namely mathematical modeling and sense-making--inventing new equations to capture a physical situation and focusing on proportionalities, inverse proportionalities, and other functional relations to infer what the equation ``says'' about the physical world. In this talk, I discuss examples of these qualitative-quantitative translation questions, highlighting how they differ from both standard quantitative and standard qualitative questions. I then discuss the kinds of modeling activities that can help AP and college students develop these skills and habits of mind.

The Relationship between Students' Performance on Conventional Standardized Mathematics Assessments and Complex Mathematical Modeling Problems

ERIC Educational Resources Information Center

Kartal, Ozgul; Dunya, Beyza Aksu; Diefes-Dux, Heidi A.; Zawojewski, Judith S.

2016-01-01

Critical to many science, technology, engineering, and mathematics (STEM) career paths is mathematical modeling--specifically, the creation and adaptation of mathematical models to solve problems in complex settings. Conventional standardized measures of mathematics achievement are not structured to directly assess this type of mathematical…

78 FR 37590 - Advisory Committee for Mathematical and Physical Sciences #66; Notice of Meeting

Federal Register 2010, 2011, 2012, 2013, 2014

2013-06-21

... NATIONAL SCIENCE FOUNDATION Advisory Committee for Mathematical and Physical Sciences 66; Notice... Physical Sciences ( 66). Dates/Time: July 18, 2013 1:00 p.m.-5:15 p.m. Place: National Science Foundation... Federal Officer, Directorate for Mathematical and Physical Sciences, National Science Foundation, 4201...

Toda hierarchies and their applications

NASA Astrophysics Data System (ADS)

Takasaki, Kanehisa

2018-05-01

The 2D Toda hierarchy occupies a central position in the family of integrable hierarchies of the Toda type. The 1D Toda hierarchy and the Ablowitz–Ladik (aka relativistic Toda) hierarchy can be derived from the 2D Toda hierarchy as reductions. These integrable hierarchies have been applied to various problems of mathematics and mathematical physics since 1990s. A recent example is a series of studies on models of statistical mechanics called the melting crystal model. This research has revealed that the aforementioned two reductions of the 2D Toda hierarchy underlie two different melting crystal models. Technical clues are a fermionic realization of the quantum torus algebra, special algebraic relations therein called shift symmetries, and a matrix factorization problem. The two melting crystal models thus exhibit remarkable similarity with the Hermitian and unitary matrix models for which the two reductions of the 2D Toda hierarchy play the role of fundamental integrable structures.

Numerical solution of system of boundary value problems using B-spline with free parameter

NASA Astrophysics Data System (ADS)

Gupta, Yogesh

2017-01-01

This paper deals with method of B-spline solution for a system of boundary value problems. The differential equations are useful in various fields of science and engineering. Some interesting real life problems involve more than one unknown function. These result in system of simultaneous differential equations. Such systems have been applied to many problems in mathematics, physics, engineering etc. In present paper, B-spline and B-spline with free parameter methods for the solution of a linear system of second-order boundary value problems are presented. The methods utilize the values of cubic B-spline and its derivatives at nodal points together with the equations of the given system and boundary conditions, ensuing into the linear matrix equation.

Deformation Theory and Physics Model Building

NASA Astrophysics Data System (ADS)

Sternheimer, Daniel

2006-08-01

The mathematical theory of deformations has proved to be a powerful tool in modeling physical reality. We start with a short historical and philosophical review of the context and concentrate this rapid presentation on a few interrelated directions where deformation theory is essential in bringing a new framework - which has then to be developed using adapted tools, some of which come from the deformation aspect. Minkowskian space-time can be deformed into Anti de Sitter, where massless particles become composite (also dynamically): this opens new perspectives in particle physics, at least at the electroweak level, including prediction of new mesons. Nonlinear group representations and covariant field equations, coming from interactions, can be viewed as some deformation of their linear (free) part: recognizing this fact can provide a good framework for treating problems in this area, in particular global solutions. Last but not least, (algebras associated with) classical mechanics (and field theory) on a Poisson phase space can be deformed to (algebras associated with) quantum mechanics (and quantum field theory). That is now a frontier domain in mathematics and theoretical physics called deformation quantization, with multiple ramifications, avatars and connections in both mathematics and physics. These include representation theory, quantum groups (when considering Hopf algebras instead of associative or Lie algebras), noncommutative geometry and manifolds, algebraic geometry, number theory, and of course what is regrouped under the name of M-theory. We shall here look at these from the unifying point of view of deformation theory and refer to a limited number of papers as a starting point for further study.

Increasing science literacy among the educated elite

NASA Astrophysics Data System (ADS)

Bender, Carl M.

1997-03-01

The Physics Department at Washington University is making a serious and continuing effort to raise the level of understanding of science for bright students who do not intend to take further courses in science or mathematics. We have established a course called Physics and Society, which considers such issues as availability of energy, nuclear power, nuclear weapons, the greenhouse effect, the ozone hole, risk analysis, the scientific method, and claims of the paranormal. By examining such topics quantitatively, we hope to improve the students' ability to grasp and assess critically the problems that society faces.

Investigating Mathematics Teachers Candidates' Knowledge about Problem Solving Strategies through Problem Posing

ERIC Educational Resources Information Center

Ünlü, Melihan

2017-01-01

The aim of the study was to determine mathematics teacher candidates' knowledge about problem solving strategies through problem posing. This qualitative research was conducted with 95 mathematics teacher candidates studying at education faculty of a public university during the first term of the 2015-2016 academic year in Turkey. Problem Posing…

Problem Posing and Solving with Mathematical Modeling

ERIC Educational Resources Information Center

English, Lyn D.; Fox, Jillian L.; Watters, James J.

2005-01-01

Mathematical modeling is explored as both problem posing and problem solving from two perspectives, that of the child and the teacher. Mathematical modeling provides rich learning experiences for elementary school children and their teachers.

A Physics Show Performed by Students for Kids: From Mechanics to Elementary Particle Physics

NASA Astrophysics Data System (ADS)

Dreiner, Herbi K.

2008-09-01

Physics students spend the early part of their training attending physics and mathematics lectures, solving problem sets, and experimenting in laboratory courses. The program is typically intensive and fairly rigid. They have little opportunity to follow their own curiosity or apply their knowledge. There have been many attempts to address this deficiency, specifically through outreach activities.1-23 For example, since 1984 Clint Sprott (University of Wisconsin) hosts a physics show entitled "The Wonders of Physics!" Dressed up as a circus director and assisted by students, Professor Sprott presents entertaining and educating experiments to a regularly packed auditorium of all age groups.5 This was in turn inspired by the "Chemistry is Fun" presentations of Basam Shakhashiri (University of Wisconsin), where the students are also involved.6

Physical data measurements and mathematical modelling of simple gas bubble experiments in glass melts

NASA Technical Reports Server (NTRS)

Weinberg, Michael C.

1986-01-01

In this work consideration is given to the problem of the extraction of physical data information from gas bubble dissolution and growth measurements. The discussion is limited to the analysis of the simplest experimental systems consisting of a single, one component gas bubble in a glassmelt. It is observed that if the glassmelt is highly under- (super-) saturated, then surface tension effects may be ignored, simplifying the task of extracting gas diffusivity values from the measurements. If, in addition, the bubble rise velocity is very small (or very large) the ease of obtaining physical property data is enhanced. Illustrations are given for typical cases.

A new asymptotic method for jump phenomena

NASA Technical Reports Server (NTRS)

Reiss, E. L.

1980-01-01

Physical phenomena involving rapid and sudden transitions, such as snap buckling of elastic shells, explosions, and earthquakes, are characterized mathematically as a small disturbance causing a large-amplitude response. Because of this, standard asymptotic and perturbation methods are ill-suited to these problems. In the present paper, a new method of analyzing jump phenomena is proposed. The principal feature of the method is the representation of the response in terms of rational functions. For illustration, the method is applied to the snap buckling of an elastic arch and to a simple combustion problem.

Time-nonlocal kinetic equations, jerk and hyperjerk in plasmas and solar physics

NASA Astrophysics Data System (ADS)

El-Nabulsi, Rami Ahmad

2018-06-01

The simulation and analysis of nonlocal effects in fluids and plasmas is an inherently complicated problem due to the massive breadth of physics required to describe the nonlocal dynamics. This is a multi-physics problem that draws upon various miscellaneous fields, such as electromagnetism and statistical mechanics. In this paper we strive to focus on one narrow but motivating mathematical way: the derivation of nonlocal plasma-fluid equations from a generalized nonlocal Liouville derivative operator motivated from Suykens's nonlocal arguments. The paper aims to provide a guideline toward modeling nonlocal effects occurring in plasma-fluid systems by means of a generalized nonlocal Boltzmann equation. The generalized nonlocal equations of fluid dynamics are derived and their implications in plasma-fluid systems are addressed, discussed and analyzed. Three main topics were discussed: Landau damping in plasma electrodynamics, ideal MHD and solar wind. A number of features were revealed, analyzed and confronted with recent research results and observations.

The Impact of Problem Posing on Elementary Teachers' Beliefs about Mathematics and Mathematics Teaching

ERIC Educational Resources Information Center

Barlow, Angela T.; Cates, Janie M.

2006-01-01

This study investigated the impact of incorporating problem posing in elementary classrooms on the beliefs held by elementary teachers about mathematics and mathematics teaching. Teachers participated in a year-long staff development project aimed at facilitating the incorporation of problem posing into their classrooms. Beliefs were examined via…

Leveling of Critical Thinking Abilities of Students of Mathematics Education in Mathematical Problem Solving

ERIC Educational Resources Information Center

Rasiman

2015-01-01

This research aims to determine the leveling of critical thinking abilities of students of mathematics education in mathematical problem solving. It includes qualitative-explorative study that was conducted at University of PGRI Semarang. The generated data in the form of information obtained problem solving question and interview guides. The…

Problem Solving in Swedish Mathematics Textbooks for Upper Secondary School

ERIC Educational Resources Information Center

Brehmer, Daniel; Ryve, Andreas; Van Steenbrugge, Hendrik

2016-01-01

The aim of this study is to analyse how mathematical problem solving is represented in mathematical textbooks for Swedish upper secondary school. The analysis comprises dominating Swedish textbook series, and relates to uncovering (a) the quantity of tasks that are actually mathematical problems, (b) their location in the chapter, (c) their…

Adolescent Mathematical Problem Solving: The Role of Metacognition, Strategies and Beliefs.

ERIC Educational Resources Information Center

Fitzpatrick, Corine

Mathematical problem solving has been the focus of much concern. This study investigated the relationship of various cognitive factors, attributions, and gender to the solution of mathematics problems by 100 high school seniors. The independent variables examined in this study included: (1) mathematics knowledge as measured by a score on the…

An Astronomical Problem in a Japanese Traditional Mathematical Text: The 49th Problem of the Kenki-sanpo of Takebe Katahiro

NASA Astrophysics Data System (ADS)

Ôhashi, Yukio

During the Edo period (Tokugawa-shogunate period) (1603-1867), there was a mathematical tradition now called "Wasan" which was primarily based on Chinese mathematics, but Japanese mathematicians also created new devices. It was quite popular, and common people could enjoy solving mathematical problems through Wasan regardless of their social status. Some astronomical problems were also treated there.

Spherical means of solutions of partial differential equations in a conical region

NASA Technical Reports Server (NTRS)

Ting, L.

1975-01-01

The spherical means of the solutions of a linear partial differential equation Lu = f in a conical region are studied. The conical region is bounded by a surface generated by curvilinear xi lines and by two truncating xi surfaces. The spherical mean is the average of u over a constant xi surface. Conditions on the linear differential operator, L, and on the orthogonal coordinates xi, eta, and zeta are established so that the problem for the determination of the spherical mean of the solution subjected to the appropriate boundary and initial conditions can be reduced to a problem with only one space variable. Conditions are then established so that the spherical mean of the solution in one conical region will be proportional to that of a known solution in another conical region. Applications to various problems of mathematical physics and their physical interpretations are presented.

A novel approach to piecewise analytic agricultural machinery path reconstruction

NASA Astrophysics Data System (ADS)

Wörz, Sascha; Mederle, Michael; Heizinger, Valentin; Bernhardt, Heinz

2017-12-01

Before analysing machinery operation in fields, it has to be coped with the problem that the GPS signals of GPS receivers located on the machines contain measurement noise, are time-discrete, and the underlying physical system describing the positions, axial and absolute velocities, angular rates and angular orientation of the operating machines during the whole working time are unknown. This research work presents a new three-dimensional mathematical approach using kinematic relations based on control variables as Euler angular velocities and angles and a discrete target control problem, such that the state control function is given by the sum of squared residuals involving the state and control variables to get such a physical system, which yields a noise-free and piecewise analytic representation of the positions, velocities, angular rates and angular orientation. It can be used for a further detailed study and analysis of the problem of why agricultural vehicles operate in practice as they do.

Obtaining Laws through Quantifying Experiments: Justifications of Pre-Service Physics Teachers in the Case of Electric Current, Voltage and Resistance

ERIC Educational Resources Information Center

Mäntylä, Terhi; Hämäläinen, Ari

2015-01-01

The language of physics is mathematics, and physics ideas, laws and models describing phenomena are usually represented in mathematical form. Therefore, an understanding of how to navigate between phenomena and the models representing them in mathematical form is important for a physics teacher so that the teacher can make physics understandable…

A brief history of the most remarkable numbers e, i and γ in mathematical sciences with applications

NASA Astrophysics Data System (ADS)

Debnath, Lokenath

2015-08-01

This paper deals with a brief history of the most remarkable Euler numbers e, i and γ in mathematical sciences. Included are many properties of the constants e, i and γ and their applications in algebra, geometry, physics, chemistry, ecology, business and industry. Special attention is given to the growth and decay phenomena in many real-world problems including stability and instability of their solutions. Some specific and modern applications of logarithms, complex numbers and complex exponential functions to electrical circuits and mechanical systems are presented with examples. Included are the use of complex numbers and complex functions in the description and analysis of chaos and fractals with the aid of modern computer technology. In addition, the phasor method is described with examples of applications in engineering science. The major focus of this paper is to provide basic information through historical approach to mathematics teaching and learning of the fundamental knowledge and skills required for students and teachers at all levels so that they can understand the concepts of mathematics, and mathematics education in science and technology.

Some applications of mathematics in theoretical physics - A review

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bora, Kalpana

2016-06-21

Mathematics is a very beautiful subject−very much an indispensible tool for Physics, more so for Theoretical Physics (by which we mean here mainly Field Theory and High Energy Physics). These branches of Physics are based on Quantum Mechanics and Special Theory of Relativity, and many mathematical concepts are used in them. In this work, we shall elucidate upon only some of them, like−differential geometry, infinite series, Mellin transforms, Fourier and integral transforms, special functions, calculus, complex algebra, topology, group theory, Riemannian geometry, functional analysis, linear algebra, operator algebra, etc. We shall also present, some physics issues, where these mathematical toolsmore » are used. It is not wrong to say that Mathematics is such a powerful tool, without which, there can not be any Physics theory!! A brief review on our research work is also presented.« less

Some applications of mathematics in theoretical physics - A review

NASA Astrophysics Data System (ADS)

Bora, Kalpana

2016-06-01

Mathematics is a very beautiful subject-very much an indispensible tool for Physics, more so for Theoretical Physics (by which we mean here mainly Field Theory and High Energy Physics). These branches of Physics are based on Quantum Mechanics and Special Theory of Relativity, and many mathematical concepts are used in them. In this work, we shall elucidate upon only some of them, like-differential geometry, infinite series, Mellin transforms, Fourier and integral transforms, special functions, calculus, complex algebra, topology, group theory, Riemannian geometry, functional analysis, linear algebra, operator algebra, etc. We shall also present, some physics issues, where these mathematical tools are used. It is not wrong to say that Mathematics is such a powerful tool, without which, there can not be any Physics theory!! A brief review on our research work is also presented.

On the tumbling toast problem

NASA Astrophysics Data System (ADS)

Borghi, Riccardo

2012-09-01

A didactical revisitation of the so-called tumbling toast problem is presented here. The numerical solution of the related Newton's equations has been found in the space domain, without resorting to the complete time-based law of motion, with a considerable reduction of the mathematical complexity of the problem. This could allow the effect of the different physical mechanisms ruling the overall dynamics to be appreciated in a more transparent way, even by undergraduates. Moreover, the availability from the literature of experimental investigations carried out on tumbling toast allows us to propose different theoretical models of growing complexity in order to show the corresponding improvement of the agreement between theory and observation.

A coherent Ising machine for 2000-node optimization problems

NASA Astrophysics Data System (ADS)

Inagaki, Takahiro; Haribara, Yoshitaka; Igarashi, Koji; Sonobe, Tomohiro; Tamate, Shuhei; Honjo, Toshimori; Marandi, Alireza; McMahon, Peter L.; Umeki, Takeshi; Enbutsu, Koji; Tadanaga, Osamu; Takenouchi, Hirokazu; Aihara, Kazuyuki; Kawarabayashi, Ken-ichi; Inoue, Kyo; Utsunomiya, Shoko; Takesue, Hiroki

2016-11-01

The analysis and optimization of complex systems can be reduced to mathematical problems collectively known as combinatorial optimization. Many such problems can be mapped onto ground-state search problems of the Ising model, and various artificial spin systems are now emerging as promising approaches. However, physical Ising machines have suffered from limited numbers of spin-spin couplings because of implementations based on localized spins, resulting in severe scalability problems. We report a 2000-spin network with all-to-all spin-spin couplings. Using a measurement and feedback scheme, we coupled time-multiplexed degenerate optical parametric oscillators to implement maximum cut problems on arbitrary graph topologies with up to 2000 nodes. Our coherent Ising machine outperformed simulated annealing in terms of accuracy and computation time for a 2000-node complete graph.

Building a Program of University Physics and Mathematics Education

NASA Astrophysics Data System (ADS)

Tanaka, Tadayoshi; Nakamura, Akira; Kagiyama, Shigenori; Namiki, Masatoshi; Ejiri, Arisato; Ohshima, Kazunari; Mishima, Akiomi; Aoki, Katsuhiko

Authors built physics learning modules which consist of lectures, experiments and practices, introducing physics experiments of elementary and secondary education. In addition, we are operating "KIT Mathematics Navigation" in order to complement mathematical basics to engineering education. Based on these results, we are building studies and development of an education program in order to support the learning paradigm shift and to help students learn physics and mathematics complimentarily for liberal arts education course in universities.

Problem Solvers: Problem--Jesse's Train

ERIC Educational Resources Information Center

James, Julie; Steimle, Alice

2014-01-01

Persevering in problem solving and constructing and critiquing mathematical arguments are some of the mathematical practices included in the Common Core State Standards for Mathematics (CCSSI 2010). To solve unfamiliar problems, students must make sense of the situation and apply current knowledge. Teachers can present such opportunities by…

Connecting the dots between math and reality: A study of critical thinking in high school physics

NASA Astrophysics Data System (ADS)

Loper, Timothy K.

The purpose of this mixed method study was to discover whether training in understanding relationships between variables would help students read and interpret equations for the purposes of problem solving in physics. Twenty students from two physics classes at a private Catholic high school participated in a one group pretest-posttest unit with the conceptually based mathematical intervention being the independent variable, and the test results being the dependent variable for the quantitative portion of the study. A random sample of students was interviewed pre and post intervention for the qualitative portion of the study to determine both how their understanding of equations changed and how their approach to the problems changed. The paired-sample t test showed a significant improvement on the Physics Critical Thinking test at the p<.01 alpha level; furthermore, the interview data indicated the students displayed a deeper understanding of equations and their purpose as opposed to the superficial understanding they had before the intervention.

2016 Final Reports from the Los Alamos National Laboratory Computational Physics Student Summer Workshop

DOE Office of Scientific and Technical Information (OSTI.GOV)

Runnels, Scott Robert; Bachrach, Harrison Ian; Carlson, Nils

The two primary purposes of LANL’s Computational Physics Student Summer Workshop are (1) To educate graduate and exceptional undergraduate students in the challenges and applications of computational physics of interest to LANL, and (2) Entice their interest toward those challenges. Computational physics is emerging as a discipline in its own right, combining expertise in mathematics, physics, and computer science. The mathematical aspects focus on numerical methods for solving equations on the computer as well as developing test problems with analytical solutions. The physics aspects are very broad, ranging from low-temperature material modeling to extremely high temperature plasma physics, radiation transportmore » and neutron transport. The computer science issues are concerned with matching numerical algorithms to emerging architectures and maintaining the quality of extremely large codes built to perform multi-physics calculations. Although graduate programs associated with computational physics are emerging, it is apparent that the pool of U.S. citizens in this multi-disciplinary field is relatively small and is typically not focused on the aspects that are of primary interest to LANL. Furthermore, more structured foundations for LANL interaction with universities in computational physics is needed; historically interactions rely heavily on individuals’ personalities and personal contacts. Thus a tertiary purpose of the Summer Workshop is to build an educational network of LANL researchers, university professors, and emerging students to advance the field and LANL’s involvement in it.« less

Zimbabwean Female Participation in Physics: The Influence of Identity Formation on Perception and Participation

ERIC Educational Resources Information Center

Gudyanga, Anna; Kurup, Raj

2017-01-01

The study investigated the influence of identity formation on the perceptions and participation of Zimbabwean Advanced Level (A' Level) female adolescent students in physics. Nine female adolescent students eighteen years and above: three doing mathematics and physics, one doing physics without mathematics and five doing mathematics without…

Categorization and analysis of explanatory writing in mathematics

NASA Astrophysics Data System (ADS)

Craig, Tracy S.

2011-10-01

The aim of this article is to present a scheme for coding and categorizing students' written explanations of mathematical problem-solving activities. The scheme was used successfully within a study project carried out to determine whether student problem-solving behaviour could be positively affected by writing explanatory strategies to mathematical problem-solving processes. The rationale for the study was the recognized importance of mathematical problem-solving, the widely acknowledged challenge of teaching problem-solving skills directly and the evidence in the literature that writing in mathematics provides a tool for learning. The study was carried out in a first-year mathematics course at the University of Cape Town, South Africa. Students' written submissions were categorized and analysed through use of an adaptation of a journal entry classification scheme. The scheme successfully observed positive changes over the experimental period in students' level of engagement with the mathematical material and with their stance towards knowledge.

Quantum Chemistry in Great Britain: Developing a Mathematical Framework for Quantum Chemistry

NASA Astrophysics Data System (ADS)

Simões, Ana; Gavroglu, Kostas

By 1935 quantum chemistry was already delineated as a distinct sub-discipline due to the contributions of Fritz London, Walter Heitler, Friedrich Hund, Erich Hückel, Robert Mulliken, Linus Pauling, John van Vleck and John Slater. These people are credited with showing that the application of quantum mechanics to the solution of chemical problems was, indeed, possible, especially so after the introduction of a number of new concepts and the adoption of certain approximation methods. And though a number of chemists had started talking of the formation of theoretical or, even, mathematical chemistry, a fully developed mathematical framework of quantum chemistry was still wanting. The work of three persons in particular-of John E. Lennard-Jones, Douglas R. Hartree, and Charles Alfred Coulson-has been absolutely crucial in the development of such a framework. In this paper we shall discuss the work of these three researchers who started their careers in the Cambridge tradition of mathematical physics and who at some point of their careers all became professors of applied mathematics. We shall argue that their work consisted of decisive contributions to the development of such a mathematical framework for quantum chemistry.

Improving of Junior High School Visual Thinking Representation Ability in Mathematical Problem Solving by CTL

ERIC Educational Resources Information Center

Surya, Edy; Sabandar, Jozua; Kusumah, Yaya S.; Darhim

2013-01-01

The students' difficulty which was found is in the problem of understanding, drawing diagrams, reading the charts correctly, conceptual formal mathematical understanding, and mathematical problem solving. The appropriate problem representation is the basic way in order to understand the problem itself and make a plan to solve it. This research was…

Polynomial-time solution of prime factorization and NP-complete problems with digital memcomputing machines

NASA Astrophysics Data System (ADS)

Traversa, Fabio L.; Di Ventra, Massimiliano

2017-02-01

We introduce a class of digital machines, we name Digital Memcomputing Machines, (DMMs) able to solve a wide range of problems including Non-deterministic Polynomial (NP) ones with polynomial resources (in time, space, and energy). An abstract DMM with this power must satisfy a set of compatible mathematical constraints underlying its practical realization. We prove this by making a connection with the dynamical systems theory. This leads us to a set of physical constraints for poly-resource resolvability. Once the mathematical requirements have been assessed, we propose a practical scheme to solve the above class of problems based on the novel concept of self-organizing logic gates and circuits (SOLCs). These are logic gates and circuits able to accept input signals from any terminal, without distinction between conventional input and output terminals. They can solve boolean problems by self-organizing into their solution. They can be fabricated either with circuit elements with memory (such as memristors) and/or standard MOS technology. Using tools of functional analysis, we prove mathematically the following constraints for the poly-resource resolvability: (i) SOLCs possess a global attractor; (ii) their only equilibrium points are the solutions of the problems to solve; (iii) the system converges exponentially fast to the solutions; (iv) the equilibrium convergence rate scales at most polynomially with input size. We finally provide arguments that periodic orbits and strange attractors cannot coexist with equilibria. As examples, we show how to solve the prime factorization and the search version of the NP-complete subset-sum problem. Since DMMs map integers into integers, they are robust against noise and hence scalable. We finally discuss the implications of the DMM realization through SOLCs to the NP = P question related to constraints of poly-resources resolvability.

Processes involved in solving mathematical problems

NASA Astrophysics Data System (ADS)

Shahrill, Masitah; Putri, Ratu Ilma Indra; Zulkardi, Prahmana, Rully Charitas Indra

2018-04-01

This study examines one of the instructional practices features utilized within the Year 8 mathematics lessons in Brunei Darussalam. The codes from the TIMSS 1999 Video Study were applied and strictly followed, and from the 183 mathematics problems recorded, there were 95 problems with a solution presented during the public segments of the video-recorded lesson sequences of the four sampled teachers. The analyses involved firstly, identifying the processes related to mathematical problem statements, and secondly, examining the different processes used in solving the mathematical problems for each problem publicly completed during the lessons. The findings revealed that for three of the teachers, their problem statements coded as `using procedures' ranged from 64% to 83%, while the remaining teacher had 40% of his problem statements coded as `making connections.' The processes used when solving the problems were mainly `using procedures', and none of the problems were coded as `giving results only'. Furthermore, all four teachers made use of making the relevant connections in solving the problems given to their respective students.

Using Technology to Meet the Developmental Needs of Deaf Students To Improve Their Mathematical Word Problem Solving Skills.

ERIC Educational Resources Information Center

Kelly, Ronald R.

2003-01-01

Presents "Project Solve," a web-based problem-solving instruction and guided practice for mathematical word problems. Discusses implications for college students for whom reading and comprehension of mathematical word problem solving are difficult, especially learning disabled students. (Author/KHR)

Incorporating the Common Core's Problem Solving Standard for Mathematical Practice into an Early Elementary Inclusive Classroom

ERIC Educational Resources Information Center

Fletcher, Nicole

2014-01-01

Mathematics curriculum designers and policy decision makers are beginning to recognize the importance of problem solving, even at the earliest stages of mathematics learning. The Common Core includes sense making and perseverance in solving problems in its standards for mathematical practice for students at all grade levels. Incorporating problem…

Promoting Access to Common Core Mathematics for Students with Severe Disabilities through Mathematical Problem Solving

ERIC Educational Resources Information Center

Spooner, Fred; Saunders, Alicia; Root, Jenny; Brosh, Chelsi

2017-01-01

There is a need to teach the pivotal skill of mathematical problem solving to students with severe disabilities, moving beyond basic skills like computation to higher level thinking skills. Problem solving is emphasized as a Standard for Mathematical Practice in the Common Core State Standards across grade levels. This article describes a…

Students’ Representation in Mathematical Word Problem-Solving: Exploring Students’ Self-efficacy

NASA Astrophysics Data System (ADS)

Sahendra, A.; Budiarto, M. T.; Fuad, Y.

2018-01-01

This descriptive qualitative research aims at investigating student represented in mathematical word problem solving based on self-efficacy. The research subjects are two eighth graders at a school in Surabaya with equal mathematical ability consisting of two female students with high and low self-efficacy. The subjects were chosen based on the results of test of mathematical ability, documentation of the result of middle test in even semester of 2016/2017 academic year, and results of questionnaire of mathematics word problem in terms of self-efficacy scale. The selected students were asked to do mathematical word problem solving and be interviewed. The result of this study shows that students with high self-efficacy tend to use multiple representations of sketches and mathematical models, whereas students with low self-efficacy tend to use single representation of sketches or mathematical models only in mathematical word problem-solving. This study emphasizes that teachers should pay attention of student’s representation as a consideration of designing innovative learning in order to increase the self-efficacy of each student to achieve maximum mathematical achievement although it still requires adjustment to the school situation and condition.

The role of a posteriori mathematics in physics

NASA Astrophysics Data System (ADS)

MacKinnon, Edward

2018-05-01

The calculus that co-evolved with classical mechanics relied on definitions of functions and differentials that accommodated physical intuitions. In the early nineteenth century mathematicians began the rigorous reformulation of calculus and eventually succeeded in putting almost all of mathematics on a set-theoretic foundation. Physicists traditionally ignore this rigorous mathematics. Physicists often rely on a posteriori math, a practice of using physical considerations to determine mathematical formulations. This is illustrated by examples from classical and quantum physics. A justification of such practice stems from a consideration of the role of phenomenological theories in classical physics and effective theories in contemporary physics. This relates to the larger question of how physical theories should be interpreted.

In memory of E.V. Shcherbinin

NASA Astrophysics Data System (ADS)

Editorial Board

2004-09-01

On August 3, 2004 died Eduard Vasilyevich Shcherbinin, an outstanding scientist, well known in the MHD world scientific community, Dr. hab. Phys., professor, the head of the Laboratory of Electrical Vortex Flows at the Institute of Physics of the University of Latvia, a member of the Advising Editorial Board of the Journal "MagnetoHydroDynamics". Just after graduation from the Leningrad Politechnical Institute (physics and mathematics faculty) in 1961, E.V. Shcherbinin joined the Institute of Physics and stayed there till his last days. He started his work as an engineer at the Institute of Physics, in 1966 he was awarded his first scientific degree of Candidate of Science, in 1977 he was awarded another scientific degree of Dr.Phys., in 1980 he became a professor of mathematics. Eduard Vasilyevich Shcherbinin has been awarded many prizes, among which are the prizes of the Presidium of the Latvian Academy of Sciences (1973, 1977, 1986) and the F.Tsander prize (1991). All his fruitful scientific activity was devoted to theoretical MHD fundamental problems and to practical application problems. E.V. Shcherbinin was the founder of a new branch in MHD - the so-called electrovortex flows, having direct relation to the optimization of many practical metallurgy processes such as aluminum reduction cells, induction channel furnaces, electric arc furnaces and electroslag re-melting of metals. E.V. Shcherbinin published 6 monographs, about 200 scientific papers, he has more than 40 patents. Alongside, E.V. Shcherbinin guided the scientific work of many post-graduates and gave lectures in mathematics for students. Under his guidance, 13 post-graduates have successfully prepared their theses in MHD. E.V. Shcherbinin was also active in organizing many international seminars and conferences and participating in them. Recently, E.V. Shcherbinin, being the head of the Laboratory of Electrical Vortex Flows has published the monograph "Theory of self-similar boundary layer in hydrodynamics and magnetohydrodynamics" devoted to the common approach to the solution of self-similar problems in the theory of boundary layer in hydrodynamics and magnetohydrodynamics. In the memory of his colleagues E.V. Shcherbinin surely will always remain as a modest and honest scientist, never striving for success in the public eye or for awards and positions, but only seeking for the scientific truth.

Strategies to Support Students' Mathematical Modeling

ERIC Educational Resources Information Center

Jung, Hyunyi

2015-01-01

An important question for mathematics teachers is this: "How can we help students learn mathematics to solve everyday problems, rather than teaching them only to memorize rules and practice mathematical procedures?" Teaching students using modeling activities can help them learn mathematics in real-world problem-solving situations that…

Profile of male-field dependent (FD) prospective teacher's reflective thinking in solving contextual mathematical problem

NASA Astrophysics Data System (ADS)

Agustan, S.; Juniati, Dwi; Siswono, Tatag Yuli Eko

2017-08-01

Reflective thinking is an important component in the world of education, especially in professional education of teachers. In learning mathematics, reflective thinking is one way to solve mathematical problem because it can improve student's curiosity when student faces a mathematical problem. Reflective thinking is also a future competence that should be taught to students to face the challenges and to respond of demands of the 21st century. There are many factors which give impact toward the student's reflective thinking when student solves mathematical problem. One of them is cognitive style. For this reason, reflective thinking and cognitive style are important things in solving contextual mathematical problem. This research paper describes aspect of reflective thinking in solving contextual mathematical problem involved solution by using some mathematical concept, namely linear program, algebra arithmetic operation, and linear equations of two variables. The participant, in this research paper, is a male-prospective teacher who has Field Dependent. The purpose of this paper is to describe aspect of prospective teachers' reflective thinking in solving contextual mathematical problem. This research paper is a descriptive by using qualitative approach. To analyze the data, the researchers focus in four main categories which describe prospective teacher's activities using reflective thinking, namely; (a) formulation and synthesis of experience, (b) orderliness of experience, (c) evaluating the experience and (d) testing the selected solution based on the experience.

An Actor-Oriented Transfer Perspective on High School Students' Development of the Use of Procedures to Solve Problems on Rate of Change

ERIC Educational Resources Information Center

Roorda, Gerrit; Vos, Pauline; Goedhart, Martin J.

2015-01-01

This article reports on a longitudinal observation study about students' development in their use of procedures to calculate instantaneous rate of change. Different procedures for solving tasks on rate of change are taught in mathematics and physics classes, and together they form a repertoire. Our study took an actor-oriented perspective, which…

Program listing for the REEDM (Rocket Exhaust Effluent Diffusion Model) computer program

NASA Technical Reports Server (NTRS)

Bjorklund, J. R.; Dumbauld, R. K.; Cheney, C. S.; Geary, H. V.

1982-01-01

The program listing for the REEDM Computer Program is provided. A mathematical description of the atmospheric dispersion models, cloud-rise models, and other formulas used in the REEDM model; vehicle and source parameters, other pertinent physical properties of the rocket exhaust cloud and meteorological layering techniques; user's instructions for the REEDM computer program; and worked example problems are contained in NASA CR-3646.