Calculating degree-based topological indices of dominating David derived networks

NASA Astrophysics Data System (ADS)

Ahmad, Muhammad Saeed; Nazeer, Waqas; Kang, Shin Min; Imran, Muhammad; Gao, Wei

2017-12-01

An important area of applied mathematics is the Chemical reaction network theory. The behavior of real world problems can be modeled by using this theory. Due to applications in theoretical chemistry and biochemistry, it has attracted researchers since its foundation. It also attracts pure mathematicians because it involves interesting mathematical structures. In this report, we compute newly defined topological indices, namely, Arithmetic-Geometric index (AG1 index), SK index, SK1 index, and SK2 index of the dominating David derived networks [1, 2, 3, 4, 5].

Mathematical computer programs: A compilation

NASA Technical Reports Server (NTRS)

1972-01-01

Computer programs, routines, and subroutines for aiding engineers, scientists, and mathematicians in direct problem solving are presented. Also included is a group of items that affords the same users greater flexibility in the use of software.

A novel paradigm for cell and molecule interaction ontology: from the CMM model to IMGT-ONTOLOGY

PubMed Central

2010-01-01

Background Biology is moving fast toward the virtuous circle of other disciplines: from data to quantitative modeling and back to data. Models are usually developed by mathematicians, physicists, and computer scientists to translate qualitative or semi-quantitative biological knowledge into a quantitative approach. To eliminate semantic confusion between biology and other disciplines, it is necessary to have a list of the most important and frequently used concepts coherently defined. Results We propose a novel paradigm for generating new concepts for an ontology, starting from model rather than developing a database. We apply that approach to generate concepts for cell and molecule interaction starting from an agent based model. This effort provides a solid infrastructure that is useful to overcome the semantic ambiguities that arise between biologists and mathematicians, physicists, and computer scientists, when they interact in a multidisciplinary field. Conclusions This effort represents the first attempt at linking molecule ontology with cell ontology, in IMGT-ONTOLOGY, the well established ontology in immunogenetics and immunoinformatics, and a paradigm for life science biology. With the increasing use of models in biology and medicine, the need to link different levels, from molecules to cells to tissues and organs, is increasingly important. PMID:20167082

Laboratory Mathematics

ERIC Educational Resources Information Center

de Mestre, Neville

2004-01-01

Computers were invented to help mathematicians perform long and complicated calculations more efficiently. By the time that a computing area became a familiar space in primary and secondary schools, the initial motivation for computer use had been submerged in the many other functions that modern computers now accomplish. Not only the mathematics…

Studies in Mathematics, Volume 22. Studies in Computer Science.

ERIC Educational Resources Information Center

Pollack, Seymour V., Ed.

The nine articles in this collection were selected because they represent concerns central to computer science, emphasize topics of particular interest to mathematicians, and underscore the wide range of areas deeply and continually affected by computer science. The contents consist of: "Introduction" (S. V. Pollack), "The…

Computer-Based Self-Instructional Modules. Final Technical Report.

ERIC Educational Resources Information Center

Weinstock, Harold

Reported is a project involving seven chemists, six mathematicians, and six physicists in the production of computer-based, self-study modules for use in introductory college courses in chemistry, physics, and mathematics. These modules were designed to be used by students and instructors with little or no computer backgrounds, in institutions…

Digital Maps, Matrices and Computer Algebra

ERIC Educational Resources Information Center

Knight, D. G.

2005-01-01

The way in which computer algebra systems, such as Maple, have made the study of complex problems accessible to undergraduate mathematicians with modest computational skills is illustrated by some large matrix calculations, which arise from representing the Earth's surface by digital elevation models. Such problems are often considered to lie in…

Computer Art--A New Tool in Advertising Graphics.

ERIC Educational Resources Information Center

Wassmuth, Birgit L.

Using computers to produce art began with scientists, mathematicians, and individuals with strong technical backgrounds who used the graphic material as visualizations of data in technical fields. People are using computer art in advertising, as well as in painting; sculpture; music; textile, product, industrial, and interior design; architecture;…

Role of mathematics in cancer research: attitudes and training of Japanese mathematicians.

PubMed

Kudô, A

1979-10-01

An extensive survey of attitude towards scientific information of scientists in Japan was conducted in Japan. It was published in a technical report, and this survey is reviewed in this paper, with the hope that this will furnish findings important in working out the plan for promoting exploitation of mathematical talent in biomedical research. Findings are concordant with the impression of foreign visitors: (1) pure mathematicians tend to concentrate on mathematics only; (2) applied mathematics and statistics are heavily oriented toward industry; (3) mathematicians and pharmacologists are very different in their attitudes to scientific information. Based on the personal experience of the author, difficulties to be circumvented in utilizing aptitudes for mathematics and/or statistics in biomedical research are discussed.

Role of mathematics in cancer research: attitudes and training of Japanese mathematicians.

PubMed Central

Kudô, A

1979-01-01

An extensive survey of attitude towards scientific information of scientists in Japan was conducted in Japan. It was published in a technical report, and this survey is reviewed in this paper, with the hope that this will furnish findings important in working out the plan for promoting exploitation of mathematical talent in biomedical research. Findings are concordant with the impression of foreign visitors: (1) pure mathematicians tend to concentrate on mathematics only; (2) applied mathematics and statistics are heavily oriented toward industry; (3) mathematicians and pharmacologists are very different in their attitudes to scientific information. Based on the personal experience of the author, difficulties to be circumvented in utilizing aptitudes for mathematics and/or statistics in biomedical research are discussed. PMID:540605

Cultivating Critique: A (Humanoid) Response to the Online Teaching of Critical Thinking

ERIC Educational Resources Information Center

Waggoner, Matt

2013-01-01

The Turing era, defined by British mathematician and computer science pioneer Alan Turing's question about whether or not computers can think, is not over. Philosophers and scientists will continue to haggle over whether thought necessitates intentionality, and whether computation can rise to that level. Meanwhile, another frontier is emerging in…

Computing Logarithms by Hand

ERIC Educational Resources Information Center

Reed, Cameron

2016-01-01

How can old-fashioned tables of logarithms be computed without technology? Today, of course, no practicing mathematician, scientist, or engineer would actually use logarithms to carry out a calculation, let alone worry about deriving them from scratch. But high school students may be curious about the process. This article develops a…

Introduction to multigrid methods

NASA Technical Reports Server (NTRS)

Wesseling, P.

1995-01-01

These notes were written for an introductory course on the application of multigrid methods to elliptic and hyperbolic partial differential equations for engineers, physicists and applied mathematicians. The use of more advanced mathematical tools, such as functional analysis, is avoided. The course is intended to be accessible to a wide audience of users of computational methods. We restrict ourselves to finite volume and finite difference discretization. The basic principles are given. Smoothing methods and Fourier smoothing analysis are reviewed. The fundamental multigrid algorithm is studied. The smoothing and coarse grid approximation properties are discussed. Multigrid schedules and structured programming of multigrid algorithms are treated. Robustness and efficiency are considered.

Overview of the SAMSI year-long program on Statistical, Mathematical and Computational Methods for Astronomy

NASA Astrophysics Data System (ADS)

Jogesh Babu, G.

2017-01-01

A year-long research (Aug 2016- May 2017) program on `Statistical, Mathematical and Computational Methods for Astronomy (ASTRO)’ is well under way at Statistical and Applied Mathematical Sciences Institute (SAMSI), a National Science Foundation research institute in Research Triangle Park, NC. This program has brought together astronomers, computer scientists, applied mathematicians and statisticians. The main aims of this program are: to foster cross-disciplinary activities; to accelerate the adoption of modern statistical and mathematical tools into modern astronomy; and to develop new tools needed for important astronomical research problems. The program provides multiple avenues for cross-disciplinary interactions, including several workshops, long-term visitors, and regular teleconferences, so participants can continue collaborations, even if they can only spend limited time in residence at SAMSI. The main program is organized around five working groups:i) Uncertainty Quantification and Astrophysical Emulationii) Synoptic Time Domain Surveysiii) Multivariate and Irregularly Sampled Time Seriesiv) Astrophysical Populationsv) Statistics, computation, and modeling in cosmology.A brief description of each of the work under way by these groups will be given. Overlaps among various working groups will also be highlighted. How the wider astronomy community can both participate and benefit from the activities, will be briefly mentioned.

Teaching Pascal's Triangle from a Computer Science Perspective

ERIC Educational Resources Information Center

Skurnick, Ronald

2004-01-01

Pascal's Triangle is named for the seventeenth-century French philosopher and mathematician Blaise Pascal (the same person for whom the computer programming language is named). Students are generally introduced to Pascal's Triangle in an algebra or precalculus class in which the Binomial Theorem is presented. This article, presents a new method…

Bridging the Vector Calculus Gap

NASA Astrophysics Data System (ADS)

Dray, Tevian; Manogue, Corinne

2003-05-01

As with Britain and America, mathematicians and physicists are separated from each other by a common language. In a nutshell, mathematics is about functions, but physics is about things. For the last several years, we have led an NSF-supported effort to "bridge the vector calculus gap" between mathematics and physics. The unifying theme we have discovered is to emphasize geometric reasoning, not (just) algebraic computation. In this talk, we will illustrate the language differences between mathematicians and physicists, and how we are trying reconcile them in the classroom. For further information about the project go to: http://www.physics.orst.edu/bridge

Becoming and Being a Mathematizing Mathematician

ERIC Educational Resources Information Center

De Geest, Els

2012-01-01

What does "to be a mathematician" mean? What is implied, and what image is created of "a mathematician"? Are "mathematicians" members of an exclusive club? Are mathematicians different to "other people"? Are mathematicians different because they are able to mathematize? These might not be the most oft asked questions, but are they questions to…

The Multiple Pendulum Problem via Maple[R

ERIC Educational Resources Information Center

Salisbury, K. L.; Knight, D. G.

2002-01-01

The way in which computer algebra systems, such as Maple, have made the study of physical problems of some considerable complexity accessible to mathematicians and scientists with modest computational skills is illustrated by solving the multiple pendulum problem. A solution is obtained for four pendulums with no restriction on the size of the…

Characteristics of the Navy Laboratory Warfare Center Technical Workforce

DTIC Science & Technology

2013-09-29

Mathematics and Information Science (M&IS) Actuarial Science 1510 Computer Science 1550 Gen. Math & Statistics 1501 Mathematics 1520 Operations...Admin. Network Systems & Data Communication Analysts Actuaries Mathematicians Operations Research Analyst Statisticians Social Science (SS...workforce was sub-divided into six broad occupational groups: Life Science , Physical Science , Engineering, Mathematics, Computer Science and Information

Climate science in the tropics: waves, vortices and PDEs

NASA Astrophysics Data System (ADS)

Khouider, Boualem; Majda, Andrew J.; Stechmann, Samuel N.

2013-01-01

Clouds in the tropics can organize the circulation on planetary scales and profoundly impact long range seasonal forecasting and climate on the entire globe, yet contemporary operational computer models are often deficient in representing these phenomena. On the other hand, contemporary observations reveal remarkably complex coherent waves and vortices in the tropics interacting across a bewildering range of scales from kilometers to ten thousand kilometers. This paper reviews the interdisciplinary contributions over the last decade through the modus operandi of applied mathematics to these important scientific problems. Novel physical phenomena, new multiscale equations, novel PDEs, and numerical algorithms are presented here with the goal of attracting mathematicians and physicists to this exciting research area.

Examining the Use of Computer Algebra Systems in University-Level Mathematics Teaching

ERIC Educational Resources Information Center

Lavicza, Zsolt

2009-01-01

The use of Computer Algebra Systems (CAS) is becoming increasingly important and widespread in mathematics research and teaching. In this paper, I will report on a questionnaire study enquiring about mathematicians' use of CAS in mathematics teaching in three countries; the United States, the United Kingdom, and Hungary. Based on the responses…

"Mathematicians Would Say It This Way": An Investigation of Teachers' Framings of Mathematicians

ERIC Educational Resources Information Center

Cirillo, Michelle; Herbel-Eisenmann, Beth

2011-01-01

Although popular media often provides negative images of mathematicians, we contend that mathematics classroom practices can also contribute to students' images of mathematicians. In this study, we examined eight mathematics teachers' framings of mathematicians in their classrooms. Here, we analyze classroom observations to explore some of the…

Fusion Simulation Project Workshop Report

NASA Astrophysics Data System (ADS)

Kritz, Arnold; Keyes, David

2009-03-01

The mission of the Fusion Simulation Project is to develop a predictive capability for the integrated modeling of magnetically confined plasmas. This FSP report adds to the previous activities that defined an approach to integrated modeling in magnetic fusion. These previous activities included a Fusion Energy Sciences Advisory Committee panel that was charged to study integrated simulation in 2002. The report of that panel [Journal of Fusion Energy 20, 135 (2001)] recommended the prompt initiation of a Fusion Simulation Project. In 2003, the Office of Fusion Energy Sciences formed a steering committee that developed a project vision, roadmap, and governance concepts [Journal of Fusion Energy 23, 1 (2004)]. The current FSP planning effort involved 46 physicists, applied mathematicians and computer scientists, from 21 institutions, formed into four panels and a coordinating committee. These panels were constituted to consider: Status of Physics Components, Required Computational and Applied Mathematics Tools, Integration and Management of Code Components, and Project Structure and Management. The ideas, reported here, are the products of these panels, working together over several months and culminating in a 3-day workshop in May 2007.

Developing an Actuarial Track Utilizing Existing Resources

ERIC Educational Resources Information Center

Rodgers, Kathy V.; Sarol, Yalçin

2014-01-01

Students earning a degree in mathematics often seek information on how to apply their mathematical knowledge. One option is to follow a curriculum with an actuarial emphasis designed to prepare students as an applied mathematician in the actuarial field. By developing only two new courses and utilizing existing courses for Validation by…

The Unified English Braille Code: Examination by Science, Mathematics, and Computer Science Technical Expert Braille Readers

ERIC Educational Resources Information Center

Holbrook, M. Cay; MacCuspie, P. Ann

2010-01-01

Braille-reading mathematicians, scientists, and computer scientists were asked to examine the usability of the Unified English Braille Code (UEB) for technical materials. They had little knowledge of the code prior to the study. The research included two reading tasks, a short tutorial about UEB, and a focus group. The results indicated that the…

Developing Data System Engineers

NASA Astrophysics Data System (ADS)

Behnke, J.; Byrnes, J. B.; Kobler, B.

2011-12-01

In the early days of general computer systems for science data processing, staff members working on NASA's data systems would most often be hired as mathematicians. Computer engineering was very often filled by those with electrical engineering degrees. Today, the Goddard Space Flight Center has special position descriptions for data scientists or as they are more commonly called: data systems engineers. These staff members are required to have very diverse skills, hence the need for a generalized position description. There is always a need for data systems engineers to develop, maintain and operate the complex data systems for Earth and space science missions. Today's data systems engineers however are not just mathematicians, they are computer programmers, GIS experts, software engineers, visualization experts, etc... They represent many different degree fields. To put together distributed systems like the NASA Earth Observing Data and Information System (EOSDIS), staff are required from many different fields. Sometimes, the skilled professional is not available and must be developed in-house. This paper will address the various skills and jobs for data systems engineers at NASA. Further it explores how to develop staff to become data scientists.

What makes a mathematician?

NASA Astrophysics Data System (ADS)

Harris, Margaret

2017-12-01

Sofia Vasilyevna Kovalevskaia is surely the only person in history who became a mathematician because of a botched redecoration project. She is one of 25 mathematicians profiled in Ian Stewart's book Significant Figures: the Lives and Work of Great Mathematicians.

Molecular modeling: An open invitation for applied mathematics

NASA Astrophysics Data System (ADS)

Mezey, Paul G.

2013-10-01

Molecular modeling methods provide a very wide range of challenges for innovative mathematical and computational techniques, where often high dimensionality, large sets of data, and complicated interrelations imply a multitude of iterative approximations. The physical and chemical basis of these methodologies involves quantum mechanics with several non-intuitive aspects, where classical interpretation and classical analogies are often misleading or outright wrong. Hence, instead of the everyday, common sense approaches which work so well in engineering, in molecular modeling one often needs to rely on rather abstract mathematical constraints and conditions, again emphasizing the high level of reliance on applied mathematics. Yet, the interdisciplinary aspects of the field of molecular modeling also generates some inertia and perhaps too conservative reliance on tried and tested methodologies, that is at least partially caused by the less than up-to-date involvement in the newest developments in applied mathematics. It is expected that as more applied mathematicians take up the challenge of employing the latest advances of their field in molecular modeling, important breakthroughs may follow. In this presentation some of the current challenges of molecular modeling are discussed.

Remembering Zoltan Dienes, a Maverick of Mathematics Teaching and Learning: Applying the Variability Principles to Teach Algebra

ERIC Educational Resources Information Center

Gningue, Serigne Mbaye

2016-01-01

This paper is written in honor of Zoltan Paul Dienes, an internationally renowned mathematician and educator, who passed away in January 2014. It is an attempt to describe, analyze and apply Dienes' theory on how mathematical structures can be taught by applying his four principles of learning upon which he believed a teacher can base concept…

Mathematical Visualization

ERIC Educational Resources Information Center

Rogness, Jonathan

2011-01-01

Advances in computer graphics have provided mathematicians with the ability to create stunning visualizations, both to gain insight and to help demonstrate the beauty of mathematics to others. As educators these tools can be particularly important as we search for ways to work with students raised with constant visual stimulation, from video games…

Quotable Quotes in Mathematics

ERIC Educational Resources Information Center

Lo, Bruce W. N.

1983-01-01

As a way to dispel negative feelings toward mathematics, a variety of quotations are given. They are categorized by: what mathematics is, mathematicians, mathematics and other disciplines, different areas of mathematics, mathematics and humor, applications of mathematics, and pure versus applied mathematics. (MNS)

An on-line system for hand-printed input

NASA Technical Reports Server (NTRS)

Williams, T. G.; Bebb, J.

1971-01-01

The capability of graphic input/output systems is described. Topics considered are a character recognizer and dictionary building program, an initial flow chart element input program, and a system entitled The Assistant Mathematician, which uses ordinary mathematics to specify numeric computation. All three parts are necessary to allow a user to carry on a mathematical dialogue with the computer in the language and notation of his discipline or problem domain.

Solving the "Hidden Line" Problem

NASA Technical Reports Server (NTRS)

1984-01-01

David Hedgley Jr., a mathematician at Dryden Flight Research Center, has developed an accurate computer program that considers whether a line in a graphic model of a three dimensional object should or should not be visible. The Hidden Line Computer Code, program automatically removes superfluous lines and permits the computer to display an object from specific viewpoints, just as the human eye would see it. Users include Rowland Institute for Science in Cambridge, MA, several departments of Lockheed Georgia Co., and Nebraska Public Power District (NPPD).

Mathematicians' Perspectives on Features of a Good Pedagogical Proof

ERIC Educational Resources Information Center

Lai, Yvonne; Weber, Keith; Mejia-Ramos, Juan Pablo

2012-01-01

In this article, we report two studies investigating what mathematicians value in a pedagogical proof. Study 1 is a qualitative study of how eight mathematicians revised two proofs that would be presented in a course for mathematics majors. These mathematicians thought that introductory and concluding sentences should be included in the proofs,…

Mathematicians' Views on Current Publishing Issues: A Survey of Researchers

ERIC Educational Resources Information Center

Fowler, Kristine K.

2011-01-01

This article reports research mathematicians' attitudes about and activity in specific scholarly communication areas, as captured in a 2010 survey of more than 600 randomly-selected mathematicians worldwide. Key findings include: (1) Most mathematicians have papers in the arXiv, but posting to their own web pages remains more common; (2) A third…

Data in the Cloud

ERIC Educational Resources Information Center

Bull, Glen; Garofalo, Joe

2010-01-01

The ability to move from one representation of data to another is one of the key characteristics of expert mathematicians and scientists. Cloud computing will offer more opportunities to create and display multiple representations of data, making this skill even more important in the future. The advent of the Internet led to widespread…

Bernoulli's Principle: Science as a Human Endeavor

ERIC Educational Resources Information Center

McCarthy, Deborah

2008-01-01

What do the ideas of Daniel Bernoulli--an 18th-century Swiss mathematician, physicist, natural scientist, and professor--and your students' next landing of the space shuttle via computer simulation have in common? Because of his contribution, referred in physical science as Bernoulli's principle, modern flight is possible. The mini learning-cycle…

An Invitation to the Mathematics of Topological Quantum Computation

NASA Astrophysics Data System (ADS)

Rowell, E. C.

2016-03-01

Two-dimensional topological states of matter offer a route to quantum computation that would be topologically protected against the nemesis of the quantum circuit model: decoherence. Research groups in industry, government and academic institutions are pursuing this approach. We give a mathematician's perspective on some of the advantages and challenges of this model, highlighting some recent advances. We then give a short description of how we might extend the theory to three-dimensional materials.

Sixteenth ARPA Systems and Technology Symposium

DTIC Science & Technology

1993-06-22

10:1 weight reduction over existing MILSTAR feed networks. 0 • In addition, EMS has demonstrated their dedication to ARPA and this technology bY cost...Corporation Computing Devices International DynCorp-Meridian COMSAT Laboratories E-Systems Inc. Context Systems Eastman Kodak Company Contraves Inc. EG&G CTA...were outstanding mathematicians and said, "Your first project is to compute how much volume and weight of water would fill the light bulb." He gave

Your Students' Images of Mathematicians and Mathematics.

ERIC Educational Resources Information Center

Picker, Susan H.; Berry, John S.

2001-01-01

Discusses the subliminal images that students might have of mathematicians. Presents the disparity between boys and girls in envisioning mathematicians of their own sex. Explores implications for pedagogy. (KHR)

Philipp Frank, Richard von Mises, and the Frank-Mises

NASA Astrophysics Data System (ADS)

Siegmund-Schultze, Reinhard

2007-01-01

The theoretical physicist Philipp Frank (1884 1966) and the applied mathematician Richard von Mises (1883 1953) both received their university education in Vienna shortly after 1900 and became friends at the latest during the Great War.They were attached to the Vienna Circle of Logical Positivists and wrote an influential two-part work on the differential and integral equations of mechanics and physics, the Frank-Mises, of 1925 and 1927, with its second edition following in 1930 and 1935.This work originated in the lectures that the mathematician Bernhard Riemann (1826 1866) delivered on partial differential equations and their applications to physical questions at the University of Göttingen between 1854 and 1862, which were edited and published posthumously in1869 by the physicist Karl Hattendorff (1834 1882).The immediate precursor of the Frank-Mises, however, was the extensive revision of Hattendorff’s edition of Riemann’s lectures that the mathematician Heinrich Weber (1842 1913) published in two volumes, the Riemann-Weber, of 1900 and 1901, with its second edition following in 1910 and 1912. I trace this historical lineage, explore the nature and contents of the Frank-Mises, and discuss its complementary relationship to the first volume of the text that the mathematicians Richard Courant (1888 1972) and David Hilbert (1862 1943) published on the methods of mathematical physics in 1924, the Courant-Hilbert,which, when it and its second volume of 1937 were translated into English and extensively revised in 1953 and 1961, eclipsed the classic Frank-Mises.

Benjamin Banneker and the Law of Sines

ERIC Educational Resources Information Center

Mahoney, John F.

2005-01-01

Benjamin Banneker, a self-taught mathematician, surveyor and astronomer published annual almanacs containing his astronomical observations and predictions. Banneker who also used logarithms to apply the Law of Sines believed that the method used to solve a mathematical problem depends on the tools available.

History of Binary and Other Nondecimal Numeration.

ERIC Educational Resources Information Center

Glaser, Anton

This study traces the development of nondecimal numeration from the 16th century to the present. The first six chapters detail the contributions of mathematicians as well as people from other fields. Applications to computers are covered in one chapter, while another chapter discusses the coverage of numeration systems in college textbooks for…

Euclid, Fibonacci, Sketchpad.

ERIC Educational Resources Information Center

Litchfield, Daniel C.; Goldenheim, David A.

1997-01-01

Describes the solution to a geometric problem by two ninth-grade mathematicians using The Geometer's Sketchpad computer software program. The problem was to divide any line segment into a regular partition of any number of parts, a variation on a problem by Euclid. The solution yielded two constructions, one a GLaD construction and the other using…

Introduction to Mathematica® for Physicists

NASA Astrophysics Data System (ADS)

Grozin, Andrey

We were taught at calculus classes that integration is an art, not a science (in contrast to differentiation—even a monkey can be trained to take derivatives). And we were taught wrong. The Risch algorithm (which is known for decades) allows one to find, in a finite number of steps, if a given indefinite integral can be taken in elementary functions, and if so, to calculate it. This algorithm has been constructed in works by an American mathematician Risch near 1970; many cases were not analyzed completely in these works and were later considered by other mathematicians. The algorithm is very complicated, and no computer algebra system implements it fully. Its implementation in Mathematica is rather complete, even with extensions to some classes of special functions, but details are not publicly known. Strictly speaking, it is not quite an algorithm, because it contains algorithmically unsolvable subproblems, such as finding out if a given combination of elementary functions vanishes. But in practice computer algebra systems are quite good in solving such problems. Here we shall consider, at a very elementary level, the main ideas of the Risch algorithm; see [16] for more details.

Marketing and commercialization of computational research services.

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

Toevs, J. W.

Physical and computational scientists and mathematicians in Russia's nuclear cities are turning their work toward generating profits from Western markets. Successful ventures require an understanding of the marketing of contract research as well as Western expectations regarding contract execution, quality, and performance. This paper will address fundamentals in business structure, marketing, and contract performance for organizations engaging in the marketing and commercialization of research services. Considerable emphasis will be placed on developing adequate communication within the organization.

Developing Mathematical Habits of Mind

ERIC Educational Resources Information Center

Mark, June; Cuoco, Al; Goldenberg, E. Paul; Sword, Sarah

2010-01-01

"Mathematical habits of mind" include reasoning by continuity, looking at extreme cases, performing thought experiments, and using abstraction that mathematicians use in their work. Current recommendations emphasize the critical nature of developing these habits of mind: "Once this kind of thinking is established, students can apply it in the…

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)

Gloria Hewitt: Mathematician.

ERIC Educational Resources Information Center

Lattimore, Randy

2001-01-01

Points out the importance of incorporating minority life histories in education. Presents biographical information on Gloria Hewitt, a woman mathematician of color, to help encourage all potential mathematicians, especially those who belong to minority groups. Includes practical suggestions that teachers can use to encourage or inspire students to…

The Characteristics of Mathematical Creativity

ERIC Educational Resources Information Center

Sriraman, Bharath

2004-01-01

Mathematical creativity ensures the growth of mathematics as a whole. However, the source of this growth, the creativity of the mathematician, is a relatively unexplored area in mathematics and mathematics education. In order to investigate how mathematicians create mathematics, a qualitative study involving five creative mathematicians was…

The Expert Mathematician. Revised. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2006

2006-01-01

"The Expert Mathematician" is designed to help middle school students develop the thinking processes for mathematical applications and communication. A three-year program of instruction, "The Expert Mathematician" uses a software and consumable print materials package with 196 lessons that teach the "Logo" programming…

Drawing Space: Mathematicians' Kinetic Conceptions of Eigenvectors

ERIC Educational Resources Information Center

Sinclair, Nathalie; Gol Tabaghi, Shiva

2010-01-01

This paper explores how mathematicians build meaning through communicative activity involving talk, gesture and diagram. In the course of describing mathematical concepts, mathematicians use these semiotic resources in ways that blur the distinction between the mathematical and physical world. We shall argue that mathematical meaning of…

What are mathematicians doing?

PubMed

Friedman, B

1966-10-21

Let me emphasize the point I have been trying to make. The mathematician's playing with the roots of equations, a play which had no practical motivations and almost no possibilities of practical application, led to the recognition of the importance of symmetry and groups. The study of theory of groups led to mathematical discoveries in geometry and differential equations, and finally to prediction of the existence of a new elementary particle. Surely a surprising outcome for the ivory-tower speculations of an impractical mathematician! Despite my professional bias, I must acknowledge that the importance of symmetry was recognized before mathematicians invented the theory of groups. In 1794 William Blake wrote: Tiger, Tiger, burning bright In the forests of the night, What immortal hand or eye Could frame thy fearful symmetry? However, to the mathematicians must be given the credit of recognizing that, to understand symmetry, you must study the theory of groups. I can now answer my original question, What are mathematicians doing? They are trying to make precise the intuitions of poets.

Mathematicians' Perspectives on the Utility of Software

ERIC Educational Resources Information Center

Quinlan, James

2016-01-01

In this study, we examine mathematicians' perspectives of the utility of software in mathematics and the teaching of mathematics. In particular, we report findings from a survey questioning 422 mathematicians with respect to their beliefs regarding the usefulness of software in mathematics research, teaching, and learning; recommended software…

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…

The Writing Mathematician

ERIC Educational Resources Information Center

Yoon, Caroline

2017-01-01

Popular culture casts mathematics and writing as opposites--a false dichotomy, which can be harmful for our discipline of mathematics education. Positioning writing outside the domain of the mathematician's abilities and cultivated skill set can create doubt in the mathematician wishing to write--not that one cannot be both writer and…

Advanced Methodologies for NASA Science Missions

NASA Astrophysics Data System (ADS)

Hurlburt, N. E.; Feigelson, E.; Mentzel, C.

2017-12-01

Most of NASA's commitment to computational space science involves the organization and processing of Big Data from space-based satellites, and the calculations of advanced physical models based on these datasets. But considerable thought is also needed on what computations are needed. The science questions addressed by space data are so diverse and complex that traditional analysis procedures are often inadequate. The knowledge and skills of the statistician, applied mathematician, and algorithmic computer scientist must be incorporated into programs that currently emphasize engineering and physical science. NASA's culture and administrative mechanisms take full cognizance that major advances in space science are driven by improvements in instrumentation. But it is less well recognized that new instruments and science questions give rise to new challenges in the treatment of satellite data after it is telemetered to the ground. These issues might be divided into two stages: data reduction through software pipelines developed within NASA mission centers; and science analysis that is performed by hundreds of space scientists dispersed through NASA, U.S. universities, and abroad. Both stages benefit from the latest statistical and computational methods; in some cases, the science result is completely inaccessible using traditional procedures. This paper will review the current state of NASA and present example applications using modern methodologies.

The Portrayal of Mathematicians and Mathematics in Popular Culture

ERIC Educational Resources Information Center

Barba, Kimberly

2018-01-01

Mathematicians are often inimically portrayed in popular culture, resulting in an abundance of non-mathematical identities in the classroom. Various tropes are propagated by the media that dominate our mental schemas of what makes a mathematician: the eccentric Einstein-like old man; the young, tortured genius; and the "genetically…

Information Seeking Behaviour of Mathematicians: Scientists and Students

ERIC Educational Resources Information Center

Sapa, Remigiusz; Krakowska, Monika; Janiak, Malgorzata

2014-01-01

Introduction: The paper presents original research designed to explore and compare selected aspects of the information seeking behaviour of mathematicians (scientists and students) on the Internet. Method: The data were gathered through a questionnaire distributed at the end of 2011 and in January 2012. Twenty-nine professional mathematicians and…

Proofs that Develop Insight

ERIC Educational Resources Information Center

Weber, Keith

2010-01-01

Many mathematics educators have noted that mathematicians do not only read proofs to gain conviction but also to obtain insight. The goal of this article is to discuss what this insight is from mathematicians' perspective. Based on interviews with nine research-active mathematicians, two sources of insight are discussed. The first is reading a…

Thinking Like a Mathematician

ERIC Educational Resources Information Center

Weiss, Michael K.; Moore-Russo, Deborah

2012-01-01

What does it mean to think like a mathematician? One of the great paradoxes of mathematics education is that, although mathematics teachers are immersed in mathematical work every day of their professional lives, most of them nevertheless have little experience with the kind of work that research mathematicians do. Their ideas of what doing…

The interaction of representation and reasoning.

PubMed

Bundy, Alan

2013-09-08

Automated reasoning is an enabling technology for many applications of informatics. These applications include verifying that a computer program meets its specification; enabling a robot to form a plan to achieve a task and answering questions by combining information from diverse sources, e.g. on the Internet, etc. How is automated reasoning possible? Firstly, knowledge of a domain must be stored in a computer, usually in the form of logical formulae. This knowledge might, for instance, have been entered manually, retrieved from the Internet or perceived in the environment via sensors, such as cameras. Secondly, rules of inference are applied to old knowledge to derive new knowledge. Automated reasoning techniques have been adapted from logic, a branch of mathematics that was originally designed to formalize the reasoning of humans, especially mathematicians. My special interest is in the way that representation and reasoning interact. Successful reasoning is dependent on appropriate representation of both knowledge and successful methods of reasoning. Failures of reasoning can suggest changes of representation. This process of representational change can also be automated. We will illustrate the automation of representational change by drawing on recent work in my research group.

Llewellyn Hilleth Thomas: An appraisal of an under-appreciated polymath

NASA Astrophysics Data System (ADS)

Jackson, John David

2010-02-01

Llewellyn Hilleth Thomas was born in 1903 and died in 1992 at the age of 88. His name is known by most for only two things, Thomas precession and the Thomas-Fermi atom. The many other facets of his career - astrophysics, atomic and molecular physics, nonlinear problems, accelerator physics, magnetohydrodynamics, computer design principles and software and hardware - are largely unknown or forgotten. I review his whole career - his early schooling, his time at Cambridge, then Copenhagen in 1925-26, and back to Cambridge, his move to the US as an assistant professor at Ohio State University in 1929, his wartime years at the Ballistic Research Laboratory, Aberdeen Proving Grounds, then in 1946 his new career as a unique resource at IBM's Watson Scientific Computing Laboratory and Columbia University until his first retirement in 1968, and his twilight years at North Carolina State University. Although the Thomas precession and the Thomas-Fermi atom may be the jewels in his crown, his many other accomplishments add to our appreciation of this consummate applied mathematician and physicist. )

Felix Klein and the NCTM's Standards: A Mathematician Considers Mathematics Education.

ERIC Educational Resources Information Center

McComas, Kim Krusen

2000-01-01

Discusses the parallels between Klein's position at the forefront of a movement to reform mathematics education and that of the National Council of Teachers of Mathematics' (NCTM) Standards. Draws a picture of Klein as an important historical figure who saw equal importance in studying pure mathematics, applying mathematics, and teaching…

Dee, John (1527-1608)

NASA Astrophysics Data System (ADS)

Murdin, P.

2000-11-01

Navigator, mathematician, traveler, polymath, mystic, charlatan, astrologer, model for Shakespeare's Prospero and King Lear, and court intriguer. Born in London, he became a navigation instructor, applying Euclidean geometry to navigation and building the instruments to do so. He advised expeditions seeking the Northwest passage to the Pacific via Canada. He cast horoscopes for Elizabeth I, recei...

Grading A-Level Double Subject Mathematicians and the Implications for Selection.

ERIC Educational Resources Information Center

Newbould, Charles A.

1981-01-01

Test data were used to compare the grading of two forms of double mathematics: pure and applied math, and regular and advanced math. Results confirm expectations that in the former system, the grading is comparable, and in the latter, it is not necessarily comparable. Implications for student admission are discussed. (MSE)

Forest-fire models

Treesearch

Haiganoush Preisler; Alan Ager

2013-01-01

For applied mathematicians forest fire models refer mainly to a non-linear dynamic system often used to simulate spread of fire. For forest managers forest fire models may pertain to any of the three phases of fire management: prefire planning (fire risk models), fire suppression (fire behavior models), and postfire evaluation (fire effects and economic models). In...

Innovative and collaborative industrial mathematics in Europe

PubMed Central

2017-01-01

This paper presents a brief review of how industrial mathematics, inspired by the Oxford Study Group activity, organized itself in Europe, gave rise to the European Consortium for Mathematics in Industry, the series of European Study Groups with Industry, and to new modes of productive contacts between industry and applied mathematicians in academia. PMID:28588414

Innovative and collaborative industrial mathematics in Europe.

PubMed

Hjorth, Poul G

2017-05-01

This paper presents a brief review of how industrial mathematics, inspired by the Oxford Study Group activity, organized itself in Europe, gave rise to the European Consortium for Mathematics in Industry, the series of European Study Groups with Industry, and to new modes of productive contacts between industry and applied mathematicians in academia.

Information Technology in University-Level Mathematics Teaching and Learning: A Mathematician's Point of View

ERIC Educational Resources Information Center

Borovik, Alexandre

2011-01-01

Although mathematicians frequently use specialist software in direct teaching of mathematics, as a means of delivery e-learning technologies have so far been less widely used. We (mathematicians) insist that teaching methods should be subject-specific and content-driven, not delivery-driven. We oppose generic approaches to teaching, including…

Commitment of mathematicians in medicine: a personal experience, and generalisations.

PubMed

Clairambault, Jean

2011-12-01

I will present here a personal point of view on the commitment of mathematicians in medicine. Starting from my personal experience, I will suggest generalisations including favourable signs and caveats to show how mathematicians can be welcome and helpful in medicine, both in a theoretical and in a practical way.

Academic Mathematicians' Dispositions toward Software Use in Mathematics Instruction: What Are the Underlying Reasons?

ERIC Educational Resources Information Center

Khoshaim, Heba Bakr

2012-01-01

Academic mathematicians' opinions are divided regarding software use in undergraduate mathematics instruction. This study explored these opinions through interviews and a subsequent survey of mathematicians at PhD-granting institutions in the United States regarding their dispositions and the underlying attitudes. Most prior related work had…

Visualizing a silicon quantum computer

NASA Astrophysics Data System (ADS)

Sanders, Barry C.; Hollenberg, Lloyd C. L.; Edmundson, Darran; Edmundson, Andrew

2008-12-01

Quantum computation is a fast-growing, multi-disciplinary research field. The purpose of a quantum computer is to execute quantum algorithms that efficiently solve computational problems intractable within the existing paradigm of 'classical' computing built on bits and Boolean gates. While collaboration between computer scientists, physicists, chemists, engineers, mathematicians and others is essential to the project's success, traditional disciplinary boundaries can hinder progress and make communicating the aims of quantum computing and future technologies difficult. We have developed a four minute animation as a tool for representing, understanding and communicating a silicon-based solid-state quantum computer to a variety of audiences, either as a stand-alone animation to be used by expert presenters or embedded into a longer movie as short animated sequences. The paper includes a generally applicable recipe for successful scientific animation production.

Liquid Sloshing Dynamics

NASA Astrophysics Data System (ADS)

Ibrahim, Raouf A.

2005-06-01

The problem of liquid sloshing in moving or stationary containers remains of great concern to aerospace, civil, and nuclear engineers; physicists; designers of road tankers and ship tankers; and mathematicians. Beginning with the fundamentals of liquid sloshing theory, this book takes the reader systematically from basic theory to advanced analytical and experimental results in a self-contained and coherent format. The book is divided into four sections. Part I deals with the theory of linear liquid sloshing dynamics; Part II addresses the nonlinear theory of liquid sloshing dynamics, Faraday waves, and sloshing impacts; Part III presents the problem of linear and nonlinear interaction of liquid sloshing dynamics with elastic containers and supported structures; and Part IV considers the fluid dynamics in spinning containers and microgravity sloshing. This book will be invaluable to researchers and graduate students in mechanical and aeronautical engineering, designers of liquid containers, and applied mathematicians.

Bruno de Finetti: the mathematician, the statistician, the economist, the forerunner.

PubMed

Rossi, C

2001-12-30

Bruno de Finetti is possibly the best known Italian applied mathematician of the 20th century, but was he really just a mathematician? Looking at his papers it is always possible to find original and pioneering contributions to the various fields he was interested in, where he always put his mathematical "formamentis" and skills at the service of the applications, often extending standard theories and models in order to achieve more general results. Many contributions are also devoted to educational issues, in mathematics in general and in probability and statistics in particular.He really thought that mathematics and, in particular, those topics related to uncertainty, should enter in everyday life as a useful support to everyone's decision making. He always imagined and lived mathematics as a basic tool both for better understanding and describing complex phenomena and for helping decision makers in assuming coherent and feasible actions. His many important contributions to the theory of probability and to mathematical statistics are well known all over the world, thus, in the following, minor, but still pioneering, aspects of his work, related both to theory and to applications of mathematical tools, and to his work in the field of education and training of teachers, are presented. Copyright 2001 John Wiley & Sons, Ltd.

Exascale computing and what it means for shock physics

NASA Astrophysics Data System (ADS)

Germann, Timothy

2015-06-01

The U.S. Department of Energy is preparing to launch an Exascale Computing Initiative, to address the myriad challenges required to deploy and effectively utilize an exascale-class supercomputer (i.e., one capable of performing 1018 operations per second) in the 2023 timeframe. Since physical (power dissipation) requirements limit clock rates to at most a few GHz, this will necessitate the coordination of on the order of a billion concurrent operations, requiring sophisticated system and application software, and underlying mathematical algorithms, that may differ radically from traditional approaches. Even at the smaller workstation or cluster level of computation, the massive concurrency and heterogeneity within each processor will impact computational scientists. Through the multi-institutional, multi-disciplinary Exascale Co-design Center for Materials in Extreme Environments (ExMatEx), we have initiated an early and deep collaboration between domain (computational materials) scientists, applied mathematicians, computer scientists, and hardware architects, in order to establish the relationships between algorithms, software stacks, and architectures needed to enable exascale-ready materials science application codes within the next decade. In my talk, I will discuss these challenges, and what it will mean for exascale-era electronic structure, molecular dynamics, and engineering-scale simulations of shock-compressed condensed matter. In particular, we anticipate that the emerging hierarchical, heterogeneous architectures can be exploited to achieve higher physical fidelity simulations using adaptive physics refinement. This work is supported by the U.S. Department of Energy, Office of Science, Office of Advanced Scientific Computing Research.

Exploring High-Achieving Students' Images of Mathematicians

ERIC Educational Resources Information Center

Aguilar, Mario Sánchez; Rosas, Alejandro; Zavaleta, Juan Gabriel Molina; Romo-Vázquez, Avenilde

2016-01-01

The aim of this study is to describe the images that a group of high-achieving Mexican students hold of mathematicians. For this investigation, we used a research method based on the Draw-A-Scientist Test (DAST) with a sample of 63 Mexican high school students. The group of students' pictorial and written descriptions of mathematicians assisted us…

How Mathematicians Determine if an Argument Is a Valid Proof

ERIC Educational Resources Information Center

Weber, Keith

2008-01-01

The purpose of this article is to investigate the mathematical practice of proof validation--that is, the act of determining whether an argument constitutes a valid proof. The results of a study with 8 mathematicians are reported. The mathematicians were observed as they read purported mathematical proofs and made judgments about their validity;…

Computational Models of Rock Failure

NASA Astrophysics Data System (ADS)

May, Dave A.; Spiegelman, Marc

2017-04-01

Practitioners in computational geodynamics, as per many other branches of applied science, typically do not analyse the underlying PDE's being solved in order to establish the existence or uniqueness of solutions. Rather, such proofs are left to the mathematicians, and all too frequently these results lag far behind (in time) the applied research being conducted, are often unintelligible to the non-specialist, are buried in journals applied scientists simply do not read, or simply have not been proven. As practitioners, we are by definition pragmatic. Thus, rather than first analysing our PDE's, we first attempt to find approximate solutions by throwing all our computational methods and machinery at the given problem and hoping for the best. Typically this approach leads to a satisfactory outcome. Usually it is only if the numerical solutions "look odd" that we start delving deeper into the math. In this presentation I summarise our findings in relation to using pressure dependent (Drucker-Prager type) flow laws in a simplified model of continental extension in which the material is assumed to be an incompressible, highly viscous fluid. Such assumptions represent the current mainstream adopted in computational studies of mantle and lithosphere deformation within our community. In short, we conclude that for the parameter range of cohesion and friction angle relevant to studying rocks, the incompressibility constraint combined with a Drucker-Prager flow law can result in problems which have no solution. This is proven by a 1D analytic model and convincingly demonstrated by 2D numerical simulations. To date, we do not have a robust "fix" for this fundamental problem. The intent of this submission is to highlight the importance of simple analytic models, highlight some of the dangers / risks of interpreting numerical solutions without understanding the properties of the PDE we solved, and lastly to stimulate discussions to develop an improved computational model of rock failure suitable for geodynamic studies.

Introducing geometry concept based on history of Islamic geometry

NASA Astrophysics Data System (ADS)

Maarif, S.; Wahyudin; Raditya, A.; Perbowo, K. S.

2018-01-01

Geometry is one of the areas of mathematics interesting to discuss. Geometry also has a long history in mathematical developments. Therefore, it is important integrated historical development of geometry in the classroom to increase’ knowledge of how mathematicians earlier finding and constructing a geometric concept. Introduction geometrical concept can be started by introducing the Muslim mathematician who invented these concepts so that students can understand in detail how a concept of geometry can be found. However, the history of mathematics development, especially history of Islamic geometry today is less popular in the world of education in Indonesia. There are several concepts discovered by Muslim mathematicians that should be appreciated by the students in learning geometry. Great ideas of mathematicians Muslim can be used as study materials to supplement religious character values taught by Muslim mathematicians. Additionally, by integrating the history of geometry in teaching geometry are expected to improve motivation and geometrical understanding concept.

Mathematicians, Attributional Complexity, and Gender

NASA Astrophysics Data System (ADS)

Stalder, Daniel R.

Given indirect indications in sex role and soda! psychology research that mathematical-deductive reasoning may negatively relate to social acuity, Study 1 investigated whether mathematicians were less attributionally complex than nonmathematicians. Study 1 administered the Attributional Complexity Scale, a measure of social acuity, to female and male faculty members and graduate students in four Midwestern schools. Atlrihutional complexity (AC) is the ability and motivation to give complex explanations for behavior. Study 1 found a significant interaction between field and gender. Only among women did mathematicians score lower on AC. In addition, an established gender difference in AC (that women score higher than men) was present only among nonmathematicians. Studies 2 and 3 offered some preliminary support for the possibility that it is generally female students who score tow on AC who aspire to he mathematicians and for the underlying view that female students' perceived similarity to mathematicians can influence their vocational choices.

Gravitation, Symmetry and Undergraduates

NASA Astrophysics Data System (ADS)

Jorgensen, Jamie

2001-04-01

This talk will discuss "Project Petrov" Which is designed to investigate gravitational fields with symmetry. Project Petrov represents a collaboration involving physicists, mathematicians as well as graduate and undergraduate math and physics students. An overview of Project Petrov will be given, with an emphasis on students' contributions, including software to classify and generate Lie algebras, to classify isometry groups, and to compute the isometry group of a given metric.

Computer Attitude, Use, Experience, Software Familiarity and Perceived Pedagogical Usefulness: The Case of Mathematics Professors

ERIC Educational Resources Information Center

Yushau, Balarabe

2006-01-01

As the pedagogical-effectiveness of information technology (IT) in mathematics education is carefully established the topic of discourse among mathematicians and mathematics educators is no longer a dispute about whether or not to use IT in the teaching and learning of mathematics but a shift to some debate about the when and how of its usage.…

A computational image analysis glossary for biologists.

PubMed

Roeder, Adrienne H K; Cunha, Alexandre; Burl, Michael C; Meyerowitz, Elliot M

2012-09-01

Recent advances in biological imaging have resulted in an explosion in the quality and quantity of images obtained in a digital format. Developmental biologists are increasingly acquiring beautiful and complex images, thus creating vast image datasets. In the past, patterns in image data have been detected by the human eye. Larger datasets, however, necessitate high-throughput objective analysis tools to computationally extract quantitative information from the images. These tools have been developed in collaborations between biologists, computer scientists, mathematicians and physicists. In this Primer we present a glossary of image analysis terms to aid biologists and briefly discuss the importance of robust image analysis in developmental studies.

On Mathematicians' Proof Skimming: A Reply to Inglis and Alcock

ERIC Educational Resources Information Center

Weber, Keith; Mejia-Ramos, Juan Pablo

2013-01-01

n a recent article, Inglis and Alcock (2012) contended that their data challenge the claim that when mathematicians validate proofs, they initially skim a proof to grasp its main idea before reading individual parts of the proof more carefully. This result is based on the fact that when mathematicians read proofs in their study, on average their…

Constructions of Mathematicians in Popular Culture and Learners' Narratives: A Study of Mathematical and Non-Mathematical Subjectivities

ERIC Educational Resources Information Center

Moreau, Marie-Pierre; Mendick, Heather; Epstein, Debbie

2010-01-01

In this paper, based on a project funded by the UK Economic and Social Research Council considering how people position themselves in relation to popular representations of mathematics and mathematicians, we explore constructions of mathematicians in popular culture and the ways learners make meanings from these. Drawing on an analysis of popular…

A FIRST STEP TOWARDS THE IMPLEMENTATION OF THE CAMBRIDGE MATHEMATICS CURRICULUM IN A K-12 UNGRADED SCHOOL.

ERIC Educational Resources Information Center

FOSTER, GARRETT R.

A SERIES OF THREE CONFERENCES WAS HELD TO EXPLORE THE FEASIBILITY OF IMPLEMENTING A LONG-RANGE CURRICULUM DEVELOPMENT PROJECT FOR AN UNGRADED, K-12 SCHOOL, BASED ON RECOMMENDATIONS OF THE CAMBRIDGE CONFERENCE ON SCHOOL MATHEMATICS. OVER 50 MATHEMATICIANS, MATHEMATICS EDUCATORS, AND PERSONS INVOLVED IN THEORETICAL AND APPLIED PSYCHOLOGICAL…

Mathematical Sense, Mathematical Sensibility: The Role of the Secondary Geometry Course in Teaching Students to Be Like Mathematicians

ERIC Educational Resources Information Center

Weiss, Michael Kevin

2009-01-01

How can the secondary Geometry course serve as an opportunity for students to learn to "be like" a mathematician--that is, to acquire a mathematical sensibility? In the first part of this dissertation, I investigate what might be meant by "mathematical sensibility". By analyzing narratives of mathematicians and their work, I identify a collection…

Intuitive Space Weather Displays to Improve Space Situational Awareness (SSA)

DTIC Science & Technology

2011-09-01

parsimonious offering. After engaging several mathematicians and space physicists to devise valid computational formulas for aggregating the four hazard... PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Aptima, Inc.,12 Gill Street Ste 200,Woburn,MA... physicists , the operational users find little use in receiving particle fluxes or magnetometer readings collected by the scientific community. Fortunately

Professional mathematicians differ from controls in their spatial-numerical associations.

PubMed

Cipora, Krzysztof; Hohol, Mateusz; Nuerk, Hans-Christoph; Willmes, Klaus; Brożek, Bartosz; Kucharzyk, Bartłomiej; Nęcka, Edward

2016-07-01

While mathematically impaired individuals have been shown to have deficits in all kinds of basic numerical representations, among them spatial-numerical associations, little is known about individuals with exceptionally high math expertise. They might have a more abstract magnitude representation or more flexible spatial associations, so that no automatic left/small and right/large spatial-numerical association is elicited. To pursue this question, we examined the Spatial Numerical Association of Response Codes (SNARC) effect in professional mathematicians which was compared to two control groups: Professionals who use advanced math in their work but are not mathematicians (mostly engineers), and matched controls. Contrarily to both control groups, Mathematicians did not reveal a SNARC effect. The group differences could not be accounted for by differences in mean response speed, response variance or intelligence or a general tendency not to show spatial-numerical associations. We propose that professional mathematicians possess more abstract and/or spatially very flexible numerical representations and therefore do not exhibit or do have a largely reduced default left-to-right spatial-numerical orientation as indexed by the SNARC effect, but we also discuss other possible accounts. We argue that this comparison with professional mathematicians also tells us about the nature of spatial-numerical associations in persons with much less mathematical expertise or knowledge.

The Psychological Four-Color Mapping Problem

ERIC Educational Resources Information Center

Francis, Gregory; Bias, Keri; Shive, Joshua

2010-01-01

Mathematicians have proven that four colors are sufficient to color 2-D maps so that no neighboring regions share the same color. Here we consider the psychological 4-color problem: Identifying which 4 colors should be used to make a map easy to use. We build a model of visual search for this design task and demonstrate how to apply it to the task…

SIAM conference on applications of dynamical systems

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

Not Available

1992-01-01

A conference (Oct.15--19, 1992, Snowbird, Utah; sponsored by SIAM (Society for Industrial and Applied Mathematics) Activity Group on Dynamical Systems) was held that highlighted recent developments in applied dynamical systems. The main lectures and minisymposia covered theory about chaotic motion, applications in high energy physics and heart fibrillations, turbulent motion, Henon map and attractor, integrable problems in classical physics, pattern formation in chemical reactions, etc. The conference fostered an exchange between mathematicians working on theoretical issues of modern dynamical systems and applied scientists. This two-part document contains abstracts, conference program, and an author index.

SIAM conference on applications of dynamical systems. Abstracts and author index

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

Not Available

1992-12-31

A conference (Oct.15--19, 1992, Snowbird, Utah; sponsored by SIAM (Society for Industrial and Applied Mathematics) Activity Group on Dynamical Systems) was held that highlighted recent developments in applied dynamical systems. The main lectures and minisymposia covered theory about chaotic motion, applications in high energy physics and heart fibrillations, turbulent motion, Henon map and attractor, integrable problems in classical physics, pattern formation in chemical reactions, etc. The conference fostered an exchange between mathematicians working on theoretical issues of modern dynamical systems and applied scientists. This two-part document contains abstracts, conference program, and an author index.

Pattern perception and computational complexity: introduction to the special issue

PubMed Central

Fitch, W. Tecumseh; Friederici, Angela D.; Hagoort, Peter

2012-01-01

Research on pattern perception and rule learning, grounded in formal language theory (FLT) and using artificial grammar learning paradigms, has exploded in the last decade. This approach marries empirical research conducted by neuroscientists, psychologists and ethologists with the theory of computation and FLT, developed by mathematicians, linguists and computer scientists over the last century. Of particular current interest are comparative extensions of this work to non-human animals, and neuroscientific investigations using brain imaging techniques. We provide a short introduction to the history of these fields, and to some of the dominant hypotheses, to help contextualize these ongoing research programmes, and finally briefly introduce the papers in the current issue. PMID:22688630

Preface: SciDAC 2006

NASA Astrophysics Data System (ADS)

Tang, William M., Dr.

2006-01-01

The second annual Scientific Discovery through Advanced Computing (SciDAC) Conference was held from June 25-29, 2006 at the new Hyatt Regency Hotel in Denver, Colorado. This conference showcased outstanding SciDAC-sponsored computational science results achieved during the past year across many scientific domains, with an emphasis on science at scale. Exciting computational science that has been accomplished outside of the SciDAC program both nationally and internationally was also featured to help foster communication between SciDAC computational scientists and those funded by other agencies. This was illustrated by many compelling examples of how domain scientists collaborated productively with applied mathematicians and computer scientists to effectively take advantage of terascale computers (capable of performing trillions of calculations per second) not only to accelerate progress in scientific discovery in a variety of fields but also to show great promise for being able to utilize the exciting petascale capabilities in the near future. The SciDAC program was originally conceived as an interdisciplinary computational science program based on the guiding principle that strong collaborative alliances between domain scientists, applied mathematicians, and computer scientists are vital to accelerated progress and associated discovery on the world's most challenging scientific problems. Associated verification and validation are essential in this successful program, which was funded by the US Department of Energy Office of Science (DOE OS) five years ago. As is made clear in many of the papers in these proceedings, SciDAC has fundamentally changed the way that computational science is now carried out in response to the exciting challenge of making the best use of the rapid progress in the emergence of more and more powerful computational platforms. In this regard, Dr. Raymond Orbach, Energy Undersecretary for Science at the DOE and Director of the OS has stated: `SciDAC has strengthened the role of high-end computing in furthering science. It is defining whole new fields for discovery.' (SciDAC Review, Spring 2006, p8). Application domains within the SciDAC 2006 conference agenda encompassed a broad range of science including: (i) the DOE core mission of energy research involving combustion studies relevant to fuel efficiency and pollution issues faced today and magnetic fusion investigations impacting prospects for future energy sources; (ii) fundamental explorations into the building blocks of matter, ranging from quantum chromodynamics - the basic theory that describes how quarks make up the protons and neutrons of all matter - to the design of modern high-energy accelerators; (iii) the formidable challenges of predicting and controlling the behavior of molecules in quantum chemistry and the complex biomolecules determining the evolution of biological systems; (iv) studies of exploding stars for insights into the nature of the universe; and (v) integrated climate modeling to enable realistic analysis of earth's changing climate. Associated research has made it quite clear that advanced computation is often the only means by which timely progress is feasible when dealing with these complex, multi-component physical, chemical, and biological systems operating over huge ranges of temporal and spatial scales. Working with the domain scientists, applied mathematicians and computer scientists have continued to develop the discretizations of the underlying equations and the complementary algorithms to enable improvements in solutions on modern parallel computing platforms as they evolve from the terascale toward the petascale regime. Moreover, the associated tremendous growth of data generated from the terabyte to the petabyte range demands not only the advanced data analysis and visualization methods to harvest the scientific information but also the development of efficient workflow strategies which can deal with the data input/output, management, movement, and storage challenges. If scientific discovery is expected to keep apace with the continuing progression from tera- to petascale platforms, the vital alliance between domain scientists, applied mathematicians, and computer scientists will be even more crucial. During the SciDAC 2006 Conference, some of the future challenges and opportunities in interdisciplinary computational science were emphasized in the Advanced Architectures Panel and by Dr. Victor Reis, Senior Advisor to the Secretary of Energy, who gave a featured presentation on `Simulation, Computation, and the Global Nuclear Energy Partnership.' Overall, the conference provided an excellent opportunity to highlight the rising importance of computational science in the scientific enterprise and to motivate future investment in this area. As Michael Strayer, SciDAC Program Director, has noted: `While SciDAC may have started out as a specific program, Scientific Discovery through Advanced Computing has become a powerful concept for addressing some of the biggest challenges facing our nation and our world.' Looking forward to next year, the SciDAC 2007 Conference will be held from June 24-28 at the Westin Copley Plaza in Boston, Massachusetts. Chairman: David Keyes, Columbia University. The Organizing Committee for the SciDAC 2006 Conference would like to acknowledge the individuals whose talents and efforts were essential to the success of the meeting. Special thanks go to Betsy Riley for her leadership in building the infrastructure support for the conference, for identifying and then obtaining contributions from our corporate sponsors, for coordinating all media communications, and for her efforts in organizing and preparing the conference proceedings for publication; to Tim Jones for handling the hotel scouting, subcontracts, and exhibits and stage production; to Angela Harris for handling supplies, shipping, and tracking, poster sessions set-up, and for her efforts in coordinating and scheduling the promotional activities that took place during the conference; to John Bui and John Smith for their superb wireless networking and A/V set-up and support; to Cindy Latham for Web site design, graphic design, and quality control of proceedings submissions; and to Pamelia Nixon-Hartje of Ambassador for budget and quality control of catering. We are grateful for the highly professional dedicated efforts of all of these individuals, who were the cornerstones of the SciDAC 2006 Conference. Thanks also go to Angela Beach of the ORNL Conference Center for her efforts in executing the contracts with the hotel, Carolyn James of Colorado State for on-site registration supervision, Lora Wolfe and Brittany Hagen for administrative support at ORNL, and Dami Rich and Andrew Sproles for graphic design and production. We are also most grateful to the Oak Ridge National Laboratory, especially Jeff Nichols, and to our corporate sponsors, Data Direct Networks, Cray, IBM, SGI, and Institute of Physics Publishing for their support. We especially express our gratitude to the featured speakers, invited oral speakers, invited poster presenters, session chairs, and advanced architecture panelists and chair for their excellent contributions on behalf of SciDAC 2006. We would like to express our deep appreciation to Lali Chatterjee, Graham Douglas, Margaret Smith, and the production team of Institute of Physics Publishing, who worked tirelessly to publish the final conference proceedings in a timely manner. Finally, heartfelt thanks are extended to Michael Strayer, Associate Director for OASCR and SciDAC Director, and to the DOE program managers associated with SciDAC for their continuing enthusiasm and strong support for the annual SciDAC Conferences as a special venue to showcase the exciting scientific discovery achievements enabled by the interdisciplinary collaborations championed by the SciDAC program.

The interaction of representation and reasoning

PubMed Central

Bundy, Alan

2013-01-01

Automated reasoning is an enabling technology for many applications of informatics. These applications include verifying that a computer program meets its specification; enabling a robot to form a plan to achieve a task and answering questions by combining information from diverse sources, e.g. on the Internet, etc. How is automated reasoning possible? Firstly, knowledge of a domain must be stored in a computer, usually in the form of logical formulae. This knowledge might, for instance, have been entered manually, retrieved from the Internet or perceived in the environment via sensors, such as cameras. Secondly, rules of inference are applied to old knowledge to derive new knowledge. Automated reasoning techniques have been adapted from logic, a branch of mathematics that was originally designed to formalize the reasoning of humans, especially mathematicians. My special interest is in the way that representation and reasoning interact. Successful reasoning is dependent on appropriate representation of both knowledge and successful methods of reasoning. Failures of reasoning can suggest changes of representation. This process of representational change can also be automated. We will illustrate the automation of representational change by drawing on recent work in my research group. PMID:24062623

Formalizing an integrative, multidisciplinary cancer therapy discovery workflow

PubMed Central

McGuire, Mary F.; Enderling, Heiko; Wallace, Dorothy I.; Batra, Jaspreet; Jordan, Marie; Kumar, Sushil; Panetta, John C.; Pasquier, Eddy

2014-01-01

Although many clinicians and researchers work to understand cancer, there has been limited success to effectively combine forces and collaborate over time, distance, data and budget constraints. Here we present a workflow template for multidisciplinary cancer therapy that was developed during the 2nd Annual Workshop on Cancer Systems Biology sponsored by Tufts University, Boston, MA in July 2012. The template was applied to the development of a metronomic therapy backbone for neuroblastoma. Three primary groups were identified: clinicians, biologists, and scientists (mathematicians, computer scientists, physicists and engineers). The workflow described their integrative interactions; parallel or sequential processes; data sources and computational tools at different stages as well as the iterative nature of therapeutic development from clinical observations to in vitro, in vivo, and clinical trials. We found that theoreticians in dialog with experimentalists could develop calibrated and parameterized predictive models that inform and formalize sets of testable hypotheses, thus speeding up discovery and validation while reducing laboratory resources and costs. The developed template outlines an interdisciplinary collaboration workflow designed to systematically investigate the mechanistic underpinnings of a new therapy and validate that therapy to advance development and clinical acceptance. PMID:23955390

Simulating the Dynamics of Earth's Core: Using NCCS Supercomputers Speeds Calculations

NASA Technical Reports Server (NTRS)

2002-01-01

If one wanted to study Earth's core directly, one would have to drill through about 1,800 miles of solid rock to reach liquid core-keeping the tunnel from collapsing under pressures that are more than 1 million atmospheres and then sink an instrument package to the bottom that could operate at 8,000 F with 10,000 tons of force crushing every square inch of its surface. Even then, several of these tunnels would probably be needed to obtain enough data. Faced with difficult or impossible tasks such as these, scientists use other available sources of information - such as seismology, mineralogy, geomagnetism, geodesy, and, above all, physical principles - to derive a model of the core and, study it by running computer simulations. One NASA researcher is doing just that on NCCS computers. Physicist and applied mathematician Weijia Kuang, of the Space Geodesy Branch, and his collaborators at Goddard have what he calls the,"second - ever" working, usable, self-consistent, fully dynamic, three-dimensional geodynamic model (see "The Geodynamic Theory"). Kuang runs his model simulations on the supercomputers at the NCCS. He and Jeremy Bloxham, of Harvard University, developed the original version, written in Fortran 77, in 1996.

Control Circuitry for High Speed VLSI (Very Large Scale Integration) Winograd Fourier Transform Processors.

DTIC Science & Technology

1985-12-01

Office of Scientific Research , and Air Force Space Division are sponsoring research for the development of a high speed DFT processor. This DFT...to the arithmetic circuitry through a master/slave 11-15 %v OPR ONESHOT OUTPUT OUTPUT .., ~ INITIALIZATION COLUMN’ 00 N DONE CUTRPLANE PLAtNE Figure...Since the TSP is an NP-complete problem, many mathematicians, operations researchers , computer scientists and the like have proposed heuristic

The Tunnels of Samos

NASA Technical Reports Server (NTRS)

Apostol, Tom M. (Editor)

1995-01-01

This 'Project Mathematics' series video from CalTech presents the tunnel of Samos, a famous underground aquaduct tunnel located near the capital of Pithagorion (named after the famed Greek mathematician, Pythagoras, who lived there), on one of the Greek islands. This tunnel was constructed around 600 BC by King Samos and was built under a nearby mountain. Through film footage and computer animation, the mathematical principles and concepts of why and how this aquaduct tunnel was built are explained.

On the role of visual experience in mathematical development: Evidence from blind mathematicians.

PubMed

Amalric, Marie; Denghien, Isabelle; Dehaene, Stanislas

2018-04-01

Advanced mathematical reasoning, regardless of domain or difficulty, activates a reproducible set of bilateral brain areas including intraparietal, inferior temporal and dorsal prefrontal cortex. The respective roles of genetics, experience and education in the development of this math-responsive network, however, remain unresolved. Here, we investigate the role of visual experience by studying the exceptional case of three professional mathematicians who were blind from birth (n=1) or became blind during childhood (n=2). Subjects were scanned with fMRI while they judged the truth value of spoken mathematical and nonmathematical statements. Blind mathematicians activated the classical network of math-related areas during mathematical reflection, similar to that found in a group of sighted professional mathematicians. Thus, brain networks for advanced mathematical reasoning can develop in the absence of visual experience. Additional activations were found in occipital cortex, even in individuals who became blind during childhood, suggesting that either mental imagery or a more radical repurposing of visual cortex may occur in blind mathematicians. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.

Conversations about curriculum change: mathematical thinking and team-based learning in a discrete mathematics course

NASA Astrophysics Data System (ADS)

Paterson, Judy; Sneddon, Jamie

2011-10-01

This article reports on the learning conversations between a mathematician and a mathematics educator as they worked together to change the delivery model of a third year discrete mathematics course from a traditional lecture mode to team-based learning (TBL). This change prompted the mathematician to create team tasks which increasingly focused on what he calls the 'unspoken curriculum': mathematical thinking. We consider the ways in which the TBL model promoted and enabled this in the light of literature on mathematical thinking, sense-making and behaviours, and strongly suggest that this approach warrants more attention from the mathematics teaching community. We also discuss shifts in the mathematician's thinking about task construction as he refined the tasks to encourage students to think and behave like mathematicians.

A Multidimensional Approach to Training Mathematics Students at a University: Improving the Efficiency through the Unity of Social, Psychological and Pedagogical Aspects

ERIC Educational Resources Information Center

Kuznetsova, Elena; Matytcina, Marina

2018-01-01

The article deals with social, psychological and pedagogical aspects of teaching mathematics students at universities. The sociological portrait and the factors influencing a career choice of a mathematician have been investigated through the survey results of 198 first-year students of applied mathematics major at 27 state universities (Russia).…

Partially solidified systems

NASA Astrophysics Data System (ADS)

The evolution of magmas is a topic of considerable importance in geology and geophysics because it affects volcanology, igneous petrology, geothermal energy sources, mantle convection, and the thermaland chemical evolution of the earth. The dynamics and evolution of magmas are strongly affected by the presence of solid crystals that occur either in suspension in liquid or as a rigid porous matrix through which liquid magma can percolate. Such systems are physically complex and difficult to model mathematically. Similar physical situations are encountered by metallurgists who study the solidification of molten alloys, and applied mathematicians have long been interested in such moving boundary problems. Clearly, it would be of mutual benefit to bring together scientists, engineers, and mathematicians with a common interest in such systems. Such a meeting is being organized as a North Atlantic Treaty Organization (NATO) Advanced Research Workshop on the Structure and Dynamics of Partially Solidified Systems, to be held at Stanford University's Fallen Leaf Lodge at Tahoe, Calif., May 12-16, 1986 The invited speakers and their topics are

The Study Team for Early Life Asthma Research (STELAR) consortium ‘Asthma e-lab’: team science bringing data, methods and investigators together

PubMed Central

Custovic, Adnan; Ainsworth, John; Arshad, Hasan; Bishop, Christopher; Buchan, Iain; Cullinan, Paul; Devereux, Graham; Henderson, John; Holloway, John; Roberts, Graham; Turner, Steve; Woodcock, Ashley; Simpson, Angela

2015-01-01

We created Asthma e-Lab, a secure web-based research environment to support consistent recording, description and sharing of data, computational/statistical methods and emerging findings across the five UK birth cohorts. The e-Lab serves as a data repository for our unified dataset and provides the computational resources and a scientific social network to support collaborative research. All activities are transparent, and emerging findings are shared via the e-Lab, linked to explanations of analytical methods, thus enabling knowledge transfer. eLab facilitates the iterative interdisciplinary dialogue between clinicians, statisticians, computer scientists, mathematicians, geneticists and basic scientists, capturing collective thought behind the interpretations of findings. PMID:25805205

SEIZURE PREDICTION: THE FOURTH INTERNATIONAL WORKSHOP

PubMed Central

Zaveri, Hitten P.; Frei, Mark G.; Arthurs, Susan; Osorio, Ivan

2010-01-01

The recently convened Fourth International Workshop on Seizure Prediction (IWSP4) brought together a diverse international group of investigators, from academia and industry, including epileptologists, neurosurgeons, neuroscientists, computer scientists, engineers, physicists, and mathematicians who are conducting interdisciplinary research on the prediction and control of seizures. IWSP4 allowed the presentation and discussion of results, an exchange of ideas, an assessment of the status of seizure prediction, control and related fields and the fostering of collaborative projects. PMID:20674508

A gathering for Gardner

NASA Astrophysics Data System (ADS)

Crease, Robert P.

2008-07-01

Martin Gardner, who turns 94 this autumn, seems to have pulled off an astounding trick. Every other year hundreds of people gather to honour Gardner, who is the author of over 70 books and wrote the popular "Mathematical Games" column that appeared in Scientific American for a quarter of a century from 1956. What is astonishing is that the people come from a bewildering variety of professions and include jugglers, magicians, artists, puzzle-makers, logicians, computer scientists, pseudoscience debunkers and mathematicians.

Graph Theory

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

Sanfilippo, Antonio P.

2005-12-27

Graph theory is a branch of discrete combinatorial mathematics that studies the properties of graphs. The theory was pioneered by the Swiss mathematician Leonhard Euler in the 18th century, commenced its formal development during the second half of the 19th century, and has witnessed substantial growth during the last seventy years, with applications in areas as diverse as engineering, computer science, physics, sociology, chemistry and biology. Graph theory has also had a strong impact in computational linguistics by providing the foundations for the theory of features structures that has emerged as one of the most widely used frameworks for themore » representation of grammar formalisms.« less

[out of scope].

PubMed

Siegmund-Schultze, Reinhard

2008-01-01

The paper discusses several still unsettled and not systematically investigated questions concerning the situation of Jewish scientists, among them mathematicians, in the Republic of Weimar. Contemporary statements by the well-known leftist and liberal journalists Carl von Ossietzky (1932) and Rudolf Olden (1934) are used to describe the general political situation. A wide-spread feeling of a social and political crisis and changes and perturbations in international scientific communication provide explanatory background for the conditions within academia in the 1920s. A comparison of appointments of Jewish mathematicians to full professorships before and after World War I does not give significant differences. Attitudes of Jewish mathematicians such as Felix Bernstein, Richard Courant, Emil Julius Gumbel, Edmund Landau, Richard von Mises, Johann von Neumann and Adolf A. Fraenkel, but also of non-Jewish mathematicians such as Felix Klein, Walther von Dyck and Theodor Vahlen will be discussed, providing some unpublished material. One statement by Felix Klein (1920), which shows his undecided stance with respect to the problem of anti-Semitism, and an excerpt from Richard von Mises' diary (1933), where he reflects on his status as a Jewish mathematician and as a refugee, are particularly valuable as points of reference for necessary further research.

Big Data, Deep Learning and Tianhe-2 at Sun Yat-Sen University, Guangzhou

NASA Astrophysics Data System (ADS)

Yuen, D. A.; Dzwinel, W.; Liu, J.; Zhang, K.

2014-12-01

In this decade the big data revolution has permeated in many fields, ranging from financial transactions, medical surveys and scientific endeavors, because of the big opportunities people see ahead. What to do with all this data remains an intriguing question. This is where computer scientists together with applied mathematicians have made some significant inroads in developing deep learning techniques for unraveling new relationships among the different variables by means of correlation analysis and data-assimilation methods. Deep-learning and big data taken together is a grand challenge task in High-performance computing which demand both ultrafast speed and large memory. The Tianhe-2 recently installed at Sun Yat-Sen University in Guangzhou is well positioned to take up this challenge because it is currently the world's fastest computer at 34 Petaflops. Each compute node of Tianhe-2 has two CPUs of Intel Xeon E5-2600 and three Xeon Phi accelerators. The Tianhe-2 has a very large fast memory RAM of 88 Gigabytes on each node. The system has a total memory of 1,375 Terabytes. All of these technical features will allow very high dimensional (more than 10) problem in deep learning to be explored carefully on the Tianhe-2. Problems in seismology which can be solved include three-dimensional seismic wave simulations of the whole Earth with a few km resolution and the recognition of new phases in seismic wave form from assemblage of large data sets.

Artifacts in Radar Imaging of Moving Targets

DTIC Science & Technology

2012-09-01

CA, USA, 2007. [11] B. Borden, Radar imaging of airborne targets: A primer for Applied mathematicians and Physicists . New York, NY: Taylor and... Project (0704–0188) Washington DC 20503. 1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 21 September 2012 3. REPORT TYPE AND DATES COVERED...CW Continuous Wave DAC Digital to Analog Convertor DFT Discrete Fourier Transform FBP Filtered Back Projection FFT Fast Fourier Transform GPS

Terrorism/Criminalogy/Sociology via Magnetism-Hamiltonian ``Models''?!: Black Swans; What Secrets Lie Buried in Magnetism?; ``Magnetism Will Conquer the Universe?''(Charles Middleton, aka ``His Imperial Majesty The Emperior Ming `The Merciless!!!''

NASA Astrophysics Data System (ADS)

Carrott, Anthony; Siegel, Edward Carl-Ludwig; Hoover, John-Edgar; Ness, Elliott

2013-03-01

Terrorism/Criminalogy//Sociology : non-Linear applied-mathematician (``nose-to-the grindstone / ``gearheadism'') ''modelers'': Worden,, Short, ...criminologists/counter-terrorists/sociologists confront [SIAM Conf. on Nonlinearity, Seattle(12); Canadian Sociology Conf,. Burnaby(12)]. ``The `Sins' of the Fathers Visited Upon the Sons'': Zeno vs Ising vs Heisenberg vs Stoner vs Hubbard vs Siegel ''SODHM''(But NO Y!!!) vs ...??? Magntism and it turn are themselves confronted BY MAGNETISM,via relatively magnetism/metal-insulator conductivity / percolation-phase-transitions critical-phenomena -illiterate non-linear applied-mathematician (nose-to-the-grindstone/ ``gearheadism'')''modelers''. What Secrets Lie Buried in Magnetism?; ``Magnetism Will Conquer the Universe!!!''[Charles Middleton, aka ``His Imperial Majesty The Emperior Ming `The Merciless!!!']'' magnetism-Hamiltonian phase-transitions percolation-``models''!: Zeno(~2350 BCE) to Peter the Pilgrim(1150) to Gilbert(1600) to Faraday(1815-1820) to Tate (1870-1880) to Ewing(1882) hysteresis to Barkhausen(1885) to Curie(1895)-Weiss(1895) to Ising-Lenz(r-space/Localized-Scalar/ Discrete/1911) to Heisenberg(r-space/localized-vector/discrete/1927) to Priesich(1935) to Stoner (electron/k-space/ itinerant-vector/discrete/39) to Stoner-Wohlfarth (technical-magnetism hysteresis /r-space/ itinerant-vector/ discrete/48) to Hubbard-Longuet-Higgins (k-space versus r-space/

The collaboration between anatomists and mathematicians in the mid-seventeenth century with a study of images as experiments and Galileo's role in Steno's Myology.

PubMed

Meli, Domenico Bertoloni

2008-01-01

Moving from Paris, Pisa, and Oxford to London, Amsterdam, and Cambridge, this essay documents extensive collaborations between anatomists and mathematicians. At a time when no standard way to acknowledge collaboration existed, it is remarkable that in all the cases I discuss anatomists expressed in print their debt to mathematicians. The cases I analyze document an extraordinarily fertile period in the history of anatomy and science and call into question historiographic divisions among historians of science and medicine. I focus on Steno's Myology, showing how his collaboration with mathematician Viviani led to a geometrical treatment of muscular contraction and to an epistemology inspired by Galileo. The collaboration between Steno and Viviani enables us to interpret a major text in the history of anatomy, one whose implications had so far eluded historians.

The Transition from Mathematician to Astrophysicist

NASA Astrophysics Data System (ADS)

Flannery, M. R.

Various landmarks in the evolution of Alexander Dalgarno from a gifted mathematician to becoming the acknowledged Father of Molecular Astrophysics are noted. His researches in basic atomic and molecular physics, aeronomy (the study of the upper atmosphere) and astrophysics are highlighted.

[Image guided and robotic treatment--the advance of cybernetics in clinical medicine].

PubMed

Fosse, E; Elle, O J; Samset, E; Johansen, M; Røtnes, J S; Tønnessen, T I; Edwin, B

2000-01-10

The introduction of advanced technology in hospitals has changed the treatment practice towards more image guided and minimal invasive procedures. Modern computer and communication technology opens up for robot aided and pre-programmed intervention. Several robotic systems are in clinical use today both in microsurgery and in major cardiac and orthopedic operations. As this trend develops, professions which are new in this context such as physicists, mathematicians and cybernetic engineers will be increasingly important in the treatment of patients.

Neurocomputing

NASA Technical Reports Server (NTRS)

Hecht-Nielsen, Robert

1990-01-01

The present work is intended to give technologists, research scientists, and mathematicians a graduate-level overview of the field of neurocomputing. After exploring the relationship of this field to general neuroscience, attention is given to neural network building blocks, the self-adaptation equations of learning laws, the data-transformation structures of associative networks, and the multilayer data-transformation structures of mapping networks. Also treated are the neurocomputing frontiers of spatiotemporal, stochastic, and hierarchical networks, 'neurosoftware', the creation of neural network-based computers, and neurocomputing applications in sensor processing, control, and data analysis.

Sines and Cosines. Part 3 of 3

NASA Technical Reports Server (NTRS)

Apostol, Tom M. (Editor)

1994-01-01

In this 'Project Mathematics' series video, the addition formulas of sines and cosines are explained and their real life applications are demonstrated. Both film footage and computer animation is used. Several mathematical concepts are discussed and include: Ptolemy's theorem concerned with quadrilaterals; the difference between a central angle and an inscribed angle; sines and chord lengths; special angles; subtraction formulas; and a application to simple harmonic motion. A brief history of the city Alexandria, its mathematicians, and their contribution to the field of mathematics is shown.

Mathematics delivering the advantage: the role of mathematicians in manufacturing and beyond.

PubMed

Saward, Vicki

2017-05-01

Much has been written about the benefits that mathematics can bring to the UK economy and the manufacturing sector in particular, but less on the value of mathematicians and a mathematical training. This article, written from an industry perspective, considers the value of mathematicians to the UK's industrial base and the importance to the UK economy of encouraging young people in the UK to choose to study mathematics at school as a gateway to a wide range of careers. The points are illustrated using examples from the author's 20 years' experience in the security and intelligence and manufacturing sectors.

Accommodation in the formal world of mathematical thinking

NASA Astrophysics Data System (ADS)

Stewart, Sepideh; Schmidt, Ralf

2017-11-01

In this study, we examined a mathematician and one of his students' teaching journals and thought processes concurrently as the class was moving towards the proof of the Fundamental Theorem of Galois Theory. We employed Tall's framework of three worlds of mathematical thinking as well as Piaget's notion of accommodation to theoretically study the narratives. This paper reveals the pedagogical challenges of proving an elegant theory as the events unfolded. Although the mathematician was conscious of the students' abilities as he carefully made the path accessible, the disparity between the mind of the mathematician and the student became apparent.

Leonid Pavlovich Shil'nikov (obituary)

NASA Astrophysics Data System (ADS)

Anosov, Dmitry V.; Afraimovich, Valentin S.; Bunimovich, Leonid A.; Gonchenko, Sergei V.; Grines, Vyacheslav Z.; Ilyashenko, Yulij S.; Katok, Anatolii B.; Kashchenko, Sergey A.; Kozlov, Valerii V.; Lerman, Lev M.; Morozov, Albert D.; Neishtadt, Anatolii I.; Pesin, Yakov B.; Samoilenko, Anatoly M.; Sinai, Yakov G.; Treschev, Dmitrii V.; Turaev, Dmitry V.; Sharkovskii, Aleksandr N.; Shil'nikov, Andrei L.

2012-06-01

A remarkable mathematician, one of the most prominent specialists in the theory of dynamical systems and bifurcation theory, a laureate of the Lyapunov Prize of the Russian Academy of Sciences and of the Lavren'ev Prize of the National Academy of Sciences of Ukraine, a Humboldt Professor, Head of the Department of Differential Equations of the Research Institute of Applied Mathematics and Cybernetics of Nizhnii Novgorod University, Professor Leonid Pavlovich Shil'nikov passed away on 26 December 2011.

Wave Propagation in Inhomogeneous Excitable Media

NASA Astrophysics Data System (ADS)

Zykov, Vladimir S.; Bodenschatz, Eberhard

2018-03-01

Excitable media are ubiquitous in nature and can be found in physical, chemical, and biological systems that are far from thermodynamic equilibrium. The spatiotemporal self-organization of these systems has long attracted the deep interest of condensed matter physicists and applied mathematicians alike. Spatial inhomogeneity of excitable media leads to nontrivial spatiotemporal dynamics. Here, we report on well-established as well as recent developments in the experimental and theoretical studies of inhomogeneous excitable media.

Making Mathematics.

ERIC Educational Resources Information Center

Huckstep, Peter

2002-01-01

Contends teachers must resist the temptation to suggest that, while children can create stories and melodies, they cannot create mathematics. Quotes mathematician G. H. Hardy: "A mathematician, like a painter or poet, is a 'maker' of patterns." Considers mathematics should be able to stand up for itself. (BT)

The Vector Calculus Gap: Mathematics (Does Not Equal) Physics.

ERIC Educational Resources Information Center

Dray, Tevian; Manogue, Corinne A.

1999-01-01

Discusses some of the differences between the ways mathematicians and physicists view vector calculus and the gap between the way this material is traditionally taught by mathematicians and the way physicists use it. Suggests some ways to narrow the gap. (Author/ASK)

REVIEWS OF TOPICAL PROBLEMS: Analytic calculations on digital computers for applications in physics and mathematics

NASA Astrophysics Data System (ADS)

Gerdt, V. P.; Tarasov, O. V.; Shirkov, Dmitrii V.

1980-01-01

The present state of analytic calculations on computers is reviewed. Several programming systems which are used for analytic calculations are discussed: SCHOONSCHIP, CLAM, REDUCE-2, SYMBAL, CAMAL, AVTO-ANALITIK, MACSYMA, etc. It is shown that these systems can be used to solve a wide range of problems in physics and mathematics. Some physical applications are discussed in celestial mechanics, the general theory of relativity, quantum field theory, plasma physics, hydrodynamics, atomic and molecular physics, and quantum chemistry. Some mathematical applications which are discussed are evaluating indefinite integrals, solving differential equations, and analyzing mathematical expressions. This review is addressed to physicists and mathematicians working in a wide range of fields.

The Story of PI

NASA Technical Reports Server (NTRS)

Apostol, Tom M. (Editor)

1989-01-01

The early history and the uses of the mathematical notation - pi - are presented through both film footage and computer animation in this 'Project Mathematics' series video. Pi comes from the first letter in the Greek word for perimeter. Archimedes, and early Greek mathematician, formulated the equations for the computation of a circle's area using pi and was the first person to seriously approximate pi numerically, although only to a few decimal places. By 1985, pi had been approximated to over one billion decimal places and was found to have no repeating pattern. One use of pi is the application of its approximation calculation as an analytical tool for determining the accuracy of supercomputers and software designs.

Giftedness and Aesthetics: Perspectives of Expert Mathematicians and Mathematically Gifted Students

ERIC Educational Resources Information Center

Tjoe, Hartono

2015-01-01

Giftedness in mathematics has been characterized by exceptional attributes including strong mathematical memory, formalizing perception, generalization, curtailment, flexibility, and elegance. Focusing on the last attribute, this study examined the following: (a) the criteria which expert mathematicians and mathematically gifted students fleshed…

Mathematics delivering the advantage: the role of mathematicians in manufacturing and beyond

PubMed Central

2017-01-01

Much has been written about the benefits that mathematics can bring to the UK economy and the manufacturing sector in particular, but less on the value of mathematicians and a mathematical training. This article, written from an industry perspective, considers the value of mathematicians to the UK's industrial base and the importance to the UK economy of encouraging young people in the UK to choose to study mathematics at school as a gateway to a wide range of careers. The points are illustrated using examples from the author's 20 years' experience in the security and intelligence and manufacturing sectors. PMID:28588416

Mathematicians and the Selection Task

ERIC Educational Resources Information Center

Inglis, Matthew; Simpson, Adrian

2004-01-01

Learning to think logically and present ideas in a logical fashion has always been considered a central part of becoming a mathematician. In this paper we compare the performance of three groups: mathematics undergraduates, mathematics staff and history undergraduates (representative of a "general population"). These groups were asked to solve…

The Great Mathematician Project

ERIC Educational Resources Information Center

Goldberg, Sabrina R.

2013-01-01

The Great Mathematician Project (GMP) introduces both mathematically sophisticated and struggling students to the history of mathematics. The rationale for the GMP is twofold: first, mathematics is a uniquely people-centered discipline that is used to make sense of the world; and second, students often express curiosity about the history of…

Final Technical Progress Report; Closeout Certifications; CSSV Newsletter Volume I; CSSV Newsletter Volume II; CSSV Activity Journal; CSSV Final Financial Report

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

Houston, Johnny L; Geter, Kerry

This Project?s third year of implementation in 2007-2008, the final year, as designated by Elizabeth City State University (ECSU), in cooperation with the National Association of Mathematicians (NAM) Inc., in an effort to promote research and research training programs in computational science ? scientific visualization (CSSV). A major goal of the Project was to attract the energetic and productive faculty, graduate and upper division undergraduate students of diverse ethnicities to a program that investigates science and computational science issues of long-term interest to the Department of Energy (DoE) and the nation. The breadth and depth of computational science?scientific visualization andmore » the magnitude of resources available are enormous for permitting a variety of research activities. ECSU?s Computational Science-Science Visualization Center will serve as a conduit for directing users to these enormous resources.« less

System biology of gene regulation.

PubMed

Baitaluk, Michael

2009-01-01

A famous joke story that exhibits the traditionally awkward alliance between theory and experiment and showing the differences between experimental biologists and theoretical modelers is when a University sends a biologist, a mathematician, a physicist, and a computer scientist to a walking trip in an attempt to stimulate interdisciplinary research. During a break, they watch a cow in a field nearby and the leader of the group asks, "I wonder how one could decide on the size of a cow?" Since a cow is a biological object, the biologist responded first: "I have seen many cows in this area and know it is a big cow." The mathematician argued, "The true volume is determined by integrating the mathematical function that describes the outer surface of the cow's body." The physicist suggested: "Let's assume the cow is a sphere...." Finally the computer scientist became nervous and said that he didn't bring his computer because there is no Internet connection up there on the hill. In this humorous but explanatory story suggestions proposed by theorists can be taken to reflect the view of many experimental biologists that computer scientists and theorists are too far removed from biological reality and therefore their theories and approaches are not of much immediate usefulness. Conversely, the statement of the biologist mirrors the view of many traditional theoretical and computational scientists that biological experiments are for the most part simply descriptive, lack rigor, and that much of the resulting biological data are of questionable functional relevance. One of the goals of current biology as a multidisciplinary science is to bring people from different scientific areas together on the same "hill" and teach them to speak the same "language." In fact, of course, when presenting their data, most experimentalist biologists do provide an interpretation and explanation for the results, and many theorists/computer scientists aim to answer (or at least to fully describe) questions of biological relevance. Thus systems biology could be treated as such a socioscientific phenomenon and a new approach to both experiments and theory that is defined by the strategy of pursuing integration of complex data about the interactions in biological systems from diverse experimental sources using interdisciplinary tools and personnel.

Yeast for Mathematicians: A Ferment of Discovery and Model Competition to Describe Data.

PubMed

Lewis, Matthew; Powell, James

2017-02-01

In addition to the memorization, algorithmic skills and vocabulary which are the default focus in many mathematics classrooms, professional mathematicians are expected to creatively apply known techniques, construct new mathematical approaches and communicate with and about mathematics. We propose that students can learn these professional, higher-level skills through Laboratory Experiences in Mathematical Biology which put students in the role of mathematics researcher creating mathematics to describe and understand biological data. Here we introduce a laboratory experience centered on yeast (Saccharomyces cerevisiae) growing in a small capped flask with a jar to collect carbon dioxide created during yeast growth and respiration. The lab requires no specialized equipment and can easily be run in the context of a college math class. Students collect data and develop mathematical models to explain the data. To help place instructors in the role of mentor/collaborator (as opposed to jury/judge), we facilitate the lab using model competition judged via Bayesian Information Criterion. This article includes details about the class activity conducted, student examples and pedagogical strategies for success.

A Review of Mathematical Models for Leukemia and Lymphoma

PubMed Central

Clapp, Geoffrey; Levy, Doron

2014-01-01

Recently, there has been significant activity in the mathematical community, aimed at developing quantitative tools for studying leukemia and lymphoma. Mathematical models have been applied to evaluate existing therapies and to suggest novel therapies. This article reviews the recent contributions of mathematical modeling to leukemia and lymphoma research. These developments suggest that mathematical modeling has great potential in this field. Collaboration between mathematicians, clinicians, and experimentalists can significantly improve leukemia and lymphoma therapy. PMID:26744598

Cultural and Technological Issues and Solutions for Geodynamics Software Citation

NASA Astrophysics Data System (ADS)

Heien, E. M.; Hwang, L.; Fish, A. E.; Smith, M.; Dumit, J.; Kellogg, L. H.

2014-12-01

Computational software and custom-written codes play a key role in scientific research and teaching, providing tools to perform data analysis and forward modeling through numerical computation. However, development of these codes is often hampered by the fact that there is no well-defined way for the authors to receive credit or professional recognition for their work through the standard methods of scientific publication and subsequent citation of the work. This in turn may discourage researchers from publishing their codes or making them easier for other scientists to use. We investigate the issues involved in citing software in a scientific context, and introduce features that should be components of a citation infrastructure, particularly oriented towards the codes and scientific culture in the area of geodynamics research. The codes used in geodynamics are primarily specialized numerical modeling codes for continuum mechanics problems; they may be developed by individual researchers, teams of researchers, geophysicists in collaboration with computational scientists and applied mathematicians, or by coordinated community efforts such as the Computational Infrastructure for Geodynamics. Some but not all geodynamics codes are open-source. These characteristics are common to many areas of geophysical software development and use. We provide background on the problem of software citation and discuss some of the barriers preventing adoption of such citations, including social/cultural barriers, insufficient technological support infrastructure, and an overall lack of agreement about what a software citation should consist of. We suggest solutions in an initial effort to create a system to support citation of software and promotion of scientific software development.

Three Styles Characterising Mathematicians' Pedagogical Perspectives on Proof

ERIC Educational Resources Information Center

Hemmi, Kirsti

2010-01-01

The article describes mathematicians' pedagogical perspectives on proof in the teaching of first year university students at a mathematics department in Sweden. A conceptual frame that was used in the data analysis combines theories about proof from earlier mathematics education research with a social practice approach of Lave and Wenger. A…

How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition

ERIC Educational Resources Information Center

Weber, Keith; Inglis, Matthew; Mejia-Ramos, Juan Pablo

2014-01-01

The received view of mathematical practice is that mathematicians gain certainty in mathematical assertions by deductive evidence rather than empirical or authoritarian evidence. This assumption has influenced mathematics instruction where students are expected to justify assertions with deductive arguments rather than by checking the assertion…

Expert and Novice Approaches to Reading Mathematical Proofs

ERIC Educational Resources Information Center

Inglis, Matthew; Alcock, Lara

2012-01-01

A comparison of the proof validation behavior of beginning undergraduate students and research-active mathematicians is explored. Participants' eye movements were recorded as they validated purported proofs. The main findings are that (a) contrary to previous suggestions, mathematicians sometimes appear to disagree about the validity of even short…

Mathematicians' and Math Educators' Views on "Doing Mathematics"

ERIC Educational Resources Information Center

Brandt, Jim; Lunt, Jana; Meilstrup, Gretchen Rimmasch

2016-01-01

Educators often argue that mathematics should be taught so that the students in the course are actually "doing mathematics." Is there a consensus among mathematicians and mathematics educators as to the meaning of "doing mathematics?" In an effort to answer this question, we administered a survey to hundreds of university-level…

CIMAC: A Coordinated Introduction to Calculus and Mechanics

NASA Astrophysics Data System (ADS)

Fathe, Laurie; Quinn, Jennifer; McDonald, Michael A.

1997-04-01

CIMAC, new course incorporating Mechanics, Precalculus, and Calculus, targets the growing number of motivated but underprepared students who wish to pursue a major in science or mathematics. Team-taught by a Physicist and a Mathematician, CIMAC, a new course incorporating Mechanics, Precalculus, and Calculus, targets the growing number of motivated but underprepared students who wish to pursue a major in science or mathematics. Team-taught by a Physicist and a Mathematician, the class contains specific content while exploiting the substantial commonality of these subjects. CIMAC also addresses variety of non-content areas, including supplementing basic mathematics and communication skills, accommodating various learning styles, and building student confidence. Specific approaches include class formats; gateway exams; group assignments; emphasis on writing and reading; use of computers and graphing calculators for comprehension, data acquisition, analysis, and modeling; student-led help sessions; and use of the Web http://www.oxy.edu/ departments/math/cimac/ This talk highlights the development of the course and teaching insights and innovations which have arisen from it, and addresses benefits and difficulties of coordinating material and team teaching across disciplinary lines. Finally, it presents data on student success and retention.

The Cyclic Nature of Problem Solving: An Emergent Multidimensional Problem-Solving Framework

ERIC Educational Resources Information Center

Carlson, Marilyn P.; Bloom, Irene

2005-01-01

This paper describes the problem-solving behaviors of 12 mathematicians as they completed four mathematical tasks. The emergent problem-solving framework draws on the large body of research, as grounded by and modified in response to our close observations of these mathematicians. The resulting "Multidimensional Problem-Solving Framework" has four…

Final Report of Cambridge Conference on School Mathematics, January 1962 - August 1970.

ERIC Educational Resources Information Center

Cambridge Conference on School Mathematics, Newton, MA.

The Cambridge Conference on School Mathematics (CCSM) was an association of prominent mathematicians who had a concern for mathematics education at school level, from kindergarten through grade twelve. These mathematicians organized three main conferences in three areas of mathematics education, and have carried on activities related to the…

The Experience of Security in Mathematics

ERIC Educational Resources Information Center

Charalampous, Eleni; Rowland, Tim

2013-01-01

In this paper, we report some findings from an investigation of a topic related to affect and mathematics which is not well-represented in the literature. For some mathematicians, mathematics itself is a source of security in an uncertain world, and we investigated this feeling and experience in the case of 19 adult mathematicians working in…

How Do Mathematicians Learn Math?: Resources and Acts for Constructing and Understanding Mathematics

ERIC Educational Resources Information Center

Wilkerson-Jerde, Michelle H.; Wilensky, Uri J.

2011-01-01

In this paper, we present an analytic framework for investigating expert mathematical learning as the process of building a "network of mathematical resources" by establishing relationships between different components and properties of mathematical ideas. We then use this framework to analyze the reasoning of ten mathematicians and mathematics…

Imagining the Mathematician: Young People Talking about Popular Representations of Maths

ERIC Educational Resources Information Center

Epstein, Debbie; Mendick, Heather; Moreau, Marie-Pierre

2010-01-01

This paper makes both a critical analysis of some popular cultural texts about mathematics and mathematicians, and explores the ways in which young people deploy the discourses produced in these texts. We argue that there are particular (and sometimes contradictory) meanings and discourses about mathematics that circulate in popular culture, that…

Learning at the Boundaries: Collaboration between Mathematicians and Mathematics Educators within and across Institutions

ERIC Educational Resources Information Center

Bennison, Anne; Goos, Merrilyn

2016-01-01

Collaboration between mathematicians and mathematics educators may provide a means of improving the quality of pre-service teacher education for prospective teachers of mathematics. Some preliminary findings of a project that investigates this type of interdisciplinary collaboration, both within and across institutions, are reported on in this…

A Fruitful Exchange/Conflict: Engineers and Mathematicians in Early Modern Italy

ERIC Educational Resources Information Center

Maffioli, Cesare S.

2013-01-01

Exchanges of learning and controversies between engineers and mathematicians were important factors in the development of early modern science. This theme is discussed by focusing, first, on architectural and mathematical dynamism in mid 16th-century Milan. While some engineers-architects referred to Euclid and Vitruvius for improving their…

Teachers' Beliefs about School Mathematics and Mathematicians' Mathematics and Their Relationship to Practice

ERIC Educational Resources Information Center

Beswick, Kim

2012-01-01

There is broad acceptance that mathematics teachers' beliefs about the nature of mathematics influence the ways in which they teach the subject. It is also recognised that mathematics as practised in typical school classrooms is different from the mathematical activity of mathematicians. This paper presents case studies of two secondary…

Increasing Awareness of Practice through Interaction across Communities: The Lived Experiences of a Mathematician and Mathematics Teacher Educator

ERIC Educational Resources Information Center

Bleiler, Sarah K.

2015-01-01

Collaborations between mathematicians and mathematics teacher educators are increasingly being expected, and realized, within the context of mathematics teacher education. Most research related to collaborative efforts between members of the mathematics and mathematics education communities has focused on the products, rather than the process of…

Applied Mathematicians and Naval Operators. Revised.

DTIC Science & Technology

1982-03-01

sensor . They guided me into areas that few of the officers were aware of. 2.4. Hemibel Thinking. A complicated analysis that leads to a 2 percent increase...Editor, Journal of Documentation, Vol. 31, PP 226 No. 4. pages 298-501), Deceber 1975), AD A054 426 Ralston, J. N. and J. W. Mann,* " Temperatura end...Apr 78, AD A054 443 AD A058 542 PP 221 PP 231 Wainlad. Robert G.. "Superpower Navel Diplo nacy In the Wilson, De ond P., Jr., "Noval Projection

Aerospace applications of integer and combinatorial optimization

NASA Technical Reports Server (NTRS)

Padula, S. L.; Kincaid, R. K.

1995-01-01

Research supported by NASA Langley Research Center includes many applications of aerospace design optimization and is conducted by teams of applied mathematicians and aerospace engineers. This paper investigates the benefits from this combined expertise in solving combinatorial optimization problems. Applications range from the design of large space antennas to interior noise control. A typical problem, for example, seeks the optimal locations for vibration-damping devices on a large space structure and is expressed as a mixed/integer linear programming problem with more than 1500 design variables.

NRL Fact Book

DTIC Science & Technology

2004-12-31

and engineers work together with industry , academia, state or local governments, or other Federal agencies to develop NRL technologies for government...http://www.nrl.navy.mil) annually. It is printed every other year. NRL has a continuing need for physical scientists, mathematicians, engineers , and...listed for each activity. NRL has a continuing need for physical scientists, mathematicians, engineers , and support personnel. Vacancies are filled

Conversations about Curriculum Change: Mathematical Thinking and Team-Based Learning in a Discrete Mathematics Course

ERIC Educational Resources Information Center

Paterson, Judy; Sneddon, Jamie

2011-01-01

This article reports on the learning conversations between a mathematician and a mathematics educator as they worked together to change the delivery model of a third year discrete mathematics course from a traditional lecture mode to team-based learning (TBL). This change prompted the mathematician to create team tasks which increasingly focused…

Examining the Image of Prospective Teachers towards Mathematicians

ERIC Educational Resources Information Center

Yazlik, Derya Ozlem; Erdogan, Ahmet

2018-01-01

The aim of this study is to identify how prospective teachers see mathematicians by the pictures they visualized. In accordance with this purpose phenomenology pattern which is one of the qualitative patterns was used. The study was carried out with 160 volunteered prospective teachers. The data collection tool to be used in this study consists of…

John Todd--Numerical Mathematics Pioneer

ERIC Educational Resources Information Center

Albers, Don

2007-01-01

John Todd, now in his mid-90s, began his career as a pure mathematician, but World War II interrupted that. In this interview, he talks about his education, the significant developments in his becoming a numerical analyst, and the journey that concluded at Caltech. Among the interesting stories are how he met his wife-to-be the mathematician Olga…

My Experience with Alcohol, a 17th-Century Mathematician, and a Personal Decision

ERIC Educational Resources Information Center

Eaton, Dennis R.; Rector, Sheila M.

2009-01-01

This writing shares the first author's personal experience with alcohol, the negative consequences of his choices, and the ultimate answering of the question, "Am I an alcoholic and should I drink again?" The decision-making process and the eventual answer come from Blaise Pascal, a 17th-century mathematician. This process is explained and…

Voices of Women Mathematicians: Understanding Their Success Using a Narrative Approach to Inquiry.

ERIC Educational Resources Information Center

Anderson, Dawn Leigh

This study investigated the lives of six women mathematicians to describe the factors and experiences that led each woman to become successful in mathematics. Because "voice" was used as a metaphor in this study, emphasis was placed on listening to and interpreting the participants' voices. The study used narrative inquiry to investigate…

The Academic and the Everyday in Mathematicians' Talk: The Case of the Hyper-Bagel

ERIC Educational Resources Information Center

Barwell, Richard

2013-01-01

Mathematics curricula increasingly emphasise the importance of mathematical communication. Students are seen as progressing from the use of a more informal or everyday form of communication to a more mathematical approach. There have, however, been very few studies of how mathematicians actually talk about mathematics. This paper reports analysis…

Mathematical Experiences and Parental Involvement of Parents Who Are and Who Are Not Mathematicians

ERIC Educational Resources Information Center

Antolin Drešar, Darja; Lipovec, Alenka

2017-01-01

Previous studies suggest that parental involvement in children's mathematics education is more established for parents who feel competent in mathematics. This qualitative study aimed to gain an in-depth insight into the experiences of parental involvement of two different groups of parents: those who are mathematicians and those who are not. Data…

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

Cameron, Maria K., E-mail: cameron@math.umd.edu

We develop computational tools for spectral analysis of stochastic networks representing energy landscapes of atomic and molecular clusters. Physical meaning and some properties of eigenvalues, left and right eigenvectors, and eigencurrents are discussed. We propose an approach to compute a collection of eigenpairs and corresponding eigencurrents describing the most important relaxation processes taking place in the system on its way to the equilibrium. It is suitable for large and complex stochastic networks where pairwise transition rates, given by the Arrhenius law, vary by orders of magnitude. The proposed methodology is applied to the network representing the Lennard-Jones-38 cluster created bymore » Wales's group. Its energy landscape has a double funnel structure with a deep and narrow face-centered cubic funnel and a shallower and wider icosahedral funnel. However, the complete spectrum of the generator matrix of the Lennard-Jones-38 network has no appreciable spectral gap separating the eigenvalue corresponding to the escape from the icosahedral funnel. We provide a detailed description of the escape process from the icosahedral funnel using the eigencurrent and demonstrate a superexponential growth of the corresponding eigenvalue. The proposed spectral approach is compared to the methodology of the Transition Path Theory. Finally, we discuss whether the Lennard-Jones-38 cluster is metastable from the points of view of a mathematician and a chemical physicist, and make a connection with experimental works.« less

Proteomics, lipidomics, metabolomics: a mass spectrometry tutorial from a computer scientist's point of view.

PubMed

Smith, Rob; Mathis, Andrew D; Ventura, Dan; Prince, John T

2014-01-01

For decades, mass spectrometry data has been analyzed to investigate a wide array of research interests, including disease diagnostics, biological and chemical theory, genomics, and drug development. Progress towards solving any of these disparate problems depends upon overcoming the common challenge of interpreting the large data sets generated. Despite interim successes, many data interpretation problems in mass spectrometry are still challenging. Further, though these challenges are inherently interdisciplinary in nature, the significant domain-specific knowledge gap between disciplines makes interdisciplinary contributions difficult. This paper provides an introduction to the burgeoning field of computational mass spectrometry. We illustrate key concepts, vocabulary, and open problems in MS-omics, as well as provide invaluable resources such as open data sets and key search terms and references. This paper will facilitate contributions from mathematicians, computer scientists, and statisticians to MS-omics that will fundamentally improve results over existing approaches and inform novel algorithmic solutions to open problems.

Mary Somerville, mathematician and astronomer of underused talents

NASA Astrophysics Data System (ADS)

Bruck, M. T.

1996-08-01

Mary Somerville (1780-1872), self-taught mathematician, expert on theoretical astronomy and successful writer, has been described as `the most remarkable woman of her generation'. The publication of her mathematical treatise The Mechanism of the Heavens in 1831, followed by the more popular Connexion of the Physical Sciences in 1834, made her an international celebrity. Her life and work is described.

"I Can Actually Be Very Feminine Here": Contradiction and Hybridity in becoming a Female Mathematician

ERIC Educational Resources Information Center

Solomon, Yvette; Radovic, Darinka; Black, Laura

2016-01-01

A common theme in accounts of choosing mathematics is that of persistence in the face of troubles or difficulties which are often associated with the structuring effects of gender, class, culture and ethnicity. Centring on an analysis of one woman's account of becoming a mathematician, we build on our understanding of multiple and developing…

Why and How Mathematicians Read Proofs: An Exploratory Study

ERIC Educational Resources Information Center

Weber, Keith; Mejia-Ramos, Juan Pablo

2011-01-01

In this paper, we report a study in which nine research mathematicians were interviewed with regard to the goals guiding their reading of published proofs and the type of reasoning they use to reach these goals. Using the data from this study as well as data from a separate study (Weber, "Journal for Research in Mathematics Education" 39:431-459,…

Acting Like a Mathematician: A Project to Encourage Inquiry Early in the Math Major

ERIC Educational Resources Information Center

Camenga, Kristin A.

2017-01-01

Inquiry is promoted as a way to engage students so that they learn more deeply; inquiry is also an end in itself, introducing students to the research process and the behaviors of a mathematician. This article reflects on an individual exploratory project used in a sophomore-level number theory course, examining how it supported student inquiry…

Multicultural and Gender Equity Issues in a History of Mathematics Course: Not Only Dead European Males

ERIC Educational Resources Information Center

Flores, Alfinio; Kimpton, Kelly E.

2012-01-01

We address issues related to gender and cultural equity in a history of mathematics course. We first look at the preponderance of male European mathematicians represented in textbooks of mathematics and history or mathematics. Then we discuss ways to highlight the presence of female and non-European mathematicians in the history of mathematics.…

The Influence of Sources in the Reading of Mathematical Text: A Reply to Shanahan, Shanahan, and Misischia

ERIC Educational Resources Information Center

Weber, Keith; Mejia-Ramos, Juan Pablo

2013-01-01

In a recent article published in this journal, Shanahan, Shanahan, and Misischia investigated the differences in how chemists, historians, and mathematicians read text specific to their disciplines. Unlike the chemists and historians, the pair of mathematicians in this study did not consider sources when reading and evaluating their text. In this…

On the Sophistication of Naïve Empirical Reasoning: Factors Influencing Mathematicians' Persuasion Ratings of Empirical Arguments

ERIC Educational Resources Information Center

Weber, Keith

2013-01-01

This paper presents the results of an experiment in which mathematicians were asked to rate how persuasive they found two empirical arguments. There were three key results from this study: (a) Participants judged an empirical argument as more persuasive if it verified that integers possessed an infrequent property than if it verified that integers…

The Infinite in the Finite

NASA Astrophysics Data System (ADS)

Macintosh Wilson, Alistair

1996-01-01

A conversation between Euclid and the ghost of Socrates. . . the paths of the moon and the sun charted by the stone-builders of ancient Europe. . .the Greek ideal of the golden mean by which they measured beauty. . . Combining historical fact with a retelling of ancient myths and legends, this lively and engaging book describes the historical, religious and geographical background that gave rise to mathematics in ancient Egypt, Babylon, China, Greece, India, and the Arab world. Each chapter contains a case study where mathematics is applied to the problems of the era, including the area of triangles and volume of the Egyptian pyramids; the Babylonian sexagesimal number system and our present measure of space and time which grew out of it; the use of the abacus and remainder theory in China; the invention of trigonometry by Arab mathematicians; and the solution of quadratic equations by completing the square developed in India. These insightful commentaries will give mathematicians and general historians a better understanding of why and how mathematics arose from the problems of everyday life, while the author's easy, accessible writing style will open fascinating chapters in the history of mathematics to a wide audience of general readers.

Extraordinary Tools for Extraordinary Science: The Impact ofSciDAC on Accelerator Science&Technology

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

Ryne, Robert D.

2006-08-10

Particle accelerators are among the most complex and versatile instruments of scientific exploration. They have enabled remarkable scientific discoveries and important technological advances that span all programs within the DOE Office of Science (DOE/SC). The importance of accelerators to the DOE/SC mission is evident from an examination of the DOE document, ''Facilities for the Future of Science: A Twenty-Year Outlook''. Of the 28 facilities listed, 13 involve accelerators. Thanks to SciDAC, a powerful suite of parallel simulation tools has been developed that represent a paradigm shift in computational accelerator science. Simulations that used to take weeks or more now takemore » hours, and simulations that were once thought impossible are now performed routinely. These codes have been applied to many important projects of DOE/SC including existing facilities (the Tevatron complex, the Relativistic Heavy Ion Collider), facilities under construction (the Large Hadron Collider, the Spallation Neutron Source, the Linac Coherent Light Source), and to future facilities (the International Linear Collider, the Rare Isotope Accelerator). The new codes have also been used to explore innovative approaches to charged particle acceleration. These approaches, based on the extremely intense fields that can be present in lasers and plasmas, may one day provide a path to the outermost reaches of the energy frontier. Furthermore, they could lead to compact, high-gradient accelerators that would have huge consequences for US science and technology, industry, and medicine. In this talk I will describe the new accelerator modeling capabilities developed under SciDAC, the essential role of multi-disciplinary collaboration with applied mathematicians, computer scientists, and other IT experts in developing these capabilities, and provide examples of how the codes have been used to support DOE/SC accelerator projects.« less

Extraordinary tools for extraordinary science: the impact of SciDAC on accelerator science and technology

NASA Astrophysics Data System (ADS)

Ryne, Robert D.

2006-09-01

Particle accelerators are among the most complex and versatile instruments of scientific exploration. They have enabled remarkable scientific discoveries and important technological advances that span all programs within the DOE Office of Science (DOE/SC). The importance of accelerators to the DOE/SC mission is evident from an examination of the DOE document, ''Facilities for the Future of Science: A Twenty-Year Outlook.'' Of the 28 facilities listed, 13 involve accelerators. Thanks to SciDAC, a powerful suite of parallel simulation tools has been developed that represent a paradigm shift in computational accelerator science. Simulations that used to take weeks or more now take hours, and simulations that were once thought impossible are now performed routinely. These codes have been applied to many important projects of DOE/SC including existing facilities (the Tevatron complex, the Relativistic Heavy Ion Collider), facilities under construction (the Large Hadron Collider, the Spallation Neutron Source, the Linac Coherent Light Source), and to future facilities (the International Linear Collider, the Rare Isotope Accelerator). The new codes have also been used to explore innovative approaches to charged particle acceleration. These approaches, based on the extremely intense fields that can be present in lasers and plasmas, may one day provide a path to the outermost reaches of the energy frontier. Furthermore, they could lead to compact, high-gradient accelerators that would have huge consequences for US science and technology, industry, and medicine. In this talk I will describe the new accelerator modeling capabilities developed under SciDAC, the essential role of multi-disciplinary collaboration with applied mathematicians, computer scientists, and other IT experts in developing these capabilities, and provide examples of how the codes have been used to support DOE/SC accelerator projects.

Transactions of the Conference of Army Mathematicians (23rd), held at U. S. Army Mobility Research and Development Laboratory, Langley Research Center, Hampton, Virginia, 11-13 May 1977

DTIC Science & Technology

1978-02-01

Trans. ASME, Vol. 81, 1959, pp. 259- 264 . 112 0 C> 0 LJj 0 CD 0 D ~) . [") r "-’ . 1’ n -- 1 . 2 0 1 . lj 0 1. :iO 1 • 13 0 ? . (JO p;a...n ntout Compute determinant elements forb n, Comoute and write backsc~tter cross-section\\ (Figure 2.2-1) 264 J. BACKSCATTER CROSS-SECTION FOR A...Overrelaxation Iteration Methods," Report WAPD -TM-1038, Bettis Atomic Power Laboratory, Westinghouse Electric Corp., Pittsburgh, Pennsylvania. 10

Taking the mystery out of mathematical model applications to karst aquifers—A primer

USGS Publications Warehouse

Kuniansky, Eve L.

2014-01-01

Advances in mathematical model applications toward the understanding of the complex flow, characterization, and water-supply management issues for karst aquifers have occurred in recent years. Different types of mathematical models can be applied successfully if appropriate information is available and the problems are adequately identified. The mathematical approaches discussed in this paper are divided into three major categories: 1) distributed parameter models, 2) lumped parameter models, and 3) fitting models. The modeling approaches are described conceptually with examples (but without equations) to help non-mathematicians understand the applications.

Transactions of the Conference of Army Mathematicians (21st) Held at White Sands Missile Range, N. Mex. on 14-16 May 1975

DTIC Science & Technology

1976-02-01

A. Hussain and S. L. Pu . . . . . . . . . . . . . 81 Development and Application of Dynamic r~athematical Models for Evaluation of Military Systems ...Reacting Diffusive Systems Donald S. Cohen ......•.......••..• A New Numerical Method of Solution of Schrodinger’s Equation George Morales and Robert G...Eisenhower Avenue Alexandria. Virginia 22304 DEVELOPMENT AND APPLI CATION OF DYNA~lI C r·1ATHH1ATI CAL MODELS FOR EVALUATION OF MILITARY SYSTEMS , FORCES

Aerospace Applications of Integer and Combinatorial Optimization

NASA Technical Reports Server (NTRS)

Padula, S. L.; Kincaid, R. K.

1995-01-01

Research supported by NASA Langley Research Center includes many applications of aerospace design optimization and is conducted by teams of applied mathematicians and aerospace engineers. This paper investigates the benefits from this combined expertise in formulating and solving integer and combinatorial optimization problems. Applications range from the design of large space antennas to interior noise control. A typical problem, for example, seeks the optimal locations for vibration-damping devices on an orbiting platform and is expressed as a mixed/integer linear programming problem with more than 1500 design variables.

Aerospace applications on integer and combinatorial optimization

NASA Technical Reports Server (NTRS)

Padula, S. L.; Kincaid, R. K.

1995-01-01

Research supported by NASA Langley Research Center includes many applications of aerospace design optimization and is conducted by teams of applied mathematicians and aerospace engineers. This paper investigates the benefits from this combined expertise in formulating and solving integer and combinatorial optimization problems. Applications range from the design of large space antennas to interior noise control. A typical problem. for example, seeks the optimal locations for vibration-damping devices on an orbiting platform and is expressed as a mixed/integer linear programming problem with more than 1500 design variables.

Defining Computational Thinking for Mathematics and Science Classrooms

NASA Astrophysics Data System (ADS)

Weintrop, David; Beheshti, Elham; Horn, Michael; Orton, Kai; Jona, Kemi; Trouille, Laura; Wilensky, Uri

2016-02-01

Science and mathematics are becoming computational endeavors. This fact is reflected in the recently released Next Generation Science Standards and the decision to include "computational thinking" as a core scientific practice. With this addition, and the increased presence of computation in mathematics and scientific contexts, a new urgency has come to the challenge of defining computational thinking and providing a theoretical grounding for what form it should take in school science and mathematics classrooms. This paper presents a response to this challenge by proposing a definition of computational thinking for mathematics and science in the form of a taxonomy consisting of four main categories: data practices, modeling and simulation practices, computational problem solving practices, and systems thinking practices. In formulating this taxonomy, we draw on the existing computational thinking literature, interviews with mathematicians and scientists, and exemplary computational thinking instructional materials. This work was undertaken as part of a larger effort to infuse computational thinking into high school science and mathematics curricular materials. In this paper, we argue for the approach of embedding computational thinking in mathematics and science contexts, present the taxonomy, and discuss how we envision the taxonomy being used to bring current educational efforts in line with the increasingly computational nature of modern science and mathematics.

The Multimedia Case as a Tool for Professional Development: An Analysis of Online and Face-to-Face Interaction among Mathematics Pre-Service Teachers, In-Service Teachers, Mathematicians, and Mathematics Teacher Educators

ERIC Educational Resources Information Center

McGraw, Rebecca; Lynch, Kathleen; Koc, Yusuf; Budak, Ayfer; Brown, Catherine A.

2007-01-01

In this study, we consider the potential of multimedia cases as tools for teacher professional development. Specifically, we examined online and face-to-face discussions that occurred within groups composed of pre-service mathematics teachers, in-service mathematics teachers, mathematicians, and mathematics teacher educators. Discussions within…

Boundary crossing and brokering between disciplines in pre-service mathematics teacher education

NASA Astrophysics Data System (ADS)

Goos, Merrilyn; Bennison, Anne

2017-12-01

In many countries, pre-service teacher education programs are structured so that mathematics content is taught in the university's mathematics department and mathematics pedagogy in the education department. Such program structures make it difficult to authentically interweave content with pedagogy in ways that acknowledge the roles of both mathematicians and mathematics educators in preparing future teachers. This article reports on a project that deliberately fostered collaboration between mathematicians and mathematics educators in six Australian universities in order to investigate the potential for learning at the boundaries between the two disciplinary communities. Data sources included two rounds of interviews with mathematicians and mathematics educators and annual reports prepared by each participating university over the three years of the project. The study identified interdisciplinary boundary practices that led to integration of content and pedagogy through new courses co-developed and co-taught by mathematicians and mathematics educators, and new approaches to building communities of pre-service teachers. It also developed an evidence-based classification of conditions that enable or hinder sustained collaboration across disciplinary boundaries, together with an empirical grounding for Akkerman and Bakker's conceptualisation of transformation as a mechanism for learning at the boundary between communities. The study additionally highlighted the ambiguous nature of boundaries and implications for brokers who work there to connect disciplinary paradigms.

An engineering design approach to systems biology.

PubMed

Janes, Kevin A; Chandran, Preethi L; Ford, Roseanne M; Lazzara, Matthew J; Papin, Jason A; Peirce, Shayn M; Saucerman, Jeffrey J; Lauffenburger, Douglas A

2017-07-17

Measuring and modeling the integrated behavior of biomolecular-cellular networks is central to systems biology. Over several decades, systems biology has been shaped by quantitative biologists, physicists, mathematicians, and engineers in different ways. However, the basic and applied versions of systems biology are not typically distinguished, which blurs the separate aspirations of the field and its potential for real-world impact. Here, we articulate an engineering approach to systems biology, which applies educational philosophy, engineering design, and predictive models to solve contemporary problems in an age of biomedical Big Data. A concerted effort to train systems bioengineers will provide a versatile workforce capable of tackling the diverse challenges faced by the biotechnological and pharmaceutical sectors in a modern, information-dense economy.

Origins of the brain networks for advanced mathematics in expert mathematicians

PubMed Central

Amalric, Marie; Dehaene, Stanislas

2016-01-01

The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advanced mathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit. PMID:27071124

Origins of the brain networks for advanced mathematics in expert mathematicians.

PubMed

Amalric, Marie; Dehaene, Stanislas

2016-05-03

The origins of human abilities for mathematics are debated: Some theories suggest that they are founded upon evolutionarily ancient brain circuits for number and space and others that they are grounded in language competence. To evaluate what brain systems underlie higher mathematics, we scanned professional mathematicians and mathematically naive subjects of equal academic standing as they evaluated the truth of advanced mathematical and nonmathematical statements. In professional mathematicians only, mathematical statements, whether in algebra, analysis, topology or geometry, activated a reproducible set of bilateral frontal, Intraparietal, and ventrolateral temporal regions. Crucially, these activations spared areas related to language and to general-knowledge semantics. Rather, mathematical judgments were related to an amplification of brain activity at sites that are activated by numbers and formulas in nonmathematicians, with a corresponding reduction in nearby face responses. The evidence suggests that high-level mathematical expertise and basic number sense share common roots in a nonlinguistic brain circuit.

Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction?

PubMed Central

Pan, Xiaochuan; Sidky, Emil Y; Vannier, Michael

2010-01-01

Despite major advances in x-ray sources, detector arrays, gantry mechanical design and especially computer performance, one component of computed tomography (CT) scanners has remained virtually constant for the past 25 years—the reconstruction algorithm. Fundamental advances have been made in the solution of inverse problems, especially tomographic reconstruction, but these works have not been translated into clinical and related practice. The reasons are not obvious and seldom discussed. This review seeks to examine the reasons for this discrepancy and provides recommendations on how it can be resolved. We take the example of field of compressive sensing (CS), summarizing this new area of research from the eyes of practical medical physicists and explaining the disconnection between theoretical and application-oriented research. Using a few issues specific to CT, which engineers have addressed in very specific ways, we try to distill the mathematical problem underlying each of these issues with the hope of demonstrating that there are interesting mathematical problems of general importance that can result from in depth analysis of specific issues. We then sketch some unconventional CT-imaging designs that have the potential to impact on CT applications, if the link between applied mathematicians and engineers/physicists were stronger. Finally, we close with some observations on how the link could be strengthened. There is, we believe, an important opportunity to rapidly improve the performance of CT and related tomographic imaging techniques by addressing these issues. PMID:20376330

TOPICAL REVIEW: Why do commercial CT scanners still employ traditional, filtered back-projection for image reconstruction?

NASA Astrophysics Data System (ADS)

Pan, Xiaochuan; Sidky, Emil Y.; Vannier, Michael

2009-12-01

Despite major advances in x-ray sources, detector arrays, gantry mechanical design and especially computer performance, one component of computed tomography (CT) scanners has remained virtually constant for the past 25 years—the reconstruction algorithm. Fundamental advances have been made in the solution of inverse problems, especially tomographic reconstruction, but these works have not been translated into clinical and related practice. The reasons are not obvious and seldom discussed. This review seeks to examine the reasons for this discrepancy and provides recommendations on how it can be resolved. We take the example of field of compressive sensing (CS), summarizing this new area of research from the eyes of practical medical physicists and explaining the disconnection between theoretical and application-oriented research. Using a few issues specific to CT, which engineers have addressed in very specific ways, we try to distill the mathematical problem underlying each of these issues with the hope of demonstrating that there are interesting mathematical problems of general importance that can result from in depth analysis of specific issues. We then sketch some unconventional CT-imaging designs that have the potential to impact on CT applications, if the link between applied mathematicians and engineers/physicists were stronger. Finally, we close with some observations on how the link could be strengthened. There is, we believe, an important opportunity to rapidly improve the performance of CT and related tomographic imaging techniques by addressing these issues.

Biophysics and systems biology.

PubMed

Noble, Denis

2010-03-13

Biophysics at the systems level, as distinct from molecular biophysics, acquired its most famous paradigm in the work of Hodgkin and Huxley, who integrated their equations for the nerve impulse in 1952. Their approach has since been extended to other organs of the body, notably including the heart. The modern field of computational biology has expanded rapidly during the first decade of the twenty-first century and, through its contribution to what is now called systems biology, it is set to revise many of the fundamental principles of biology, including the relations between genotypes and phenotypes. Evolutionary theory, in particular, will require re-assessment. To succeed in this, computational and systems biology will need to develop the theoretical framework required to deal with multilevel interactions. While computational power is necessary, and is forthcoming, it is not sufficient. We will also require mathematical insight, perhaps of a nature we have not yet identified. This article is therefore also a challenge to mathematicians to develop such insights.

Biophysics and systems biology

PubMed Central

Noble, Denis

2010-01-01

Biophysics at the systems level, as distinct from molecular biophysics, acquired its most famous paradigm in the work of Hodgkin and Huxley, who integrated their equations for the nerve impulse in 1952. Their approach has since been extended to other organs of the body, notably including the heart. The modern field of computational biology has expanded rapidly during the first decade of the twenty-first century and, through its contribution to what is now called systems biology, it is set to revise many of the fundamental principles of biology, including the relations between genotypes and phenotypes. Evolutionary theory, in particular, will require re-assessment. To succeed in this, computational and systems biology will need to develop the theoretical framework required to deal with multilevel interactions. While computational power is necessary, and is forthcoming, it is not sufficient. We will also require mathematical insight, perhaps of a nature we have not yet identified. This article is therefore also a challenge to mathematicians to develop such insights. PMID:20123750

Design Graphics

NASA Technical Reports Server (NTRS)

1990-01-01

A mathematician, David R. Hedgley, Jr. developed a computer program that considers whether a line in a graphic model of a three-dimensional object should or should not be visible. Known as the Hidden Line Computer Code, the program automatically removes superfluous lines and displays an object from a specific viewpoint, just as the human eye would see it. An example of how one company uses the program is the experience of Birdair which specializes in production of fabric skylights and stadium covers. The fabric called SHEERFILL is a Teflon coated fiberglass material developed in cooperation with DuPont Company. SHEERFILL glazed structures are either tension structures or air-supported tension structures. Both are formed by patterned fabric sheets supported by a steel or aluminum frame or cable network. Birdair uses the Hidden Line Computer Code, to illustrate a prospective structure to an architect or owner. The program generates a three- dimensional perspective with the hidden lines removed. This program is still used by Birdair and continues to be commercially available to the public.

Feasibility of Single and Dual Satellite Systems to Enable Continuous Communication Capability to a Manned Mars Mission

DTIC Science & Technology

2014-09-01

periodicity for many centuries but it was not until Johannes Kepler (1619), a German mathematician, developed his three laws of planetary motion in the early...ORBITS Johannes Kepler was a brilliant mathematician hired to map the orbit of Mars by the infamous elk owner, duelist, and astronomer Tycho Brahe...Dreyer & Brahe, 1890). Despite a difference in viewpoints ( Kepler supported Copernicus while Brahe developed his own model of planetary motion in

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.

The Effect of Gender in the Publication Patterns in Mathematics.

PubMed

Mihaljević-Brandt, Helena; Santamaría, Lucía; Tullney, Marco

2016-01-01

Despite the increasing number of women graduating in mathematics, a systemic gender imbalance persists and is signified by a pronounced gender gap in the distribution of active researchers and professors. Especially at the level of university faculty, women mathematicians continue being drastically underrepresented, decades after the first affirmative action measures have been put into place. A solid publication record is of paramount importance for securing permanent positions. Thus, the question arises whether the publication patterns of men and women mathematicians differ in a significant way. Making use of the zbMATH database, one of the most comprehensive metadata sources on mathematical publications, we analyze the scholarly output of ∼150,000 mathematicians from the past four decades whose gender we algorithmically inferred. We focus on development over time, collaboration through coautorships, presumed journal quality and distribution of research topics-factors known to have a strong impact on job perspectives. We report significant differences between genders which may put women at a disadvantage when pursuing an academic career in mathematics.

The Effect of Gender in the Publication Patterns in Mathematics

PubMed Central

2016-01-01

Despite the increasing number of women graduating in mathematics, a systemic gender imbalance persists and is signified by a pronounced gender gap in the distribution of active researchers and professors. Especially at the level of university faculty, women mathematicians continue being drastically underrepresented, decades after the first affirmative action measures have been put into place. A solid publication record is of paramount importance for securing permanent positions. Thus, the question arises whether the publication patterns of men and women mathematicians differ in a significant way. Making use of the zbMATH database, one of the most comprehensive metadata sources on mathematical publications, we analyze the scholarly output of ∼150,000 mathematicians from the past four decades whose gender we algorithmically inferred. We focus on development over time, collaboration through coautorships, presumed journal quality and distribution of research topics—factors known to have a strong impact on job perspectives. We report significant differences between genders which may put women at a disadvantage when pursuing an academic career in mathematics. PMID:27780266

Mathematical Practices and Arts Integration in an Activity-Based Projective Geometry Course

NASA Astrophysics Data System (ADS)

Ernest, Jessica Brooke

It is a general assumption that the mathematical activity of students in school should, at least to some degree, parallel the practices of professional mathematicians (Brown, Collins, Duguid, 1989; Moschkovich, 2013). This assumption is reflected in the Common Core State Standards (CCSSI, 2010) and National Council of Teachers of Mathematics (NCTM, 2000) standards documents. However, the practices included in these standards documents, while developed to reflect the practices of professional mathematicians, may be idealized versions of what mathematicians actually do (Moschkovich, 2013). This might lead us to question then: "What is it that mathematicians do, and what practices are not being represented in the standards documents?" In general, the creative work of mathematicians is absent from the standards and, in turn, from school mathematics curricula, much to the dismay of some mathematicians and researchers (Lockhart, 2009; Rogers, 1999). As a result, creativity is not typically being fostered in mathematics students. As a response to this lack of focus on fostering creativity (in each of the science, technology, engineering, and mathematics disciplines--the STEM disciplines), a movement to integrate the arts emerged. This movement, called the STEAM movement--introducing the letter A into the acronym STEM to signify incorporating the arts--has been gaining momentum, yet limited research has been carried out on the efficacy of integrating the arts into mathematics courses. My experiences as the co-instructor for an activity-based course focused on projective geometry led me to consider the course as a setting for investigating both mathematical practices and arts integration. In this work, I explored the mathematical practices in which students engaged while working to develop an understanding of projective geometry through group activities. Furthermore, I explored the way in which students' learning experiences were enriched through artistic engagement in the course. I discuss mathematical play and acts of imagination--two mathematical practices in which students engaged, and which emerged from a grounded theory approach to analysis of the classroom data. In addition, I discuss particular ways in which artistic engagement, including creating two mathematically inspired artistic pieces, enriched students' learning experiences in the course. The six themes I address are artistic engagement (a) fostering mathematical play, (b) giving students the opportunity to make sense of pop-up topics, (c) providing students with the opportunity to develop coordination of mathematical tools, (d) allowing students to weave their personal experiences with mathematics, (e) contributing to students' notions of the connections between mathematics and art, and (f) changing students' relationships with art.

Avoiding numerical pitfalls in social force models

NASA Astrophysics Data System (ADS)

Köster, Gerta; Treml, Franz; Gödel, Marion

2013-06-01

The social force model of Helbing and Molnár is one of the best known approaches to simulate pedestrian motion, a collective phenomenon with nonlinear dynamics. It is based on the idea that the Newtonian laws of motion mostly carry over to pedestrian motion so that human trajectories can be computed by solving a set of ordinary differential equations for velocity and acceleration. The beauty and simplicity of this ansatz are strong reasons for its wide spread. However, the numerical implementation is not without pitfalls. Oscillations, collisions, and instabilities occur even for very small step sizes. Classic solution ideas from molecular dynamics do not apply to the problem because the system is not Hamiltonian despite its source of inspiration. Looking at the model through the eyes of a mathematician, however, we realize that the right hand side of the differential equation is nondifferentiable and even discontinuous at critical locations. This produces undesirable behavior in the exact solution and, at best, severe loss of accuracy in efficient numerical schemes even in short range simulations. We suggest a very simple mollified version of the social force model that conserves the desired dynamic properties of the original many-body system but elegantly and cost efficiently resolves several of the issues concerning stability and numerical resolution.

Partial differential equation models in macroeconomics.

PubMed

Achdou, Yves; Buera, Francisco J; Lasry, Jean-Michel; Lions, Pierre-Louis; Moll, Benjamin

2014-11-13

The purpose of this article is to get mathematicians interested in studying a number of partial differential equations (PDEs) that naturally arise in macroeconomics. These PDEs come from models designed to study some of the most important questions in economics. At the same time, they are highly interesting for mathematicians because their structure is often quite difficult. We present a number of examples of such PDEs, discuss what is known about their properties, and list some open questions for future research. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Synthetic biology through biomolecular design and engineering.

PubMed

Channon, Kevin; Bromley, Elizabeth H C; Woolfson, Derek N

2008-08-01

Synthetic biology is a rapidly growing field that has emerged in a global, multidisciplinary effort among biologists, chemists, engineers, physicists, and mathematicians. Broadly, the field has two complementary goals: To improve understanding of biological systems through mimicry and to produce bio-orthogonal systems with new functions. Here we review the area specifically with reference to the concept of synthetic biology space, that is, a hierarchy of components for, and approaches to generating new synthetic and functional systems to test, advance, and apply our understanding of biological systems. In keeping with this issue of Current Opinion in Structural Biology, we focus largely on the design and engineering of biomolecule-based components and systems.

Quantitative Finance

NASA Astrophysics Data System (ADS)

James, Jessica

2017-01-01

Quantitative finance is a field that has risen to prominence over the last few decades. It encompasses the complex models and calculations that value financial contracts, particularly those which reference events in the future, and apply probabilities to these events. While adding greatly to the flexibility of the market available to corporations and investors, it has also been blamed for worsening the impact of financial crises. But what exactly does quantitative finance encompass, and where did these ideas and models originate? We show that the mathematics behind finance and behind games of chance have tracked each other closely over the centuries and that many well-known physicists and mathematicians have contributed to the field.

Fermi-Pasta-Ulam, solitons and the fabric of nonlinear and computational science: History, synergetics, and visiometricsa)

NASA Astrophysics Data System (ADS)

Zabusky, Norman J.

2005-03-01

This paper is mostly a history of the early years of nonlinear and computational physics and mathematics. I trace how the counterintuitive result of near-recurrence to an initial condition in the first scientific digital computer simulation led to the discovery of the soliton in a later computer simulation. The 1955 report by Fermi, Pasta, and Ulam (FPU) described their simulation of a one-dimensional nonlinear lattice which did not show energy equipartition. The 1965 paper by Zabusky and Kruskalshowed that the Korteweg-de Vries (KdV) nonlinear partial differential equation, a long wavelength model of the α-lattice (or cubic nonlinearity), derived by Kruskal, gave quantitatively the same results obtained by FPU. In 1967, Zabusky and Deem showed that a localized short wavelength initial excitation (then called an "optical" and now a "zone-boundary mode" excitation ) of the α-lattice revealed "n-curve" coherent states. If the initial amplitude was sufficiently large energy equipartition followed in a short time. The work of Kruskal and Miura (KM), Gardner and Greene (GG), and myself led to the appreciation of the infinity of denumerable invariants (conservation laws) for Hamiltonian systems and to a procedure by GGKM in 1967 for solving KdV exactly. The nonlinear science field exponentiated in diversity of linkages (as described in Appendix A). Included were pure and applied mathematics and all branches of basic and applied physics, including the first nonhydrodynamic application to optical solitons, as described in a brief essay (Appendix B) by Hasegawa. The growth was also manifest in the number of meetings held and institutes founded, as described briefly in Appendix D. Physicists and mathematicians in Japan, USA, and USSR (in the latter two, people associated with plasma physics) contributed to the diversification of the nonlinear paradigm which continues worldwide to the present. The last part of the paper (and Appendix C) discuss visiometrics: the visualization and quantification of simulation data, e.g., projection to lower dimensions, to facilitate understanding of nonlinear phenomena for modeling and prediction (or design). Finally, I present some recent developments that are linked to my early work by: Dritschel (vortex dynamics via contour dynamics/surgery in two and three dimensions); Friedland (pattern formation by synchronization in Hamiltonian nonlinear wave, vortex, plasma, systems, etc.); and the author ("n-curve" states and energy equipartition in a FPU lattice).

Fermi-Pasta-Ulam, solitons and the fabric of nonlinear and computational science: history, synergetics, and visiometrics.

PubMed

Zabusky, Norman J

2005-03-01

This paper is mostly a history of the early years of nonlinear and computational physics and mathematics. I trace how the counterintuitive result of near-recurrence to an initial condition in the first scientific digital computer simulation led to the discovery of the soliton in a later computer simulation. The 1955 report by Fermi, Pasta, and Ulam (FPU) described their simulation of a one-dimensional nonlinear lattice which did not show energy equipartition. The 1965 paper by Zabusky and Kruskalshowed that the Korteweg-de Vries (KdV) nonlinear partial differential equation, a long wavelength model of the alpha-lattice (or cubic nonlinearity), derived by Kruskal, gave quantitatively the same results obtained by FPU. In 1967, Zabusky and Deem showed that a localized short wavelength initial excitation (then called an "optical" and now a "zone-boundary mode" excitation ) of the alpha-lattice revealed "n-curve" coherent states. If the initial amplitude was sufficiently large energy equipartition followed in a short time. The work of Kruskal and Miura (KM), Gardner and Greene (GG), and myself led to the appreciation of the infinity of denumerable invariants (conservation laws) for Hamiltonian systems and to a procedure by GGKM in 1967 for solving KdV exactly. The nonlinear science field exponentiated in diversity of linkages (as described in Appendix A). Included were pure and applied mathematics and all branches of basic and applied physics, including the first nonhydrodynamic application to optical solitons, as described in a brief essay (Appendix B) by Hasegawa. The growth was also manifest in the number of meetings held and institutes founded, as described briefly in Appendix D. Physicists and mathematicians in Japan, USA, and USSR (in the latter two, people associated with plasma physics) contributed to the diversification of the nonlinear paradigm which continues worldwide to the present. The last part of the paper (and Appendix C) discuss visiometrics: the visualization and quantification of simulation data, e.g., projection to lower dimensions, to facilitate understanding of nonlinear phenomena for modeling and prediction (or design). Finally, I present some recent developments that are linked to my early work by: Dritschel (vortex dynamics via contour dynamics/surgery in two and three dimensions); Friedland (pattern formation by synchronization in Hamiltonian nonlinear wave, vortex, plasma, systems, etc.); and the author ("n-curve" states and energy equipartition in a FPU lattice).

Modeling high-temperature superconductors and metallic alloys on the Intel IPSC/860

NASA Astrophysics Data System (ADS)

Geist, G. A.; Peyton, B. W.; Shelton, W. A.; Stocks, G. M.

Oak Ridge National Laboratory has embarked on several computational Grand Challenges, which require the close cooperation of physicists, mathematicians, and computer scientists. One of these projects is the determination of the material properties of alloys from first principles and, in particular, the electronic structure of high-temperature superconductors. While the present focus of the project is on superconductivity, the approach is general enough to permit study of other properties of metallic alloys such as strength and magnetic properties. This paper describes the progress to date on this project. We include a description of a self-consistent KKR-CPA method, parallelization of the model, and the incorporation of a dynamic load balancing scheme into the algorithm. We also describe the development and performance of a consolidated KKR-CPA code capable of running on CRAYs, workstations, and several parallel computers without source code modification. Performance of this code on the Intel iPSC/860 is also compared to a CRAY 2, CRAY YMP, and several workstations. Finally, some density of state calculations of two perovskite superconductors are given.

In accordance with a "more majestic order". The new math and the nature of mathematics at midcentury.

PubMed

Phillips, Christopher J

2014-09-01

The "new math" curriculum, one version of which was developed in the 1950s and 1960s by the School Mathematics Study Group under the auspices of the National Science Foundation, occasioned a great deal of controversy among mathematicians. Well before its rejection by parents and teachers, some mathematicians were vocal critics, decrying the new curriculum because of the way it described the practice and history of the discipline. The nature of mathematics, despite the field's triumphs in helping to win World War II and its midcentury promotion as the key to a modern technological society, was surprisingly contested in this period. Supporters of the School Mathematics Study Group, like its director, Edward Begle, emphasized the importance of portraying mathematics as a system of abstract structures, while opponents like Morris Kline argued that math was essentially a tool for understanding the natural world. The debate about the curriculum--and the role of mathematicians in its design--was also a debate about the underlying identity of the subject itself.

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"!!!

Grand minima of solar activity and sociodynamics of culture

NASA Astrophysics Data System (ADS)

Vladimirsky, B. M.

2012-12-01

Indices of creative productivity introduced by C. Murrey were used to verify S. Ertel's conclusion about a global increase in creative productivity during the prolonged minimum of solar activity in 1640-1710. It was found that these indices for mathematicians, philosophers, and scientists increase in the Maunder era by factor of 1.6 in comparison with intervals of the same length before and after the minimum. A similar effect was obtained for mathematicians and philosophers for five earlier equitype minima in total (an increase by a factor of 1.9). The regularity that is revealed is confirmed by the fact that the most important achievements of high-ranking mathematicians and philosophers during the whole time period (2300 years) considered in this study fall on epochs of reduced levels of solar activity. The rise in the probability of the generation of rational ideas during grand minima is reflected also in the fact that they precede the appearance of written language and farming. Ultra-low-frequency electromagnetic fields appear to serve as a physical agent stimulating the activity of the brain's left hemisphere during the epochs of minima.

Obituary: Eugene Richard Tomer, 1932-2007

NASA Astrophysics Data System (ADS)

Dunkl, Charles F.

2009-01-01

Dr. Eugene R. Tomer passed away on 2 July 2007 at his home in San Francisco, California. The cause of death was cancer. Tomer was a consulting applied mathematician with a wide range of interests in dynamical astronomy, electromagnetic theory for use in communications, and computational methods of applied mathematics. He was a member of AAS, and the Society for Applied and Industrial Mathematics [SIAM]. With K. H. Prendergast, he co-wrote the influential paper "Self-consistent Models of Elliptical Galaxies," published in the Astronomical Journal 75 (1970), 674-679. This paper has been cited over eighty times. Tomer was born on 13 June 1932. He earned the Ph.D. in Mathematics at the University of California-Berkeley in 1978 (title of dissertation: On the C*-algebra of the Hermite Operator). In 1996 he and A. F. Peterson wrote "Meeting the Challenges Presented by Computational Electromagnetics," a publication of the Naval Postgraduate School at Monterey, California. This writer met Eugene at the 1992 Annual SIAM meeting in Los Angeles in connection with the Activity Group on Orthogonal Polynomials and Special Functions, which the writer chaired at the time. Eugene volunteered to edit the Newsletter of the group, which he did from July 1992 to July 1995. Thanks to his skills and efforts, the Newsletter became a carefully edited, professional publication. Eugene not only organized a Problems Column, attracting questions in pure and applied mathematics, but he also designed the logo for the group. He gave much time and effort to this service, in an era when copy had to be physically assembled and mailed to SIAM Headquarters. Eventually he felt he had done what he could for the Activity Group. He told me that he hoped the Group would get seriously involved with applications such as in astronomy, physics, and sciences that use special function solutions of differential equations. During Tomer's editorship, we communicated mostly by e-mail, our homes being far apart. He was a good friend to the Group and to me, as much as one can be over a separation of thousands of miles. As well, Eugene was an active amateur radio operator, much appreciated by his local amateur radio community, with call sign WI6X. He left behind family, friends, and one son.

Leonid Vital'evich Kantorovich (on the 100th anniversary of his birth)

NASA Astrophysics Data System (ADS)

Vershik, Anatolii M.; Kutateladze, Semen S.; Novikov, Sergei P.

2012-06-01

The 19th of January 2012 was the 100th anniversary of the birth of Leonid Vital'evich Kantorovich, an outstanding mathematician and economist of international fame. A child prodigy, who graduated from the university at 18 and became a professor at 20, an academician in the mathematical sciences and a laureate of the Nobel Prize in economics, - these are extraordinary circumstances of his life. They are remarkable in themselves, but also the results he achieved were exceptional and immensely impressive, and the younger generations of researchers, first and foremost mathematicians and economists, must know about them.

Opening Comments: SciDAC 2009

NASA Astrophysics Data System (ADS)

Strayer, Michael

2009-07-01

Welcome to San Diego and the 2009 SciDAC conference. Over the next four days, I would like to present an assessment of the SciDAC program. We will look at where we've been, how we got to where we are and where we are going in the future. Our vision is to be first in computational science, to be best in class in modeling and simulation. When Ray Orbach asked me what I would do, in my job interview for the SciDAC Director position, I said we would achieve that vision. And with our collective dedicated efforts, we have managed to achieve this vision. In the last year, we have now the most powerful supercomputer for open science, Jaguar, the Cray XT system at the Oak Ridge Leadership Computing Facility (OLCF). We also have NERSC, probably the best-in-the-world program for productivity in science that the Office of Science so depends on. And the Argonne Leadership Computing Facility offers architectural diversity with its IBM Blue Gene/P system as a counterbalance to Oak Ridge. There is also ESnet, which is often understated—the 40 gigabit per second dual backbone ring that connects all the labs and many DOE sites. In the President's Recovery Act funding, there is exciting news that ESnet is going to build out to a 100 gigabit per second network using new optical technologies. This is very exciting news for simulations and large-scale scientific facilities. But as one noted SciDAC luminary said, it's not all about the computers—it's also about the science—and we are also achieving our vision in this area. Together with having the fastest supercomputer for science, at the SC08 conference, SciDAC researchers won two ACM Gordon Bell Prizes for the outstanding performance of their applications. The DCA++ code, which solves some very interesting problems in materials, achieved a sustained performance of 1.3 petaflops, an astounding result and a mark I suspect will last for some time. The LS3DF application for studying nanomaterials also required the development of a new and novel algorithm to produce results up to 400 times faster than a similar application, and was recognized with a prize for algorithm innovation—a remarkable achievement. Day one of our conference will include examples of petascale science enabled at the OLCF. Although Jaguar has not been officially commissioned, it has gone through its acceptance tests, and during its shakedown phase there have been pioneer applications used for the acceptance tests, and they are running at scale. These include applications in the areas of astrophysics, biology, chemistry, combustion, fusion, geosciences, materials science, nuclear energy and nuclear physics. We also have a whole compendium of science we do at our facilities; these have been documented and reviewed at our last SciDAC conference. Many of these were highlighted in our Breakthroughs Report. One session at this week's conference will feature a cross-section of these breakthroughs. In the area of scalable electromagnetic simulations, the Auxiliary-space Maxwell Solver (AMS) uses specialized finite element discretizations and multigrid-based techniques, which decompose the original problem into easier-to-solve subproblems. Congratulations to the mathematicians on this. Another application on the list of breakthroughs was the authentication of PETSc, which provides scalable solvers used in many DOE applications and has solved problems with over 3 billion unknowns and scaled to over 16,000 processors on DOE leadership-class computers. This is becoming a very versatile and useful toolkit to achieve performance at scale. With the announcement of SIAM's first class of Fellows, we are remarkably well represented. Of the group of 191, more than 40 of these Fellows are in the 'DOE space.' We are so delighted that SIAM has recognized them for their many achievements. In the coming months, we will illustrate our leadership in applied math and computer science by looking at our contributions in the areas of programming models, development and performance tools, math libraries, system software, collaboration, and visualization and data analytics. This is a large and diverse list of libraries. We have asked for two panels, one chaired by David Keyes and composed of many of the nation's leading mathematicians, to produce a report on the most significant accomplishments in applied mathematics over the last eight years, taking us back to the start of the SciDAC program. In addition, we have a similar panel in computer science to be chaired by Kathy Yelick. They are going to identify the computer science accomplishments of the past eight years. These accomplishments are difficult to get a handle on, and I'm looking forward to this report. We will also have a follow-on to our report on breakthroughs in computational science and this will also go back eight years, looking at the many accomplishments under the SciDAC and INCITE programs. This will be chaired by Tony Mezzacappa. So, where are we going in the SciDAC program? It might help to take a look at computational science and how it got started. I go back to Ken Wilson, who made the model and has written on computational science and computational science education. His model was thus: The computational scientist plays the role of the experimentalist, and the math and CS researchers play the role of theorists, and the computers themselves are the experimental apparatus. And that in simulation science, we are carrying out numerical experiments as to the nature of physical and biological sciences. Peter Lax, in the same time frame, developed a report on large-scale computing in science and engineering. Peter remarked, 'Perhaps the most important applications of scientific computing come not in the solution of old problems, but in the discovery of new phenomena through numerical experimentation.' And in the early years, I think the person who provided the most guidance, the most innovation and the most vision for where the future might lie was Ed Oliver. Ed Oliver died last year. Ed did a number of things in science. He had this personality where he knew exactly what to do, but he preferred to stay out of the limelight so that others could enjoy the fruits of his vision. We in the SciDAC program and ASCR Facilities are still enjoying the benefits of his vision. We will miss him. Twenty years after Ken Wilson, Ray Orbach laid out the fundamental premise for SciDAC in an interview that appeared in SciDAC Review: 'SciDAC is unique in the world. There isn't any other program like it anywhere else, and it has the remarkable ability to do science by bringing together physical scientists, mathematicians, applied mathematicians, and computer scientists who recognize that computation is not something you do at the end, but rather it needs to be built into the solution of the very problem that one is addressing. ' As you look at the Lax report from 1982, it talks about how 'Future significant improvements may have to come from architectures embodying parallel processing elements—perhaps several thousands of processors.' And it continues, 'esearch in languages, algorithms and numerical analysis will be crucial in learning to exploit these new architectures fully.' In the early '90s, Sterling, Messina and Smith developed a workshop report on petascale computing and concluded, 'A petaflops computer system will be feasible in two decades, or less, and rely in part on the continual advancement of the semiconductor industry both in speed enhancement and cost reduction through improved fabrication processes.' So they were not wrong, and today we are embarking on a forward look that is at a different scale, the exascale, going to 1018 flops. In 2007, Stevens, Simon and Zacharia chaired a series of town hall meetings looking at exascale computing, and in their report wrote, 'Exascale computer systems are expected to be technologically feasible within the next 15 years, or perhaps sooner. These systems will push the envelope in a number of important technologies: processor architecture, scale of multicore integration, power management and packaging.' The concept of computing on the Jaguar computer involves hundreds of thousands of cores, as do the IBM systems that are currently out there. So the scale of computing with systems with billions of processors is staggering to me, and I don't know how the software and math folks feel about it. We have now embarked on a road toward extreme scale computing. We have created a series of town hall meetings and we are now in the process of holding workshops that address what I call within the DOE speak 'the mission need,' or what is the scientific justification for computing at that scale. We are going to have a total of 13 workshops. The workshops on climate, high energy physics, nuclear physics, fusion, and nuclear energy have been held. The report from the workshop on climate is actually out and available, and the other reports are being completed. The upcoming workshops are on biology, materials, and chemistry; and workshops that engage science for nuclear security are a partnership between NNSA and ASCR. There are additional workshops on applied math, computer science, and architecture that are needed for computing at the exascale. These extreme scale workshops will provide the foundation in our office, the Office of Science, the NNSA and DOE, and we will engage the National Science Foundation and the Department of Defense as partners. We envision a 10-year program for an exascale initiative. It will be an integrated R&D program initially—you can think about five years for research and development—that would be in hardware, operating systems, file systems, networking and so on, as well as software for applications. Application software and the operating system and the hardware all need to be bundled in this period so that at the end the system will execute the science applications at scale. We also believe that this process will have to have considerable investment from the manufacturers and vendors to be successful. We have formed laboratory, university and industry working groups to start this process and formed a panel to look at where SciDAC needs to go to compute at the extreme scale, and we have formed an executive committee within the Office of Science and the NNSA to focus on these activities. We will have outreach to DoD in the next few months. We are anticipating a solicitation within the next two years in which we will compete this bundled R&D process. We don't know how we will incorporate SciDAC into extreme scale computing, but we do know there will be many challenges. And as we have shown over the years, we have the expertise and determination to surmount these challenges.

A Succinct Naming Convention for Lengthy Hexadecimal Numbers

NASA Technical Reports Server (NTRS)

Grant, Michael S.

1997-01-01

Engineers, computer scientists, mathematicians and others must often deal with lengthy hexadecimal numbers. As memory requirements for software increase, the associated memory address space for systems necessitates the use of longer and longer strings of hexadecimal characters to describe a given number. For example, the address space of some digital signal processors (DSP's) now ranges in the billions of words, requiring eight hexadecimal characters for many of the addresses. This technical memorandum proposes a simple grouping scheme for more clearly representing lengthy hexadecimal numbers in written material, as well as a "code" for naming and more quickly verbalizing such numbers. This should facilitate communications among colleagues in engineering and related fields, and aid in comprehension and temporary memorization of important hexadecimal numbers during design work.

Positron emission tomography

NASA Astrophysics Data System (ADS)

Yamamoto, Y. Lucas; Thompson, Christopher J.; Diksic, Mirko; Meyer, Ernest; Feindel, William H.

One of the most exciting new technologies introduced in the last 10 yr is positron emission tomography (PET). PET provides quantitative, three-dimensional images for the study of specific biochemical and physiological processes in the human body. This approach is analogous to quantitative in-vivo autoradiography but has the added advantage of permitting non-invasive in vivo studies. PET scanning requires a small cyclotron to produce short-lived positron emitting isotopes such as oxygen-15, carbon-11, nitrogen-13 and fluorine-18. Proper radiochemical facilities and advanced computer equipment are also needed. Most important, PET requires a multidisciplinary scientific team of physicists, radiochemists, mathematicians, biochemists and physicians. This review analyzes the most recent trends in the imaging technology, radiochemistry, methodology and clinical applications of positron emission tomography.

T-Duality for Orientifolds and Twisted KR-Theory

NASA Astrophysics Data System (ADS)

Doran, Charles; Méndez-Diez, Stefan; Rosenberg, Jonathan

2014-08-01

D-brane charges in orientifold string theories are classified by the KR-theory of Atiyah. However, this is assuming that all O-planes have the same sign. When there are O-planes of different signs, physics demands a "KR-theory with a sign choice" which up until now has not been studied by mathematicians (with the unique exception of Moutuou, who did not have a specific application in mind). We give a definition of this theory and compute it for orientifold theories compactified on S 1 and T 2. We also explain how and why additional "twisting" is implemented. We show that our results satisfy all possible T-duality relationships for orientifold string theories on elliptic curves, which will be studied further in subsequent work.

Modulation theory, dispersive shock waves and Gerald Beresford Whitham

NASA Astrophysics Data System (ADS)

Minzoni, A. A.; Smyth, Noel F.

2016-10-01

Gerald Beresford (GB) Whitham, FRS, (13th December, 1927-26th January, 2014) was one of the leading applied mathematicians of the twentieth century whose work over forty years had a profound, formative impact on research on wave motion across a broad range of areas. Many of the ideas and techniques he developed have now become the standard tools used to analyse and understand wave motion, as the papers of this special issue of Physica D testify. Many of the techniques pioneered by GB Whitham have spread beyond wave propagation into other applied mathematics areas, such as reaction-diffusion, and even into theoretical physics and pure mathematics, in which Whitham modulation theory is an active area of research. GB Whitham's classic textbook Linear and Nonlinear Waves, published in 1974, is still the standard reference for the applied mathematics of wave motion. In honour of his scientific achievements, GB Whitham was elected a Fellow of the American Academy of Arts and Sciences in 1959 and a Fellow of the Royal Society in 1965. He was awarded the Norbert Wiener Prize for Applied Mathematics in 1980.

Multistate Memristive Tantalum Oxide Devices for Ternary Arithmetic

PubMed Central

Kim, Wonjoo; Chattopadhyay, Anupam; Siemon, Anne; Linn, Eike; Waser, Rainer; Rana, Vikas

2016-01-01

Redox-based resistive switching random access memory (ReRAM) offers excellent properties to implement future non-volatile memory arrays. Recently, the capability of two-state ReRAMs to implement Boolean logic functionality gained wide interest. Here, we report on seven-states Tantalum Oxide Devices, which enable the realization of an intrinsic modular arithmetic using a ternary number system. Modular arithmetic, a fundamental system for operating on numbers within the limit of a modulus, is known to mathematicians since the days of Euclid and finds applications in diverse areas ranging from e-commerce to musical notations. We demonstrate that multistate devices not only reduce the storage area consumption drastically, but also enable novel in-memory operations, such as computing using high-radix number systems, which could not be implemented using two-state devices. The use of high radix number system reduces the computational complexity by reducing the number of needed digits. Thus the number of calculation operations in an addition and the number of logic devices can be reduced. PMID:27834352

Multistate Memristive Tantalum Oxide Devices for Ternary Arithmetic.

PubMed

Kim, Wonjoo; Chattopadhyay, Anupam; Siemon, Anne; Linn, Eike; Waser, Rainer; Rana, Vikas

2016-11-11

Redox-based resistive switching random access memory (ReRAM) offers excellent properties to implement future non-volatile memory arrays. Recently, the capability of two-state ReRAMs to implement Boolean logic functionality gained wide interest. Here, we report on seven-states Tantalum Oxide Devices, which enable the realization of an intrinsic modular arithmetic using a ternary number system. Modular arithmetic, a fundamental system for operating on numbers within the limit of a modulus, is known to mathematicians since the days of Euclid and finds applications in diverse areas ranging from e-commerce to musical notations. We demonstrate that multistate devices not only reduce the storage area consumption drastically, but also enable novel in-memory operations, such as computing using high-radix number systems, which could not be implemented using two-state devices. The use of high radix number system reduces the computational complexity by reducing the number of needed digits. Thus the number of calculation operations in an addition and the number of logic devices can be reduced.

Multistate Memristive Tantalum Oxide Devices for Ternary Arithmetic

NASA Astrophysics Data System (ADS)

Kim, Wonjoo; Chattopadhyay, Anupam; Siemon, Anne; Linn, Eike; Waser, Rainer; Rana, Vikas

2016-11-01

Redox-based resistive switching random access memory (ReRAM) offers excellent properties to implement future non-volatile memory arrays. Recently, the capability of two-state ReRAMs to implement Boolean logic functionality gained wide interest. Here, we report on seven-states Tantalum Oxide Devices, which enable the realization of an intrinsic modular arithmetic using a ternary number system. Modular arithmetic, a fundamental system for operating on numbers within the limit of a modulus, is known to mathematicians since the days of Euclid and finds applications in diverse areas ranging from e-commerce to musical notations. We demonstrate that multistate devices not only reduce the storage area consumption drastically, but also enable novel in-memory operations, such as computing using high-radix number systems, which could not be implemented using two-state devices. The use of high radix number system reduces the computational complexity by reducing the number of needed digits. Thus the number of calculation operations in an addition and the number of logic devices can be reduced.

History of mathematics and history of science reunited?

PubMed

Gray, Jeremy

2011-09-01

For some years now, the history of modern mathematics and the history of modern science have developed independently. A step toward a reunification that would benefit both disciplines could come about through a revived appreciation of mathematical practice. Detailed studies of what mathematicians actually do, whether local or broadly based, have often led in recent work to examinations of the social, cultural, and national contexts, and more can be done. Another recent approach toward a historical understanding of the abstractness of modern mathematics has been to see it as a species of modernism, and this thesis will be tested by the raft of works on the history of modern applied mathematics currently under way.

Study of the neural dynamics for understanding communication in terms of complex hetero systems.

PubMed

Tsuda, Ichiro; Yamaguchi, Yoko; Hashimoto, Takashi; Okuda, Jiro; Kawasaki, Masahiro; Nagasaka, Yasuo

2015-01-01

The purpose of the research project was to establish a new research area named "neural information science for communication" by elucidating its neural mechanism. The research was performed in collaboration with applied mathematicians in complex-systems science and experimental researchers in neuroscience. The project included measurements of brain activity during communication with or without languages and analyses performed with the help of extended theories for dynamical systems and stochastic systems. The communication paradigm was extended to the interactions between human and human, human and animal, human and robot, human and materials, and even animal and animal. Copyright © 2014 Elsevier Ireland Ltd and the Japan Neuroscience Society. All rights reserved.

Methodologies for Optimum Capital Expenditure Decisions for New Medical Technology

PubMed Central

Landau, Thomas P.; Ledley, Robert S.

1980-01-01

This study deals with the development of a theory and an analytical model to support decisions regarding capital expenditures for complex new medical technology. Formal methodologies and quantitative techniques developed by applied mathematicians and management scientists can be used by health planners to develop cost-effective plans for the utilization of medical technology on a community or region-wide basis. In order to maximize the usefulness of the model, it was developed and tested against multiple technologies. The types of technologies studied include capital and labor-intensive technologies, technologies whose utilization rates vary with hospital occupancy rate, technologies whose use can be scheduled, and limited-use and large-use technologies.

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

Lewis, Jennifer

The Association for Women in Mathematics (AWM) seeks to advance the rates of participation by women in events at national mathematical sciences conference primarily in the U.S. The grant was funded from 8/1/2007 through 3/31/2015. The first component is the lecture series (Noether, Kovalevsky and Falconer Lectures) named after celebrated mathematicians, and featuring prominent women mathematicians, with the result that men, as well as women, will learn about the achievements of women in the mathematical sciences. 22 women mathematicians gave lectures at the annual JMM, SIAM Annual Meetings, and the MAA MathFest. The second component is AWM’s “Workshops for Womenmore » Graduate Students and Recent PhDs,” which select junior women to give research talks and research poster presentations at the SIAM Annual Meeting. The workshop activities allow wider recruitment of participants and increased attention to mentoring. 122 women gave mathematics research presentations. The third component is the AWM’s 40th Anniversary Research Symposium, 2011. 300 women and men attended the two-day symposium with 135 women presenting mathematics research. These activities have succeeded in increasing the number of women speakers and presenters at meetings and have brought more women attendees to the meetings.« less

Basic and Advanced Numerical Performances Relate to Mathematical Expertise but Are Fully Mediated by Visuospatial Skills

PubMed Central

2016-01-01

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. PMID:26913930

Surfing through Hyperspace - Understanding Higher Universes in Six Easy Lessons

NASA Astrophysics Data System (ADS)

Pickover, Clifford A.

1999-09-01

Do a little armchair time-travel, rub elbows with a four-dimensional intelligent life form, or stretch your mind to the furthest corner of an uncharted universe. With this astonishing guidebook, Surfing Through Hyperspace , you need not be a mathematician or an astrophysicist to explore the all-but-unfathomable concepts of hyperspace and higher-dimensional geometry.No subject in mathematics has intrigued both children and adults as much as the idea of a fourth dimension. Philosophers and parapsychologists have meditated on this mysterious space that no one can point to but may be all around us. Yet this extra dimension has a very real, practical value to mathematicians and physicists who use it every day in their calculations. In the tradtion of Flatland , and with an infectious enthusiasm, Clifford Pickover tackles the problems inherent in our 3-D brains trying to visualize a 4-D world, muses on the religious implications of the existence of higher-dimensional consciousness, and urges all curious readers to venture into "the unexplored territory lying beyond the prison of the obvious." Pickover alternates sections that explain the science of hyperspace with sections that dramatize mind-expanding concepts through a fictional dialogue between two futuristic FBI agents who dabble in the fourth dimension as a matter of national security. This highly accessible and entertaining approach turns an intimidating subject into a scientific game open to all dreamers.Surfing Through Hyperspace concludes with a number of puzzles, computer experiments and formulas for further exploration, inviting readers to extend their minds across this inexhaustibly intriguing scientific terrain.

Surfing through Hyperspace - Understanding Higher Universes in Six Easy Lessons

NASA Astrophysics Data System (ADS)

Pickover, Clifford A.

2001-05-01

Do a little armchair time-travel, rub elbows with a four-dimensional intelligent life form, or stretch your mind to the furthest corner of an uncharted universe. With this astonishing guidebook, Surfing Through Hyperspace , you need not be a mathematician or an astrophysicist to explore the all-but-unfathomable concepts of hyperspace and higher-dimensional geometry.No subject in mathematics has intrigued both children and adults as much as the idea of a fourth dimension. Philosophers and parapsychologists have meditated on this mysterious space that no one can point to but may be all around us. Yet this extra dimension has a very real, practical value to mathematicians and physicists who use it every day in their calculations. In the tradition of Flatland , and with an infectious enthusiasm, Clifford Pickover tackles the problems inherent in our 3-D brains trying to visualize a 4-D world, muses on the religious implications of the existence of higher-dimensional consciousness, and urges all curious readers to venture into "the unexplored territory lying beyond the prison of the obvious." Pickover alternates sections that explain the science of hyperspace with sections that dramatize mind-expanding concepts through a fictional dialogue between two futuristic FBI agents who dabble in the fourth dimension as a matter of national security. This highly accessible and entertaining approach turns an intimidating subject into a scientific game open to all dreamers.Surfing Through Hyperspace concludes with a number of puzzles, computer experiments and formulas for further exploration, inviting readers to extend their minds across this inexhaustibly intriguing scientific terrain.

Virtual Observatories, Data Mining, and Astroinformatics

NASA Astrophysics Data System (ADS)

Borne, Kirk

The historical, current, and future trends in knowledge discovery from data in astronomy are presented here. The story begins with a brief history of data gathering and data organization. A description of the development ofnew information science technologies for astronomical discovery is then presented. Among these are e-Science and the virtual observatory, with its data discovery, access, display, and integration protocols; astroinformatics and data mining for exploratory data analysis, information extraction, and knowledge discovery from distributed data collections; new sky surveys' databases, including rich multivariate observational parameter sets for large numbers of objects; and the emerging discipline of data-oriented astronomical research, called astroinformatics. Astroinformatics is described as the fourth paradigm of astronomical research, following the three traditional research methodologies: observation, theory, and computation/modeling. Astroinformatics research areas include machine learning, data mining, visualization, statistics, semantic science, and scientific data management.Each of these areas is now an active research discipline, with significantscience-enabling applications in astronomy. Research challenges and sample research scenarios are presented in these areas, in addition to sample algorithms for data-oriented research. These information science technologies enable scientific knowledge discovery from the increasingly large and complex data collections in astronomy. The education and training of the modern astronomy student must consequently include skill development in these areas, whose practitioners have traditionally been limited to applied mathematicians, computer scientists, and statisticians. Modern astronomical researchers must cross these traditional discipline boundaries, thereby borrowing the best of breed methodologies from multiple disciplines. In the era of large sky surveys and numerous large telescopes, the potential for astronomical discovery is equally large, and so the data-oriented research methods, algorithms, and techniques that are presented here will enable the greatest discovery potential from the ever-growing data and information resources in astronomy.

Purposive discovery of operations

NASA Technical Reports Server (NTRS)

Sims, Michael H.; Bresina, John L.

1992-01-01

The Generate, Prune & Prove (GPP) methodology for discovering definitions of mathematical operators is introduced. GPP is a task within the IL exploration discovery system. We developed GPP for use in the discovery of mathematical operators with a wider class of representations than was possible with the previous methods by Lenat and by Shen. GPP utilizes the purpose for which an operator is created to prune the possible definitions. The relevant search spaces are immense and there exists insufficient information for a complete evaluation of the purpose constraint, so it is necessary to perform a partial evaluation of the purpose (i.e., pruning) constraint. The constraint is first transformed so that it is operational with respect to the partial information, and then it is applied to examples in order to test the generated candidates for an operator's definition. In the GPP process, once a candidate definition survives this empirical prune, it is passed on to a theorem prover for formal verification. We describe the application of this methodology to the (re)discovery of the definition of multiplication for Conway numbers, a discovery which is difficult for human mathematicians. We successfully model this discovery process utilizing information which was reasonably available at the time of Conway's original discovery. As part of this discovery process, we reduce the size of the search space from a computationally intractable size to 3468 elements.

Multiple Scales in Fluid Dynamics and Meteorology: The DFG Priority Programme 1276 MetStröm

NASA Astrophysics Data System (ADS)

von Larcher, Th; Klein, R.

2012-04-01

Geophysical fluid motions are characterized by a very wide range of length and time scales, and by a rich collection of varying physical phenomena. The mathematical description of these motions reflects this multitude of scales and mechanisms in that it involves strong non-linearities and various scale-dependent singular limit regimes. Considerable progress has been made in recent years in the mathematical modelling and numerical simulation of such flows in detailed process studies, numerical weather forecasting, and climate research. One task of outstanding importance in this context has been and will remain for the foreseeable future the subgrid scale parameterization of the net effects of non-resolved processes that take place on spacio-temporal scales not resolvable even by the largest most recent supercomputers. Since the advent of numerical weather forecasting some 60 years ago, one simple but efficient means to achieve improved forecasting skills has been increased spacio-temporal resolution. This seems quite consistent with the concept of convergence of numerical methods in Applied Mathematics and Computational Fluid Dynamics (CFD) at a first glance. Yet, the very notion of increased resolution in atmosphere-ocean science is very different from the one used in Applied Mathematics: For the mathematician, increased resolution provides the benefit of getting closer to the ideal of a converged solution of some given partial differential equations. On the other hand, the atmosphere-ocean scientist would naturally refine the computational grid and adjust his mathematical model, such that it better represents the relevant physical processes that occur at smaller scales. This conceptual contradiction remains largely irrelevant as long as geophysical flow models operate with fixed computational grids and time steps and with subgrid scale parameterizations being optimized accordingly. The picture changes fundamentally when modern techniques from CFD involving spacio-temporal grid adaptivity get invoked in order to further improve the net efficiency in exploiting the given computational resources. In the setting of geophysical flow simulation one must then employ subgrid scale parameterizations that dynamically adapt to the changing grid sizes and time steps, implement ways to judiciously control and steer the newly available flexibility of resolution, and invent novel ways of quantifying the remaining errors. The DFG priority program MetStröm covers the expertise of Meteorology, Fluid Dynamics, and Applied Mathematics to develop model- as well as grid-adaptive numerical simulation concepts in multidisciplinary projects. The goal of this priority programme is to provide simulation models which combine scale-dependent (mathematical) descriptions of key physical processes with adaptive flow discretization schemes. Deterministic continuous approaches and discrete and/or stochastic closures and their possible interplay are taken into consideration. Research focuses on the theory and methodology of multiscale meteorological-fluid mechanics modelling. Accompanying reference experiments support model validation.

What are the ultimate limits to computational techniques: verifier theory and unverifiability

NASA Astrophysics Data System (ADS)

Yampolskiy, Roman V.

2017-09-01

Despite significant developments in proof theory, surprisingly little attention has been devoted to the concept of proof verifiers. In particular, the mathematical community may be interested in studying different types of proof verifiers (people, programs, oracles, communities, superintelligences) as mathematical objects. Such an effort could reveal their properties, their powers and limitations (particularly in human mathematicians), minimum and maximum complexity, as well as self-verification and self-reference issues. We propose an initial classification system for verifiers and provide some rudimentary analysis of solved and open problems in this important domain. Our main contribution is a formal introduction of the notion of unverifiability, for which the paper could serve as a general citation in domains of theorem proving, as well as software and AI verification.

Enabling the Discovery of Gravitational Radiation

NASA Astrophysics Data System (ADS)

Isaacson, Richard

2017-01-01

The discovery of gravitational radiation was announced with the publication of the results of a physics experiment involving over a thousand participants. This was preceded by a century of theoretical work, involving a similarly large group of physicists, mathematicians, and computer scientists. This huge effort was enabled by a substantial commitment of resources, both public and private, to develop the different strands of this complex research enterprise, and to build a community of scientists to carry it out. In the excitement following the discovery, the role of key enablers of this success has not always been adequately recognized in popular accounts. In this talk, I will try to call attention to a few of the key ingredients that proved crucial to enabling the successful discovery of gravitational waves, and the opening of a new field of science.

Mathematical Games

ERIC Educational Resources Information Center

Gardner, Martin

1978-01-01

Describes zoo creatures of interest to recreational mathematicians. Includes the geometrical symmetries of micro- and macroorganisms, topological studies, and imaginary creatures of scientific interest. (MA)

Basic and advanced numerical performances relate to mathematical expertise but are fully mediated by visuospatial skills.

PubMed

Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi

2016-09-01

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic number line task, which required mapping positive and negative numbers on a physical horizontal line, and has been shown to correlate with more advanced numerical abilities and mathematical achievement. We found that mathematicians were more accurate compared with nonmathematicians when mapping positive, but not negative numbers, which are considered numerical primitives and cultural artifacts, respectively. Moreover, performance on positive number mapping could predict whether one is a mathematician or not, and was mediated by more advanced mathematical skills. This finding might suggest a link between basic and advanced mathematical skills. However, when we included visuospatial skills, as measured by block design subtest, the mediation analysis revealed that the relation between the performance in the number line task and the group membership was explained by non-numerical visuospatial skills. These results demonstrate that relation between basic, even specific, numerical skills and advanced mathematical achievement can be artifactual and explained by visuospatial processing. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Searching the Heavens: Astronomy, Computation, Statistics, Data Mining and Philosophy

NASA Astrophysics Data System (ADS)

Glymour, Clark

2012-03-01

Our first and purest science, the mother of scientific methods, sustained by sheer curiosity, searching the heavens we cannot manipulate. From the beginning, astronomy has combined mathematical idealization, technological ingenuity, and indefatigable data collection with procedures to search through assembled data for the processes that govern the cosmos. Astronomers are, and ever have been, data miners, and for that reason astronomical methods (but not astronomical discoveries) have often been despised by statisticians and philosophers. Epithets laced the statistical literature: Ransacking! Data dredging! Double Counting! Statistical disdain was usually directed at social scientists and biologists, rarely if ever at astronomers, but the methodological attitudes and goals that many twentieth-century philosophers and statisticians rejected were creations of the astronomical tradition. The philosophical criticisms were earlier and more direct. In the shadow (or in Alexander Pope’s phrasing, the light) cast on nature in the eighteenth century by the Newtonian triumph, David Hume revived arguments from the ancient Greeks to challenge the very possibility of coming to know what causes what. His conclusion was endorsed in the twentieth century by many philosophers who found talk of causation unnecessary or unacceptably metaphysical, and absorbed by many statisticians as a general suspicion of causal claims, except possibly when they are founded on experimental manipulation. And yet in the hands of a mathematician, Thomas Bayes, and another mathematician and philosopher, Richard Price, Hume’s essays prompted the development of a new kind of statistics, the kind we now call "Bayesian." The computer and new data acquisition methods have begun to dissolve the antipathy between astronomy, philosophy, and statistics. But the resolution is practical, without much reflection on the arguments or the course of events. So, I offer a largely unoriginal history, substituting rather dry commentary on method for the fuller, livelier history of astronomers’ ambitions, politics, and passions. My accounts of various episodes in the astronomical tradition are taken from standard sources, especially Neugebauer (1952), Baum & Sheehan (1997), Crelensten (2006), and Stigler (1990). Methodological commentary is mine, not that of these sources.

Geochemistry of post-spreading lavas from fossil Mathematician and Galapagos spreading axes, revisited

NASA Astrophysics Data System (ADS)

Tian, L.; Castillo, P. R.; Hilton, D. R.

2010-12-01

The Mathematician Ridge, located west of the northern end of the EPR at about 10-20°N, 110°W, was abandoned during the Pliocene when the Pacific plate captured the Mathematician microplate. The Galapagos Rise, located east of the southern segment of the EPR at about 10-18°S, 95°W, ceased spreading after the Late Miocene capture of the Bauer microplate by the Nazca plate. Here we report new major and trace element and Sr, Nd and Pb isotope data for lavas dredged from seamounts and volcanic ridges along the crest of Mathematician Ridge [Batiza and Vanko, J. Petrol. 26, 1985] and from narrow volcanic ridges built along extinct segments of the Galapagos Rise [Batiza et al., Mar. Geol. 49, 1982]. These lavas consist predominantly of alkalic basalts and their differentiates, similar to the post-spreading alkalic lava series in other fossil spreading axes (e.g., Davidson Seamount, Guide Seamount, Socorro Island, and fossil spreading axes off Baja California Sur) and alkalic lavas from near-ridge seamounts in the eastern Pacific [Castillo et al., G3 11, 2010; Tian et al., sub. to G3]. Collectively, the alkalic lavas have higher incompatible trace element contents and highly/moderately incompatible trace element ratios (e.g., Ba/Zr >1.3, La/Sm >2.7 and Nb/Zr >0.14) than EPR basalts, and are similar to average alkalic OIB. They also have similar 87Sr/86Sr (0.7027 - 0.7037), 143Nd/144Nd (0.51289 - 0.51306) and 206Pb/204Pb (18.70 - 19.84) compositions, which overlap with geochemically enriched (E-) MORB and ~depleted OIB from major hotspot volcanic chains such as Galapagos, Hawaii and Iceland. The new data suggest that intraplate lavas from fossil spreading axes and non-hotspot seamounts in the eastern Pacific share a common enriched source which is geographically dispersed in the upper mantle.

Northern East Pacific Rise: Magnetic anomaly and bathymetric framework

USGS Publications Warehouse

Klitgord, Kim D.; Mammerickx, Jacqueline

1982-01-01

The oceanic crust in the eastern Pacific between 7°N and 30°N and east of 127°W contains a fairly complete history of the spreading centers associated with the East Pacific Rise since 25 m.y. B.P. (late Oligocene). In this paper, we have summarized the seafloor spreading magnetic-anomaly data and the bathymetric data that reflect the record of this tectonic history. The well-defined magnetic lineations north of the Clarion fracture zone, in the mouth of the Gulf of California, and on the east flank of the East Pacific Rise (EPR) are carefully examined and used to provide a guide for interpreting the spreading pattern between the Clarion and Clipperton fracture zones, southward of the Rivera fracture zone over the Mathematician Ridge, and over the entire EPR east of the Mathematician Ridge between the Rivera and Siqueiros fracture zones. The bathymetric data provide a trace of the fracture zone pattern in each of the above mentioned areas. The fracture zone bathymetry and the seafloor spreading magnetic lineations on the EPR south of the Rivera fracture zone have a distinctive fanning pattern caused by close poles of rotation and plate boundary reorganizations. All these data provide a good record of the plate reorganizations in the middle Miocene at magnetic anomaly 5 A time (12.5 to 11 m.y. B.P.), in the late Miocene at magnetic anomaly 3′−4 time (6.5 m.y. B.P.), and in the Pliocene at magnetic anomaly 2′−3 time (3.5 m.y. B.P.). Several abandoned spreading centers, including the Mathematician Ridge, were left behind as a result of these reorganizations. The Mathematician Ridge is shown to be a set of ridges and trough whose origin is related to the tectonic activity associated with each of the above mentioned reorganizations since anomaly 5A.

Linear Elastic Waves - Series: Cambridge Texts in Applied Mathematics (No. 26)

NASA Astrophysics Data System (ADS)

Harris, John G.

2001-10-01

Wave propagation and scattering are among the most fundamental processes that we use to comprehend the world around us. While these processes are often very complex, one way to begin to understand them is to study wave propagation in the linear approximation. This is a book describing such propagation using, as a context, the equations of elasticity. Two unifying themes are used. The first is that an understanding of plane wave interactions is fundamental to understanding more complex wave interactions. The second is that waves are best understood in an asymptotic approximation where they are free of the complications of their excitation and are governed primarily by their propagation environments. The topics covered include reflection, refraction, the propagation of interfacial waves, integral representations, radiation and diffraction, and propagation in closed and open waveguides. Linear Elastic Waves is an advanced level textbook directed at applied mathematicians, seismologists, and engineers. Aimed at beginning graduate students Includes examples and exercises Has application in a wide range of disciplines

The foundation: Mechanism, prediction, and falsification in Bayesian enactivism. Comment on "Answering Schrödinger's question: A free-energy formulation" by Maxwell James Désormeau Ramstead et al.

NASA Astrophysics Data System (ADS)

Allen, Micah

2018-03-01

In Isaac Asimov's science fiction classic, Foundation, fictional mathematician Hari Seldon applies his theory of psychohistory, a synthesis of psychology, history, and statistical physics, to predict that humanity will suffer a dark age lasting thirty millennia [1]. Although Seldon's psychohistory successfully predicts the future of human society, its basis in the physical law of mass action carries a limitation - it can only do so for sufficiently massive populations (i.e., billions of individuals), rendering it inert at an individual level. This limitation is of course a key source of dramatic tension in the series, in which the individual characters of Asimov's universe grapple with the challenges inherent to applying a lawlike theory of collective action to the constitutive individuals. To avert crisis, Seldon ultimately assembles the namesake Foundation, an interdisciplinary, intergalactic research centre bringing together various biological, physical, and social scientists who ultimately attempt to alter the predicted course of history.

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.

The analysis of crystallographic symmetry types in finite groups

NASA Astrophysics Data System (ADS)

Sani, Atikah Mohd; Sarmin, Nor Haniza; Adam, Nooraishikin; Zamri, Siti Norziahidayu Amzee

2014-06-01

Undeniably, it is human nature to prefer objects which are considered beautiful. Most consider beautiful as perfection, hence they try to create objects which are perfectly balance in shape and patterns. This creates a whole different kind of art, the kind that requires an object to be symmetrical. This leads to the study of symmetrical objects and pattern. Even mathematicians and ethnomathematicians are very interested with the essence of symmetry. One of these studies were conducted on the Malay traditional triaxial weaving culture. The patterns derived from this technique are symmetrical and this allows for further research. In this paper, the 17 symmetry types in a plane, known as the wallpaper groups, are studied and discussed. The wallpaper groups will then be applied to the triaxial patterns of food cover in Malaysia.

Mathematical Games

ERIC Educational Resources Information Center

Gardner, Martin

1978-01-01

Describes the life and work of Charles Peirce, U.S. mathematician and philosopher. His accomplishments include contributions to logic, the foundations of mathematics and scientific method, and decision theory and probability theory. (MA)

Heavenly Networks. Celestial Maps and Globes in Circulation between Artisans, Mathematicians, and Noblemen in Renaissance Europe.

PubMed

Gessner, Samuel

2015-01-01

The aim of this paper is to examine the iconography on a set of star charts by Albrecht Dürer (1515), and celestial globes by Caspar Vopel (1536) and Christoph Schissler (1575). The iconography on these instruments is conditioned by strong traditions which include not only the imagery on globes and planispheres (star charts), but also ancient literature about the constellations. Where this iconography departs from those traditions, the change had to do with humanism in the sixteenth century. This "humanistic" dimension is interwoven with other concerns that involve both "social" and "technical" motivations. The interplay of these three dimensions illustrates how the iconography on celestial charts and globes expresses some features of the shared knowledge and shared culture between artisans, mathematicians, and nobles in Renaissance Europe.

T198. A SCHIZOPHRENIA-LIKE BIRTH SEASONALITY AMONG MATHEMATICIANS AND AN OPPOSITE SEASONALITY AMONG BIOLOGISTS: MORE EVIDENCE IMPLICATING BIMODAL RHYTHMS OF GENERAL BIRTHS

PubMed Central

Marzullo, Giovanni

2018-01-01

Abstract Background Based on early-20th century births, a pre-electric illumination time of comparatively normal human exposure to sunlight, studies of schizophrenia (SCZ) found a birth seasonality with two opposite effects: a SCZ-liability peak among subjects born around late-February and an equally significant SCZ-resistance peak among those born six months later, around late-August. We previously investigated this rhythm in connection with a sunlight-dependent bimodal rhythm of general births that, prior to the full advent of electric lighting (but not later), occurred ubiquitously in non-equatorial parts of the world. We found that the SCZ-liability peak coincided with a first, Feb-Mar peak of general-population births (the GP1) while the SCZ-resistance peak coincided with a second, Aug-Sep peak of those births (the GP2). Moreover, in a study of hand and visual-field preferences among professional baseball players, we found the SCZ-liability, GP1-coincident seasonality among players with preferences denoting cerebral asymmetry “deficits” (CADs) and the SCZ-resistance, GP2-coincident seasonality among those with preferences denoting cerebral asymmetry “excesses.” Also, in a study suggested by associations of CADs with artistic abilities, we found the SCZ-liability, GP1-coincident seasonality among groups representing visual, performing and literary art “creators” (VPL-Artists) and the SCZ-resistance, GP2-coincident seasonality among groups representing art critics, historians, curators and other art “observers” (Para-Artists). Together, these findings suggested, as one possibility (but see later), that the SCZ-liability, CAD effects and artistic abilities could all three represent traits genetically or otherwise selected into the GP1 excess population of newborns and out of the GP2 population. The present study of “scientists” was initially aimed at the purported arts/science antithesis. Methods Birth seasonalities were examined among early-20th century born American scientists and among yet earlier European biologists and mathematicians. Results A group representing 1,925 American scientists showed the SCZ-resistance, GP2-coincident seasonality. However, this effect proved to be mostly due to biologists because biochemists, chemists, and physicists showed gradually less seasonality while mathematicians suggested an altogether artist-like, GP1-coincident seasonality. This intimation of a biologist-mathematician antithesis was pursued with an investigation of most major figures in the history of the two sciences from the 15th to the early-20th century. The two groups, numbering 576 mathematicians and 787 biologists, shared the same mean decade of birth, the 1780s, and essentially the same geographic origin in Western Europe. The mathematicians showed a very significant SCZ liability-like, GP1-coincident seasonality while the biologists showed an even more significant SCZ resistance-like, GP2-coincident seasonality. The latter effect was particularly strong among naturalists, anatomists and other groups representing biological “observationalism” as opposed to “experimentalism.” Discussion The findings are discussed in light of a) new evidence that the annual photoperiod is indeed alone responsible for both peaks of general births, with the GP1 and the GP2 being caused by maternal periconceptional exposure to, respectively, the summer-solstice sunlight maximum and the winter-solstice minimum, and b) an approach/withdrawal theory of lateralization of basic emotions where the left cerebral cortex would handle external stimuli eliciting complacent emotions towards external realities while the right cortex would handle internal stimuli eliciting disdain for those realities.

What Are the Odds?

ERIC Educational Resources Information Center

Beam, John

2012-01-01

Students and mathematicians alike have long struggled to understand the nature of probability. This article explores the use of gambling activities as a basis for defining probabilities. (Contains 1 table and 1 figure.)

A Look at Infinite Series

ERIC Educational Resources Information Center

Basor, Estelle

1978-01-01

Sums for divergent series that were seriously considered by eighteenth century mathematicians are shown to have reappeared as result of new interpretations for divergent series that make these previous conclusions valid. (MN)

Attractors of equations of non-Newtonian fluid dynamics

NASA Astrophysics Data System (ADS)

Zvyagin, V. G.; Kondrat'ev, S. K.

2014-10-01

This survey describes a version of the trajectory-attractor method, which is applied to study the limit asymptotic behaviour of solutions of equations of non-Newtonian fluid dynamics. The trajectory-attractor method emerged in papers of the Russian mathematicians Vishik and Chepyzhov and the American mathematician Sell under the condition that the corresponding trajectory spaces be invariant under the translation semigroup. The need for such an approach was caused by the fact that for many equations of mathematical physics for which the Cauchy initial-value problem has a global (weak) solution with respect to the time, the uniqueness of such a solution has either not been established or does not hold. In particular, this is the case for equations of fluid dynamics. At the same time, trajectory spaces invariant under the translation semigroup could not be constructed for many equations of non-Newtonian fluid dynamics. In this connection, a different approach to the construction of trajectory attractors for dissipative systems was proposed in papers of Zvyagin and Vorotnikov without using invariance of trajectory spaces under the translation semigroup and is based on the topological lemma of Shura-Bura. This paper presents examples of equations of non-Newtonian fluid dynamics (the Jeffreys system describing movement of the Earth's crust, the model of motion of weak aqueous solutions of polymers, a system with memory) for which the aforementioned construction is used to prove the existence of attractors in both the autonomous and the non-autonomous cases. At the beginning of the paper there is also a brief exposition of the results of Ladyzhenskaya on the existence of attractors of the two-dimensional Navier-Stokes system and the result of Vishik and Chepyzhov for the case of attractors of the three-dimensional Navier-Stokes system. Bibliography: 34 titles.

The trials, tribulations, and triumphs of black faculty in the math and science pipeline: A life history approach

NASA Astrophysics Data System (ADS)

Williams, Lisa D.

2000-12-01

This study explores the career progression and life history of black mathematicians and scientists who teach on university faculties in the United States. It investigates the following questions: Why are there so few black mathematicians and scientists in colleges and universities in the United States? What is the experience of black students who express an interest in science and math? What barriers do black scientists and mathematicians face as they move through school towards their career in higher education? What factors facilitate their success? The current literature shows that there are few women and minorities teaching or working in math and science compared to white men, although reasons for this underrepresentation are still not well understood. I explored this phenomenon by conducting two sets of in-depth interviews with twelve black faculty, six women, six men, from both historically black and predominantly white higher educational institutions in the United States. My interviews were based upon a life history approach that identified the participants' perceptions of the barriers and obstacles, as well as the supports and facilitators encountered in their schooling and career progression. The findings from the study show the importance of a strong family, community, and teacher support for the participants throughout their schooling. Support systems continued to be important in their faculty positions. These support systems include extended family members, teachers, community members, supervisors, and classmates, who serve as role models and mentors. The life study interviews provide striking evidence of the discrimination, isolation, and harassment due to race and gender experienced by black male and female mathematicians and scientists. The racial discrimination and the compounding effect of racism and sexism play out differently for the male and female participants in this study. This study suggests directions for future research on the experiences of young black students who are currently in the math and science educational pipeline. It also offers recommendations for ways in which parents, teachers, administrators, faculty, advisors, and government officials can enhance the educational experiences of black students who express interest and have skills in math and science.

Le contenu astronomique des Sphériques de Ménélaos

NASA Astrophysics Data System (ADS)

Nadal, Robert; Taha, Abdelkaddous; Pinel, Pierre

2004-07-01

The Spherics were written by Menelaos in the form of a purely mathematical treatise. However, the material developed in the second and third book is closely linked to problems met in astronomy: computation of equatorial coordinates of the Sun, setting up of rising-time tables, study of the motion of the Sun in the sphaera obliqua, simultaneous risings. This link, which remains implicit in the text, was clearly displayed by two arabo-islamic mathematicians and astronomers, who expounded the astronomical meaning of some theorems of the Spherics. We describe, comment and complement their explanations, by classifying the implications of the theorems in three groups: direction of variation of some quantities on the sphere, spherical trigonometry and applications, direction of variation of ratios of some quantities on the sphere. An erratum to this article can be found at http://dx.doi.org/10.1007/s00407-004-0084-7

Correction to "What is a fractional derivative?" by Ortigueira and Machado [Journal of Computational Physics, Volume 293, 15 July 2015, Pages 4-13. Special issue on Fractional PDEs

NASA Astrophysics Data System (ADS)

Katugampola, Udita N.

2016-09-01

There is a debate among contemporary mathematicians about what it really means by a fractional derivative. The question arose as a consequence of introducing a 'new' definition of a fractional derivative in [1]. In a reply, Ortigueira and Machado [2] came up with several very important criteria to determine whether a given derivative is a fractional derivative. According to their criterion, the new fractional derivative, called conformable fractional derivative, introduced by Khalil et al. [1] turns out not to be a fractional derivative, but rather a controlled or conformable derivative. In proving the claim the authors in [2] use an example [2, p. 6]. It turns out that the explanation given there needs some corrections and it is the sole purpose of this note.

Quantum Information: an invitation for mathematicians

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

Perez-Garcia, David

2009-05-06

Quantum Information is the science that aims to use the unusual behavior of the microscopic world, governed by the laws of Quantum Mechanics, in order to improve the way in which we compute or communicate information. Though the first ideas in this direction come from the early 80's, it is in the last decade when Quantum Information has suffered an spectacular development. It is impossible to resume in a paper like this one the importance and complexity of the field. Therefore, I will limit to briefly explain some of the initial ideas (considered classical by now), and to briefly suggestmore » some of the modern lines of research. By the nature of this exposition, I have decided to avoid rigor and to concentrate more in ideas and intuitions. Anyhow, I have tried to provide with enough references, in such a way that an interested reader could find there proper theorems and proofs.« less

Biological insight, high-throughput datasets and the nature of neuro-degenerative disorders.

PubMed

Valente, André X C N; Oliveira, Paulo J; Khaiboullina, Svetlana F; Palotás, András; Rizvanov, Albert A

2013-09-01

Life sciences are experiencing a historical shift towards a quantitative, data-rich regime. This transition has been associated with the advent of bio-informatics: mathematicians, physicists, computer scientists and statisticians are now commonplace in the field, working on the analysis of ever larger data-sets. An open question regarding what should drive scientific progress in this new era remains: will biological insight become increasingly irrelevant in a world of hypothesis-free, unbiased data analysis? This piece offers a different perspective, pin-pointing that biological thought is more-than-ever relevant in a data-rich setting. Some of the novel highthroughput information being acquired in the field of neuro-degenerative disorders is highlighted here. As but one example of how theory and experiment can interact in this new reality, our efforts in developing an idiopathic neuro-degenerative disease hematopoietic stemcell ageing theory are described.

A Visit from Pythagoras--Using Costumes in the Classroom.

ERIC Educational Resources Information Center

Shirley, Lawrence H.

2000-01-01

Presents ways of making mathematics come alive for students including inviting historical mathematicians into the classroom. Suggests that costumes and drama add special appeal to looking at the history of mathematics. (KHR)

Relativistic Theory of Gheorghe Zapan for Psychical Phenoma

NASA Astrophysics Data System (ADS)

Sofonea, Liviu

A biography and an account of main scientific research of a Psychologist, Mathematician, Cybernetician, Teacher, Army officer, Lawyer Gheorghe Zapan (1891-1976) and of his relation with Special and General Relativity is given.

Some remarks on the genesis of scalar-tensor theories

NASA Astrophysics Data System (ADS)

Goenner, Hubert

2012-08-01

Between 1941 and 1962, scalar-tensor theories of gravitation were suggested four times by different scientists in four different countries. The earliest originator, the Swiss mathematician W. Scherrer, was virtually unknown until now whereas the chronologically latest pair gave their names to a multitude of publications on Brans-Dicke theory. P. Jordan, one of the pioneers of quantum mechanics and quantum field theory, and Y. Thiry, known by his book on celestial mechanics, a student of the mathematician Lichnerowicz, complete the quartet. Diverse motivations for and conceptual interpretations of their theories will be discussed as well as relations among them. Also, external factors like language, citation habits, or closeness to the mainstream are considered. It will become clear why Brans-Dicke theory, although structurally a déjà-vu, superseded all the other approaches.

A multidimensional approach to training mathematics students at a university: improving the efficiency through the unity of social, psychological and pedagogical aspects

NASA Astrophysics Data System (ADS)

Kuznetsova, Elena; Matytcina, Marina

2018-04-01

The article deals with social, psychological and pedagogical aspects of teaching mathematics students at universities. The sociological portrait and the factors influencing a career choice of a mathematician have been investigated through the survey results of 198 first-year students of applied mathematics major at 27 state universities (Russia). Then, psychological characteristics of mathematics students have been examined based on scientific publications. The obtained results have allowed us to reveal pedagogical conditions and specific ways of training mathematics students in the process of their education at university. The article also contains the analysis of approaches to the development of mathematics education both in Russia and in other countries. The results may be useful for teaching students whose training requires in-depth knowledge of mathematics.

How Many Spots Does a Cheetah Have?

ERIC Educational Resources Information Center

Reed, Kristine M.

2000-01-01

Describes first grade students' mathematical investigation of the number of spots on a cheetah. The exploration of counting and estimation strategies that grew from the investigation gives evidence that mathematicians come in all ages. (ASK)

Reiche, Maria (1903-98)

NASA Astrophysics Data System (ADS)

Murdin, P.

2000-11-01

German mathematician and archaeologist, born Dresden, fled the Nazi regime to Peru, identified and researched the huge figures of Nazca drawn in the desert and revealed the knowledge of astronomy of the ancient inhabitants of Peru's coastal region....

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

A historical survey of algorithms and hardware architectures for neural-inspired and neuromorphic computing applications

DOE PAGES

James, Conrad D.; Aimone, James B.; Miner, Nadine E.; ...

2017-01-04

In this study, biological neural networks continue to inspire new developments in algorithms and microelectronic hardware to solve challenging data processing and classification problems. Here in this research, we survey the history of neural-inspired and neuromorphic computing in order to examine the complex and intertwined trajectories of the mathematical theory and hardware developed in this field. Early research focused on adapting existing hardware to emulate the pattern recognition capabilities of living organisms. Contributions from psychologists, mathematicians, engineers, neuroscientists, and other professions were crucial to maturing the field from narrowly-tailored demonstrations to more generalizable systems capable of addressing difficult problem classesmore » such as object detection and speech recognition. Algorithms that leverage fundamental principles found in neuroscience such as hierarchical structure, temporal integration, and robustness to error have been developed, and some of these approaches are achieving world-leading performance on particular data classification tasks. Additionally, novel microelectronic hardware is being developed to perform logic and to serve as memory in neuromorphic computing systems with optimized system integration and improved energy efficiency. Key to such advancements was the incorporation of new discoveries in neuroscience research, the transition away from strict structural replication and towards the functional replication of neural systems, and the use of mathematical theory frameworks to guide algorithm and hardware developments.« less

A historical survey of algorithms and hardware architectures for neural-inspired and neuromorphic computing applications

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

James, Conrad D.; Aimone, James B.; Miner, Nadine E.

In this study, biological neural networks continue to inspire new developments in algorithms and microelectronic hardware to solve challenging data processing and classification problems. Here in this research, we survey the history of neural-inspired and neuromorphic computing in order to examine the complex and intertwined trajectories of the mathematical theory and hardware developed in this field. Early research focused on adapting existing hardware to emulate the pattern recognition capabilities of living organisms. Contributions from psychologists, mathematicians, engineers, neuroscientists, and other professions were crucial to maturing the field from narrowly-tailored demonstrations to more generalizable systems capable of addressing difficult problem classesmore » such as object detection and speech recognition. Algorithms that leverage fundamental principles found in neuroscience such as hierarchical structure, temporal integration, and robustness to error have been developed, and some of these approaches are achieving world-leading performance on particular data classification tasks. Additionally, novel microelectronic hardware is being developed to perform logic and to serve as memory in neuromorphic computing systems with optimized system integration and improved energy efficiency. Key to such advancements was the incorporation of new discoveries in neuroscience research, the transition away from strict structural replication and towards the functional replication of neural systems, and the use of mathematical theory frameworks to guide algorithm and hardware developments.« less

Mantle Convection on Modern Supercomputers

NASA Astrophysics Data System (ADS)

Weismüller, J.; Gmeiner, B.; Huber, M.; John, L.; Mohr, M.; Rüde, U.; Wohlmuth, B.; Bunge, H. P.

2015-12-01

Mantle convection is the cause for plate tectonics, the formation of mountains and oceans, and the main driving mechanism behind earthquakes. The convection process is modeled by a system of partial differential equations describing the conservation of mass, momentum and energy. Characteristic to mantle flow is the vast disparity of length scales from global to microscopic, turning mantle convection simulations into a challenging application for high-performance computing. As system size and technical complexity of the simulations continue to increase, design and implementation of simulation models for next generation large-scale architectures is handled successfully only in an interdisciplinary context. A new priority program - named SPPEXA - by the German Research Foundation (DFG) addresses this issue, and brings together computer scientists, mathematicians and application scientists around grand challenges in HPC. Here we report from the TERRA-NEO project, which is part of the high visibility SPPEXA program, and a joint effort of four research groups. TERRA-NEO develops algorithms for future HPC infrastructures, focusing on high computational efficiency and resilience in next generation mantle convection models. We present software that can resolve the Earth's mantle with up to 1012 grid points and scales efficiently to massively parallel hardware with more than 50,000 processors. We use our simulations to explore the dynamic regime of mantle convection and assess the impact of small scale processes on global mantle flow.

Mighty Mathematicians: Using Problem Posing and Problem Solving to Develop Mathematical Power

ERIC Educational Resources Information Center

McGatha, Maggie B.; Sheffield, Linda J.

2006-01-01

This article describes a year-long professional development institute combined with a summer camp for students. Both were designed to help teachers and students develop their problem-solving and problem-posing abilities.

Math Roots: The Beginnings of the Metric System

ERIC Educational Resources Information Center

Johnson, Art; Norris, Kit; Adams,Thomasina Lott, Ed.

2007-01-01

This article reviews the history of the metric system, from a proposal of a sixteenth-century mathematician to its implementation in Revolutionary France some 200 years later. Recent developments in the metric system are also discussed.

New Forms of Stolz-Cesaro Lemma

ERIC Educational Resources Information Center

Mortici, Cristinel

2011-01-01

The well-known Stolz-Cesaro lemma is due to the mathematicians Ernesto Cesaro (1859-1906) and Otto Stolz (1842-1905). The aim of this article is to give new forms of Stolz-Cesaro lemma involving the limit [image omitted].

Theano: The World's First Female Mathematician?

ERIC Educational Resources Information Center

Deakin, Michael A. B.

2013-01-01

Theano, an associate, most likely the wife, of Pythagoras, has some claim to be the first woman to play an active role in mathematics. The question of how far this claim can be supported is here examined.

Reflections on the Notion of Culture in the History of Mathematics: The Example of "Geometrical Equations".

PubMed

Lê, François

2016-09-01

Argument This paper challenges the use of the notion of "culture" to describe a particular organization of mathematical knowledge, shared by a few mathematicians over a short period of time in the second half of the nineteenth century. This knowledge relates to "geometrical equations," objects that proved crucial for the mechanisms of encounters between equation theory, substitution theory, and geometry at that time, although they were not well-defined mathematical objects. The description of the mathematical collective activities linked to "geometrical equations," and especially the technical aspects of these activities, is made on the basis of a sociological definition of "culture." More precisely, after an examination of the social organization of the group of mathematicians, I argue that these activities form an intricate system of patterns, symbols, and values, for which I suggest a characterization as a "cultural system."

The life-cycle research productivity of mathematicians and scientists.

PubMed

Diamond, A M

1986-07-01

Declining research productivity with age is implied by economic models of life-cycle human capital investment but is denied by some recent empirical studies. The purpose of the present study is to provide new evidence on whether a scientist's output generally declines with advancing age. A longitudinal data set has been compiled for scientists and mathematicians at six major departments, including data on age, salaries, annual citations (stock of human capital), citations to current output (flow of human capital), and quantity of current output measured both in number of articles and in number of pages. Analysis of the data indicates that salaries peak from the early to mid-60s, whereas annual citations appear to peak from age 39 to 89 for different departments with a mean age of 59 for the 6 departments. The quantity and quality of current research output appear to decline continuously with age.

Jean Baptiste Joseph Fourier

NASA Astrophysics Data System (ADS)

Sterken, C.

2003-03-01

This paper gives a short account of some key elements in the life of Jean Baptiste Joseph Fourier (1768-1830), specifically his relation to Napoleon Bonaparte. The mathematical approach to Fourier series and the original scepticism by French mathematicians are briefly illustrated.

3 CFR 8918 - Proclamation 8918 of December 17, 2012. Wright Brothers Day, 2012

Code of Federal Regulations, 2013 CFR

2013-01-01

... their lifelong dream. Like so many Americans before and after them, these two men achieved the... mother, Susan—a gifted mathematician in her own right who challenged her children to think big and dream...

The Relationship Between Mathematics and Physics at Pre-O-Level Stage

ERIC Educational Resources Information Center

Education in Science, 1976

1976-01-01

Presented are recommendations of English mathematicians and physicists for ensuring that there is an optimum match in the math/physics interface in secondary schools. Recommendations stress the need for increased cooperation between the disciplines. (SL)

Preface: Current perspectives in modelling, monitoring, and predicting geophysical fluid dynamics

NASA Astrophysics Data System (ADS)

Mancho, Ana M.; Hernández-García, Emilio; López, Cristóbal; Turiel, Antonio; Wiggins, Stephen; Pérez-Muñuzuri, Vicente

2018-02-01

The third edition of the international workshop Nonlinear Processes in Oceanic and Atmospheric Flows was held at the Institute of Mathematical Sciences (ICMAT) in Madrid from 6 to 8 July 2016. The event gathered oceanographers, atmospheric scientists, physicists, and applied mathematicians sharing a common interest in the nonlinear dynamics of geophysical fluid flows. The philosophy of this meeting was to bring together researchers from a variety of backgrounds into an environment that favoured a vigorous discussion of concepts across different disciplines. The present Special Issue on Current perspectives in modelling, monitoring, and predicting geophysical fluid dynamics contains selected contributions, mainly from attendants of the workshop, providing an updated perspective on modelling aspects of geophysical flows as well as issues on prediction and assimilation of observational data and novel tools for describing transport and mixing processes in these contexts. More details on these aspects are discussed in this preface.

A comparison of LMC and SDL complexity measures on binomial distributions

NASA Astrophysics Data System (ADS)

Piqueira, José Roberto C.

2016-02-01

The concept of complexity has been widely discussed in the last forty years, with a lot of thinking contributions coming from all areas of the human knowledge, including Philosophy, Linguistics, History, Biology, Physics, Chemistry and many others, with mathematicians trying to give a rigorous view of it. In this sense, thermodynamics meets information theory and, by using the entropy definition, López-Ruiz, Mancini and Calbet proposed a definition for complexity that is referred as LMC measure. Shiner, Davison and Landsberg, by slightly changing the LMC definition, proposed the SDL measure and the both, LMC and SDL, are satisfactory to measure complexity for a lot of problems. Here, SDL and LMC measures are applied to the case of a binomial probability distribution, trying to clarify how the length of the data set implies complexity and how the success probability of the repeated trials determines how complex the whole set is.

The invention of atmosphere.

PubMed

Martin, Craig

2015-08-01

The word "atmosphere" was a neologism Willebrord Snellius created for his Latin translation of Simon Stevin's cosmographical writings. Astronomers and mathematical practitioners, such as Snellius and Christoph Scheiner, applying the techniques of Ibn Mu'ādh and Witelo, were the first to use the term in their calculations of the height of vapors that cause twilight. Their understandings of the atmosphere diverged from Aristotelian divisions of the aerial region. From the early years of the seventeenth century, the term was often associated with atomism or corpuscular matter theory. The concept of the atmosphere changed dramatically with the advent of pneumatic experiments in the middle of the seventeenth century. Pierre Gassendi, Walter Charleton, and Robert Boyle transformed the atmosphere of the mathematicians giving it the characteristics of weight, specific gravity, and fluidity, while disputes about its extent and border remained unresolved. Copyright © 2015 Elsevier Ltd. All rights reserved.

Mechanoregulation of molecular motors in flagella

NASA Astrophysics Data System (ADS)

Gadelha, Hermes

2014-11-01

Molecular motors are nano-biological machines responsible for exerting forces that drive movement in living organisms, from cargo transport to cell division and motility. Interestingly, despite the inherent complexity of many interacting motors, order and structure may arise naturally, as exemplified by the harmonic, self-organized undulatory motion of the flagellum. The real mechanisms behind this collective spontaneous oscillation are still unknown, and it is challenging task to measure experimentally the molecular motor dynamics within the flagellar structure in real time. In this talk we will explore different competing hypotheses that are capable of generating flagellar bending waves that ``resemble'' in-vitro observations, emphasizing the need for further mathematical analysis and model validation. It also highlight that this is a fertile and challenging area of inter-disciplinary research for applied mathematicians and demonstrates the importance of future observational and theoretical studies in understanding the underlying mechanics of these motile cell appendages.

Regularization of the double period method for experimental data processing

NASA Astrophysics Data System (ADS)

Belov, A. A.; Kalitkin, N. N.

2017-11-01

In physical and technical applications, an important task is to process experimental curves measured with large errors. Such problems are solved by applying regularization methods, in which success depends on the mathematician's intuition. We propose an approximation based on the double period method developed for smooth nonperiodic functions. Tikhonov's stabilizer with a squared second derivative is used for regularization. As a result, the spurious oscillations are suppressed and the shape of an experimental curve is accurately represented. This approach offers a universal strategy for solving a broad class of problems. The method is illustrated by approximating cross sections of nuclear reactions important for controlled thermonuclear fusion. Tables recommended as reference data are obtained. These results are used to calculate the reaction rates, which are approximated in a way convenient for gasdynamic codes. These approximations are superior to previously known formulas in the covered temperature range and accuracy.

On the definition of the time evolution operator for time-independent Hamiltonians in non-relativistic quantum mechanics

NASA Astrophysics Data System (ADS)

Amaku, Marcos; Coutinho, Francisco A. B.; Masafumi Toyama, F.

2017-09-01

The usual definition of the time evolution operator e-i H t /ℏ=∑n=0∞1/n ! (-i/ℏHt ) n , where H is the Hamiltonian of the system, as given in almost every book on quantum mechanics, causes problems in some situations. The operators that appear in quantum mechanics are either bounded or unbounded. Unbounded operators are not defined for all the vectors (wave functions) of the Hilbert space of the system; when applied to some states, they give a non-normalizable state. Therefore, if H is an unbounded operator, the definition in terms of the power series expansion does not make sense because it may diverge or result in a non-normalizable wave function. In this article, we explain why this is so and suggest, as an alternative, another definition used by mathematicians.

Bridging different perspectives of the physiological and mathematical disciplines.

PubMed

Batzel, Jerry Joseph; Hinghofer-Szalkay, Helmut; Kappel, Franz; Schneditz, Daniel; Kenner, Thomas; Goswami, Nandu

2012-12-01

The goal of this report is to discuss educational approaches for bridging the different perspectives of the physiological and mathematical disciplines. These approaches can enhance the learning experience for physiology, medical, and mathematics students and simultaneously act to stimulate mathematical/physiological/clinical interdisciplinary research. While physiology education incorporates mathematics, via equations and formulas, it does not typically provide a foundation for interdisciplinary research linking mathematics and physiology. Here, we provide insights and ideas derived from interdisciplinary seminars involving mathematicians and physiologists that have been conducted over the last decade. The approaches described here can be used as templates for giving physiology and medical students insights into how sophisticated tools from mathematics can be applied and how the disciplines of mathematics and physiology can be integrated in research, thereby fostering a foundation for interdisciplinary collaboration. These templates are equally applicable to linking mathematical methods with other life and health sciences in the educational process.

An Informal History of Formal Proofs: From Vigor to Rigor?

ERIC Educational Resources Information Center

Galda, Klaus

1981-01-01

The history of formal mathematical proofs is sketched out, starting with the Greeks. Included in this document is a chronological guide to mathematics and the world, highlighting major events in the world and important mathematicians in corresponding times. (MP)

Collaborative Understanding of Cyanobacteria in Lake Ecosystems

ERIC Educational Resources Information Center

Greer, Meredith L.; Ewing, Holly A.; Cottingham, Kathryn L.; Weathers, Kathleen C.

2013-01-01

We describe a collaboration between mathematicians and ecologists studying the cyanobacterium "Gloeotrichia echinulata" and its possible role in eutrophication of New England lakes. The mathematics includes compartmental modeling, differential equations, difference equations, and testing models against high-frequency data. The ecology…

Potpourri.

ERIC Educational Resources Information Center

Orlans, Harold

1997-01-01

Offers notes and anecdotes concerning an article on the "New York Times Book Review," marginally useful research, Denis Diderot and politics, peer review of journal articles, loss of valuable literary criticism manuscripts, social sciences education, great mathematician Paul Erdos, quality of political judgment, and creation education.…

Visualization in Science and the Arts.

ERIC Educational Resources Information Center

Roth, Susan King

Visualization as a factor of intelligence includes the mental manipulation of spatial configurations and has been associated with spatial abilities, creative thinking, and conceptual problem solving. There are numerous reports of scientists and mathematicians using visualization to anticipate transformation of the external world. Artists and…

"Ex Ovo Omnia"

ERIC Educational Resources Information Center

Pagano, Todd

2012-01-01

One of history's most diverse thinkers metaphorically depicted humanity's dangerous reliance on nonrenewable energy resources as an unborn chick in an egg. American philosopher, poet, scientist, and mathematician, Buckminster Fuller, described the nutrients in an egg as the temporary and extinguishable support required for the development of an…

Supporting Assessment in Undergraduate Mathematics

ERIC Educational Resources Information Center

Steen, Lynn Arthur, Ed.

2006-01-01

This publication contains 29 case studies offering lessons learned during a four year NSF-supported MAA project designed to support mathematicians and mathematics departments in the increasingly important challenge of assessing student learning. Three introductory essays set assessment in broader academic and national contexts; an appendix…

Designing Opportunities to Learn Mathematics Theory-Building Practices

ERIC Educational Resources Information Center

Bass, Hyman

2017-01-01

Mathematicians commonly distinguish two modes of work in the discipline: "Problem solving," and "theory building." Mathematics education offers many opportunities to learn problem solving. This paper explores the possibility, and value, of designing instructional activities that provide supported opportunities for students to…

Rainforest Mathematics

ERIC Educational Resources Information Center

Kilpatrick, Jeremy

2014-01-01

This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…

Learning at the Boundaries

ERIC Educational Resources Information Center

Goos, Merrilyn

2015-01-01

This paper reports on a project that aims to foster interdisciplinary collaboration between mathematicians and mathematics educators in pre-service teacher education. The project involves 23 investigators from six universities. Interviews were conducted with selected project participants to identify conditions that enable or hinder collaboration,…

Augustus De Morgan behind the Scenes

ERIC Educational Resources Information Center

Simmons, Charlotte

2011-01-01

Augustus De Morgan's support was crucial to the achievements of the four mathematicians whose work is considered greater than his own. This article explores the contributions he made to mathematics from behind the scenes by supporting the work of Hamilton, Boole, Gompertz, and Ramchundra.

What Are You Assuming?

ERIC Educational Resources Information Center

Kennedy, Nadia Stoyanova

2012-01-01

Students are often encouraged to work on problems "like mathematicians"--to be persistent, to investigate different approaches, and to evaluate solutions. This behavior, regarded as problem solving, is an essential component of mathematical practice. Some crucial aspects of problem solving include defining and interpreting problems, working with…

Bowditch, Nathaniel (1773-1838)

NASA Astrophysics Data System (ADS)

Murdin, P.

2000-11-01

Insurance actuary, astronomer, mathematician, born in Salem, MA. Self-taught, by age 15 he had compiled an astronomical almanac. Based on practical experience at sea, he wrote the New American Practical Navigator; published papers on comets and meteors, and translated PIERRE LAPLACE's Mécanique Céleste....

The Astronomy Genealogy Project

NASA Astrophysics Data System (ADS)

Tenn, Joseph S.

2014-01-01

The Astronomy Genealogy Project, to be known as AstroGen, will list as many as possible of the world's astronomers with their academic parents (aka thesis advisors) and enable the reader to trace both academic ancestors and descendants. It will be very similar to the highly successful Mathematics Genealogy Project (MGP), available at http://genealogy.math.ndsu.nodak.edu. The MGP, which has been in operation since 1996, now contains the names of about 170,000 "mathematicians." These include many physicists and astronomers, as well as practitioners of related sciences. Mitchel Keller, the director of the MGP, has generously shared the software used in that project, and the American Astronomical Society (AAS) will host AstroGen, a project of the Historical Astronomy Division, on its website. We expect to start seeking entries soon, depending on the availability of computational assistance from the AAS IT department. We are seeking volunteers to help run the project. If you are interested, please contact me at joe.tenn@sonoma.edu.

An argument for mechanism-based statistical inference in cancer

PubMed Central

Ochs, Michael; Price, Nathan D.; Tomasetti, Cristian; Younes, Laurent

2015-01-01

Cancer is perhaps the prototypical systems disease, and as such has been the focus of extensive study in quantitative systems biology. However, translating these programs into personalized clinical care remains elusive and incomplete. In this perspective, we argue that realizing this agenda—in particular, predicting disease phenotypes, progression and treatment response for individuals—requires going well beyond standard computational and bioinformatics tools and algorithms. It entails designing global mathematical models over network-scale configurations of genomic states and molecular concentrations, and learning the model parameters from limited available samples of high-dimensional and integrative omics data. As such, any plausible design should accommodate: biological mechanism, necessary for both feasible learning and interpretable decision making; stochasticity, to deal with uncertainty and observed variation at many scales; and a capacity for statistical inference at the patient level. This program, which requires a close, sustained collaboration between mathematicians and biologists, is illustrated in several contexts, including learning bio-markers, metabolism, cell signaling, network inference and tumorigenesis. PMID:25381197

The Bruce Medalists at 100

NASA Astrophysics Data System (ADS)

Tenn, Joseph S.

2007-12-01

In 2007 the Astronomical Society of the Pacific awarded the 100th Catherine Wolfe Bruce gold medal for lifetime contributions to astronomy. The first medalist, Simon Newcomb in 1898, was a celestial mechanician who supervised the computations of orbits and compilation of almanacs, while the second, Arthur Auwers in 1899, observed visually and compiled catalogs of stellar positions and motions. In contrast the last two medalists, Martin Harwit in 2007 and Frank Low in 2006, are pioneers of infrared astronomy from airplanes and satellites. In between have come theoretical and experimental physicists, mathematicians, and radio astronomers, but the majority of medalists have been optical observers, celestial mechanicians (in the early years) and theoretical astrophysicists. Although astronomers are usually honored with the medal twenty to sixty years after their best work is done, we are starting to see more practitioners of the new astronomies, but to date there have been few representatives of the large teams that now dominate astronomical research. I will present an overview of the medalists and how their fields, styles and demographic characteristics have changed.

Chen Jingrun, China's famous mathematician: devastated by brain injuries on the doorstep to solving a fundamental mathematical puzzle.

PubMed

Lei, Ting; Belykh, Evgenii; Dru, Alexander B; Yagmurlu, Kaan; Elhadi, Ali M; Nakaji, Peter; Preul, Mark C

2016-07-01

Chen Jingrun (1933-1996), perhaps the most prodigious mathematician of his time, focused on the field of analytical number theory. His work on Waring's problem, Legendre's conjecture, and Goldbach's conjecture led to progress in analytical number theory in the form of "Chen's Theorem," which he published in 1966 and 1973. His early life was ravaged by the Second Sino-Japanese War and the Chinese Cultural Revolution. On the verge of solving Goldbach's conjecture in 1984, Chen was struck by a bicyclist while also bicycling and suffered severe brain trauma. During his hospitalization, he was also found to have Parkinson's disease. Chen suffered another serious brain concussion after a fall only a few months after recovering from the bicycle crash. With significant deficits, he remained hospitalized for several years without making progress while receiving modern Western medical therapies. In 1988 traditional Chinese medicine experts were called in to assist with his treatment. After a year of acupuncture and oxygen therapy, Chen could control his basic bowel and bladder functions, he could walk slowly, and his swallowing and speech improved. When Chen was unable to produce complex work or finish his final work on Goldbach's conjecture, his mathematical pursuits were taken up vigorously by his dedicated students. He was able to publish Youth Math, a mathematics book that became an inspiration in Chinese education. Although he died in 1996 at the age of 63 after surviving brutal political repression, being deprived of neurological function at the very peak of his genius, and having to be supported by his wife, Chen ironically became a symbol of dedication, perseverance, and motivation to his students and associates, to Chinese youth, to a nation, and to mathematicians and scientists worldwide.

The role of mathematical models in understanding pattern formation in developmental biology.

PubMed

Umulis, David M; Othmer, Hans G

2015-05-01

In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics-whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: "It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations." This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, "The laws of Nature are written in the language of mathematics[Formula: see text] the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word." Mathematics has moved beyond the geometry-based model of Galileo's time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837-838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades-that of how organisms can scale in size. Mathematical analysis alone cannot "solve" these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology.

Female Mathematicians as Role Models for All Students

ERIC Educational Resources Information Center

Wiest, Lynda R.

2009-01-01

Girls' and women's dispositions, performance, and participation in mathematics have received significant attention in recent decades. Nevertheless, females still perform below males on the mathematics portion of standardized tests, such as the Scholastic Assessment Test (SAT) (Institute of Education Sciences), and they attain fewer mathematics…

The Power of Concept Fields

ERIC Educational Resources Information Center

Stoyanova, Elena

2008-01-01

The ability to discover, explore, describe and mathematise relationships between different concepts is at the heart of scientific work of professional mathematicians and scientists. At school level, however, helping students to link, differentiate or investigate the nature of relationships between mathematics concepts remains in the shadow of…

Mathematical Heroes--No Longer Unsung

ERIC Educational Resources Information Center

Chin, Cynthia E.

2007-01-01

The history of Fermat's Last Theorem, recounted in the theatrical piece "Fermat's Last Tango," is a useful vehicle for introducing students to the variety of personalities, processes, and products involved in advanced mathematical investigation. The musical's accessible, informative, and positive portrayal of mathematicians and their work is…

Inspired by Escher.

ERIC Educational Resources Information Center

Wales, Andrew

1998-01-01

Uses the biography and work of M. C. Escher to introduce a unit on art history. Tells about Escher's influence not only on artists, but also on mathematicians and physicists. Outlines a student project in which students employed one of these themes: impossible geometry, rotating symmetry, or geometry. (DSK)

NCTM Student Math Notes.

ERIC Educational Resources Information Center

Maletsky, Evan, Ed.; Yunker, Lee E., Ed.

1986-01-01

Five sets of activities for students are included in this document. Each is designed for use in junior high and secondary school mathematics instruction. The first Note concerns mathematics on postage stamps. Historical procedures and mathematicians, metric conversion, geometric ideas, and formulas are among the topics considered. Successful…

Collaborative Learning through Formative Peer Review with Technology

ERIC Educational Resources Information Center

Eaton, Carrie Diaz; Wade, Stephanie

2014-01-01

This paper describes a collaboration between a mathematician and a compositionist who developed a sequence of collaborative writing assignments for calculus. This sequence of developmentally appropriate assignments presents peer review as a collaborative process that promotes reflection, deepens understanding, and improves exposition. First, we…

Looking at Debit and Credit Card Fraud

ERIC Educational Resources Information Center

Porkess, Roger; Mason, Stephen

2012-01-01

This article, written jointly by a mathematician and a barrister, looks at some of the statistical issues raised by court cases based on fraud involving chip and PIN cards. It provides examples and insights that statistics teachers should find helpful. (Contains 4 tables and 1 figure.)

The Evaluation of Project SEED, 1990-91.

ERIC Educational Resources Information Center

Webster, William J.; Chadbourn, Russell A.

Project Special Elementary Education for the Disadvantaged (SEED) is a national program in which professional mathematicians and scientists from universities and industry teach abstract, conceptually oriented mathematics to full-sized classes of elementary school children as a supplement to their regular mathematics instruction. In the Dallas…

The Helen of Geometry

ERIC Educational Resources Information Center

Martin, John

2010-01-01

The cycloid has been called the Helen of Geometry, not only because of its beautiful properties but also because of the quarrels it provoked between famous mathematicians of the 17th century. This article surveys the history of the cycloid and its importance in the development of the calculus.

Hydrologic Engineering Center: A Quarter Century 1964-1989

DTIC Science & Technology

1989-01-01

consisted of an engineering tech- nician, a mathematician, four hydraulic engineers and a clerk- steno . During the last 25 years, staff members have...McPherson Jack Dangermond John Lager Don Hey Clarence Korhonen Harry Schwarz James Wright John J. Buckley Mike Savage Nicholas Lally Ralph

Nurturing Young Student Mathematicians

ERIC Educational Resources Information Center

Gavin, M. Katherine; Casa, Tutita M.

2013-01-01

Developing mathematical talent in our students should be of primary consideration in education today as nations respond to the challenges of economic crises and ever-changing technological advances. This paper describes two U.S. federally funded curriculum projects, Project M[superscript 3], Mentoring Mathematical Minds, and Project M[superscript…

Math in Riley's World

ERIC Educational Resources Information Center

Kritzer, Karen L.

2011-01-01

In their overview for the prekindergarten-grade 2 Standards, the National Council for Teachers of Mathematics (NCTM) documents the value of early mathematical environments. During these early years, young children are building beliefs about what mathematics is and learning about themselves as early mathematicians. What young children learn about…

The motion behind the symbols: a vital role for dynamism in the conceptualization of limits and continuity in expert mathematics.

PubMed

Marghetis, Tyler; Núñez, Rafael

2013-04-01

The canonical history of mathematics suggests that the late 19th-century "arithmetization" of calculus marked a shift away from spatial-dynamic intuitions, grounding concepts in static, rigorous definitions. Instead, we argue that mathematicians, both historically and currently, rely on dynamic conceptualizations of mathematical concepts like continuity, limits, and functions. In this article, we present two studies of the role of dynamic conceptual systems in expert proof. The first is an analysis of co-speech gesture produced by mathematics graduate students while proving a theorem, which reveals a reliance on dynamic conceptual resources. The second is a cognitive-historical case study of an incident in 19th-century mathematics that suggests a functional role for such dynamism in the reasoning of the renowned mathematician Augustin Cauchy. Taken together, these two studies indicate that essential concepts in calculus that have been defined entirely in abstract, static terms are nevertheless conceptualized dynamically, in both contemporary and historical practice. Copyright © 2013 Cognitive Science Society, Inc.

On the mathematical treatment of the Born-Oppenheimer approximation

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

Jecko, Thierry, E-mail: thierry.jecko@u-cergy.fr

2014-05-15

Motivated by the paper by Sutcliffe and Woolley [“On the quantum theory of molecules,” J. Chem. Phys. 137, 22A544 (2012)], we present the main ideas used by mathematicians to show the accuracy of the Born-Oppenheimer approximation for molecules. Based on mathematical works on this approximation for molecular bound states, in scattering theory, in resonance theory, and for short time evolution, we give an overview of some rigorous results obtained up to now. We also point out the main difficulties mathematicians are trying to overcome and speculate on further developments. The mathematical approach does not fit exactly to the common usemore » of the approximation in Physics and Chemistry. We criticize the latter and comment on the differences, contributing in this way to the discussion on the Born-Oppenheimer approximation initiated by Sutcliffe and Woolley. The paper neither contains mathematical statements nor proofs. Instead, we try to make accessible mathematically rigourous results on the subject to researchers in Quantum Chemistry or Physics.« less

Mathematics and Physics: The Idea of a Pre-Established Harmony

NASA Astrophysics Data System (ADS)

Kragh, Helge

2015-07-01

For more than a century the notion of a pre-established harmony between the mathematical and physical sciences has played an important role not only in the rhetoric of mathematicians and theoretical physicists, but also as a doctrine guiding much of their research. Strongly mathematized branches of physics, such as the vortex theory of atoms popular in Victorian Britain, were not unknown in the nineteenth century, but it was only in the environment of fin-de-siècle Germany that the idea of a pre-established harmony really took off and became part of the mathematicians' ideology. Important historical figures were in this respect David Hilbert, Hermann Minkowski and, somewhat later, Albert Einstein. Roughly similar ideas can be found also among British theorists, among whom Arthur Eddington, Arthur Milne, and Paul Dirac are singled out. Although largely limited to the period 1870-1940, the paper also considers Max Tegmark's recent hypothesis of the universe (or multiverse) being a one-to-one reflection of mathematical structures.

The impeccable credentials of an untrained philosopher: Willem Jacob 's Gravesande's career before his Leiden professorship, 1688–1717

PubMed Central

van Besouw, Jip

2016-01-01

The mathematician, physicist and philosopher W. J. 's Gravesande is particularly known for his adherence to ‘Newtonian philosophy’. Currently, it is widely held that 's Gravesande got his main inspiration for his scholarly calling from Newton himself, whom he met in 1715 during a first career as a lawyer; and that it was mainly Newton's own intervention that ensured the appointment of the unqualified 's Gravesande at Leiden University. I challenge these views by bringing together all currently known information about 's Gravesande, including a number of as yet unused documents. I show that 's Gravesande's appointment resulted from a very carefully built up reputation in scholarly circles rather than from accidental meetings and patronage. 's Gravesande had written several innovative papers and was in contact with both leading mathematicians and local political and patrician figures already before 1715. This article therefore explains the rationale behind his appointment in Leiden.

Structure theorems and the dynamics of nitrogen catabolite repression in yeast

PubMed Central

Boczko, Erik M.; Cooper, Terrance G.; Gedeon, Tomas; Mischaikow, Konstantin; Murdock, Deborah G.; Pratap, Siddharth; Wells, K. Sam

2005-01-01

By using current biological understanding, a conceptually simple, but mathematically complex, model is proposed for the dynamics of the gene circuit responsible for regulating nitrogen catabolite repression (NCR) in yeast. A variety of mathematical “structure” theorems are described that allow one to determine the asymptotic dynamics of complicated systems under very weak hypotheses. It is shown that these theorems apply to several subcircuits of the full NCR circuit, most importantly to the URE2–GLN3 subcircuit that is independent of the other constituents but governs the switching behavior of the full NCR circuit under changes in nitrogen source. Under hypotheses that are fully consistent with biological data, it is proven that the dynamics of this subcircuit is simple periodic behavior in synchrony with the cell cycle. Although the current mathematical structure theorems do not apply to the full NCR circuit, extensive simulations suggest that the dynamics is constrained in much the same way as that of the URE2–GLN3 subcircuit. This finding leads to the proposal that mathematicians study genetic circuits to find new geometries for which structure theorems may exist. PMID:15814615

Virtual Environments for Mathematics and Geometry Education

ERIC Educational Resources Information Center

Kaufmann, Hannes

2009-01-01

Since ancient times mathematicians and geometricians have used visualisations to describe, discuss, study and teach mathematics. In mathematics education, visualisations are still used whenever possible to support teaching, to inspire students and feed their need to actually see abstract mathematical facts. In our times, virtual reality presents a…

Intellectual Discussion in Mathematics.

ERIC Educational Resources Information Center

Cavaluzzi, Christina

In an attempt to unearth the characteristic communication practices of mathematical seminars, the perceptions and beliefs about them held by regular attendees, and the normative ideals about communication in the mathematics community, this paper considers how communication in math is an integral part of how mathematicians do their work. Responding…

Characteristics of Second Graders' Mathematical Writing

ERIC Educational Resources Information Center

Cohen, Jeremy A.; Casa, Tutita M.; Miller, Heather C.; Firmender, Janine M.

2015-01-01

This study compared the characteristics of second graders' mathematical writing between an intervention and comparison group. Two six-week Project M2 units were implemented with students in the intervention group. The units position students to communicate in ways similar to mathematicians, including engaging in verbal discourse where they…

Harvard, Wisconsin Programs Aim to Improve Science Education.

ERIC Educational Resources Information Center

Krieger, James

1983-01-01

Describes two programs to improve science education. Harvard University will provide a teacher training program for mid- to late-career mathematicians/scientists in industry and will provide inservice programs for current science/mathematics teachers. University of Wisconsin's program involves a national institute to foster research in chemical…

The Evaluation of Project SEED, 1989-90.

ERIC Educational Resources Information Center

Webster, William J.; Chadbourn, Russell A.

Project Special Elementary Education for the Disadvantaged (Project SEED) is a nationwide program in which mathematicians and scientists from academia and industry teach abstract, conceptually oriented mathematics to full-sized classes of elementary school students as a supplement to their regular arithmetic classes. A Socratic group-discovery…

Collegiate Mathematics Teaching: An Unexamined Practice

ERIC Educational Resources Information Center

Speer, Natasha M.; Smith, John P., III; Horvath, Aladar

2010-01-01

Though written accounts of collegiate mathematics teaching exist (e.g., mathematicians' reflections and analyses of learning and teaching in innovative courses), research on collegiate teachers' actual classroom teaching practice is virtually non-existent. We advance this claim based on a thorough review of peer-reviewed journals where scholarship…

The Stable Pairing Problem

ERIC Educational Resources Information Center

Greenwell, Raymond N.; Seabold, Daniel E.

2014-01-01

The Gale-Shapley stable marriage theorem is a fascinating piece of twentieth-century mathematics that has many practical applications--from labor markets to school admissions--yet is accessible to secondary school mathematics students. David Gale and Lloyd Shapley were both mathematicians and economists who published their work on the Stable…

The Mathematics of Starry Nights

ERIC Educational Resources Information Center

Barman, Farshad

2008-01-01

The mathematics for finding and plotting the locations of stars and constellations are available in many books on astronomy, but the steps involve mystifying and fragmented equations, calculations, and terminology. This paper will introduce an entirely new unified and cohesive technique that is easy to understand by mathematicians, and simple…

Proof Mapping

ERIC Educational Resources Information Center

Linares, Leanne A.; Smith, Phil R.

2009-01-01

A geometry textbook or mathematics journal that prints all the work that mathematicians use as they generate proofs of mathematical results would be rare indeed. The false starts, the tentative conjectures, and the arguments that led nowhere--these are conveniently omitted; only the final successful product is presented to the world. To students…

Math Corps Summer Camp: An Inner City Intervention Program.

ERIC Educational Resources Information Center

Edwards, Thomas; Kahn, Steven; Brenton, Lawrence

2001-01-01

Describes a mathematics-focused summer camp for inner city, African American, at-risk secondary school students. Situated on a college campus, the camp grouped participants with college students and professional mathematicians. Results of pre- and posttests indicated that students' mathematics scores increased significantly. Both participants and…

Using proteomics to study sexual reproduction in angiosperms

USDA-ARS?s Scientific Manuscript database

While a relative latecomer to the post-genomics era of functional biology, the application of mass spectrometry-based proteomic analysis has increased exponentially over the past 10 years. Some of this increase is the result of transition of chemists physicists, and mathematicians to the study of ...

Laterality for music perception in musicians, mathematicians, and dancers: jumping to conclusions.

PubMed

Gordon, H W

1993-06-01

Group differences for ear asymmetries for a melodies task were reported for talented music, mathematics, and dance students. Evidence is presented that it is premature to conclude that these group differences were the result of specialized training in their areas of expertise.

An Urban Collaborative in Critical Perspective.

ERIC Educational Resources Information Center

Bruckerhoff, Charles E.; Popkewitz, Thomas S.

1991-01-01

Discusses the rationale behind the Cleveland Collaborative for Mathematics Education, which networks urban high school math teachers with college math professors and mathematicians in business. Describes a typical teaching day for one high school teacher and how environmental challenges such as family abuse, student absenteeism, and lack of…

Kentucky's New Contribution to the Global Community

ERIC Educational Resources Information Center

Gott, Tim

2007-01-01

Throughout the United States, legislators, business leaders, educators, and other stakeholders are debating the impending crisis of the shortage of mathematicians and scientists in the United States. Several books, such as Thomas Friedman's "The World Is Flat" and Ted Fishman's "China, Inc.," accentuate this growing dilemma.…

Discourse: Simple Moves that Work

ERIC Educational Resources Information Center

Rawding, Molly Rothermel; Wills, Theresa

2012-01-01

Just as students need plenty of time to practice skills such as solving fraction problems, they also need time to practice the skills of discourse to become better communicators and stronger mathematicians. Embedded within discourse strategies are specific ways to maximize communication. When repeatedly practiced, students learn to listen to one…

Challenging Perspectives on Learning and Teaching in the Disciplines: The Academic Voice

ERIC Educational Resources Information Center

Krause, Kerri-Lee D.

2014-01-01

This article reports on a study of academic staff perspectives on disciplinary communities and skill development in disciplinary contexts. Fifty-five academic staff were interviewed across eight disciplines in four Australian universities. Responses of historians and mathematicians are the focus of this article. A socio-constructivist framework…

The Menu for Every Young Mathematician's Appetite

ERIC Educational Resources Information Center

Legnard, Danielle S.; Austin, Susan L.

2012-01-01

Math Workshop offers differentiated instruction to foster a deep understanding of rich, rigorous mathematics that is attainable by all learners. The inquiry-based model provides a menu of multilevel math tasks, within the daily math block, that focus on similar mathematical content. Math Workshop promotes a culture of engagement and…

Minority Mathematicians: Who Is Responsible?

ERIC Educational Resources Information Center

Johnson, Raymond

2000-01-01

This report is comprised of a section of three talks in the special session on Mathematics and Education Reform at the January, 2000 Joint Mathematics Meeting in Washington, DC. This issue, which includes three articles based on the presentations and two additional articles, continues discussion on issues and successful approaches to improve the…

Conditional Inference and Advanced Mathematical Study: Further Evidence

ERIC Educational Resources Information Center

Inglis, Matthew; Simpson, Adrian

2009-01-01

In this paper, we examine the support given for the "theory of formal discipline" by Inglis and Simpson (Educational Studies Mathematics 67:187-204, "2008"). This theory, which is widely accepted by mathematicians and curriculum bodies, suggests that the study of advanced mathematics develops general thinking skills and, in particular, conditional…

How to Build Schools Where Adults Learn

ERIC Educational Resources Information Center

Fahey, Kevin; Ippolito, Jacy

2014-01-01

In the current, very complex, and even conflicted discourse about schools, one thing is clear: Schools need to be about student learning. Schools need to ensure that students are good readers, proficient writers, capable mathematicians, competent scientists, and knowledgeable historians. Students also need to learn to work together, be healthy, be…

Talking Maths

ERIC Educational Resources Information Center

Murray, Jenny

2006-01-01

Discussion in maths lessons has always been something encouraged by ATM but can be difficult to initiate for non-specialist and inexperienced teachers who may feel they need material in books to get them going. In this article, the author describes resources aimed at encouraging discussion among primary mathematicians. These resources include: (1)…

High School Mathematics at Work: Essays and Examples for the Education of All Students.

ERIC Educational Resources Information Center

National Academy of Sciences - National Research Council, Washington, DC. Mathematical Sciences Education Board.

Traditionally, vocational mathematics and precollege mathematics have been separate in schools. This book illuminates the interplay between technical and academic mathematics. This collection of essays by mathematicians, educators, and other experts is enhanced with illustrative tasks from workplace and everyday contexts that suggest ways to…

Kindergarteners' Achievement on Geometry and Measurement Units That Incorporate a Gifted Education Approach

ERIC Educational Resources Information Center

Casa, Tutita M.; Firmender, Janine M.; Gavin, M. Katherine; Carroll, Susan R.

2017-01-01

This research responds to the call by early childhood educators advocating for more challenging mathematics curriculum at the primary level. The kindergarten Project M[superscript 2] units focus on challenging geometry and measurement concepts by positioning students as practicing mathematicians. The research reported herein highlights the…

Introducing Summer Camp Students to Modern Cryptography

ERIC Educational Resources Information Center

Griffiths, Barry J.

2015-01-01

For countries to remain competitive in the global economy, it is important to cultivate the next generation of native mathematicians. However, this goal has been increasingly challenging in the United States where, despite the tremendous increase in university enrollment during recent decades, the number of students studying mathematics has…

Soft Drinks, Mind Reading, and Number Theory

ERIC Educational Resources Information Center

Schultz, Kyle T.

2009-01-01

Proof is a central component of mathematicians' work, used for verification, explanation, discovery, and communication. Unfortunately, high school students' experiences with proof are often limited to verifying mathematical statements or relationships that are already known to be true. As a result, students often fail to grasp the true nature of…

Graphs and Zero-Divisors

ERIC Educational Resources Information Center

Axtell, M.; Stickles, J.

2010-01-01

The last ten years have seen an explosion of research in the zero-divisor graphs of commutative rings--by professional mathematicians "and" undergraduates. The objective is to find algebraic information within the geometry of these graphs. This topic is approachable by anyone with one or two semesters of abstract algebra. This article gives the…

Multiple Visions of Teachers' Understandings of Mathematics

ERIC Educational Resources Information Center

Kajander, Ann; Mason, Ralph; Taylor, Peter; Doolittle, Edward; Boland, Tom; Jarvis, Dan; Maciejewski, Wes

2010-01-01

In this dialog, the notion of mathematical understanding as might be needed by classroom teachers is critically examined by mathematics educators, mathematicians, and a classroom teacher, based on the outcomes of recent work with expert classroom teachers. Terminology, assumptions and examples are discussed and analysed from a number of points of…

Fibonacci's Forgotten Number Revisited

ERIC Educational Resources Information Center

Maruszewski, Richard

2009-01-01

In 1225 Fibonacci visited the court of the Holy Roman Emperor, Frederick II. Because Frederick was an important patron of learning, this visit was important to Fibonacci. During the audience, Frederick's court mathematician posed three problems to test Fibonacci. The third was to find the real solution to the equation: x[superscript 3] +…

International Teachers' Judgment of Gifted Mathematics Student Characteristics

ERIC Educational Resources Information Center

Ficici, Abdullah; Siegle, Del

2008-01-01

Teachers play a key role in the identification and training of talented mathematicians, and their attitudes are important in improving math instruction for gifted students. We surveyed secondary mathematics teachers from South Korea, Turkey, and the United States. These teachers completed a survey instrument called the Teachers' Judgments of…

Word Search Packet: Climbing the Hills of Math Skills. California Demonstration Mathematics Program.

ERIC Educational Resources Information Center

Ontario-Montclair School District, Ontario, CA.

Thirty word-search puzzles on mathematics and mathematicians are presented. The puzzles are used periodically as homework assignments in a self-paced, individualized mathematics program which is designed to improve the achievement of junior high school students. Answers to the puzzles are not included. (DC)

Audience, Style and Criticism

ERIC Educational Resources Information Center

Pimm, David; Sinclair, Nathalie

2009-01-01

The primary focus for this article involves aspects of professional mathematical writing and examines the possibility of a form of literary criticism in relation to it. By means of examples from contemporary style guides for academic articles in mathematics (AMS, MAA), as well as the writing of mathematicians (Hamilton, Dedekind) from earlier…

Parabolic Mirror: Focusing on Science, Technology, Engineering, and Math

ERIC Educational Resources Information Center

Smith, Karianne; Hughes, William

2013-01-01

In the fall of 2011, Park Forest Middle School (PFMS) students approached the STEM faculty with numerous questions regarding the popular television show Myth Busters, which detailed Greek mathematician, physicist, engineer, and inventor, Archimedes. Two episodes featured attempts to test historical accounts that Archimedes developed a death ray…

Abstract Algebra to Secondary School Algebra: Building Bridges

ERIC Educational Resources Information Center

Christy, Donna; Sparks, Rebecca

2015-01-01

The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…

Ocean Spray Lubricates Winds

ERIC Educational Resources Information Center

Journal of College Science Teaching, 2005

2005-01-01

According to a new study by two University of California, Berkeley, mathematicians and their Russian colleague, the water droplets kicked up by rough seas serve to lubricate the swirling winds of hurricanes and cyclones, letting them build to speeds approaching 200 miles per hour. Without the lubricating effect of the spray, the mathematicians…

Transformational Play: Using Games to Position Person, Content, and Context

ERIC Educational Resources Information Center

Barab, Sasha A.; Gresalfi, Melissa; Ingram-Goble, Adam

2010-01-01

Videogames are a powerful medium that curriculum designers can use to create narratively rich worlds for achieving educational goals. In these worlds, youth can become scientists, doctors, writers, and mathematicians who critically engage complex disciplinary content to transform a virtual world. Toward illuminating this potential, the authors…

Educating the Young Mathematician: The Twentieth Century and Beyond

ERIC Educational Resources Information Center

Saracho, Olivia N.; Spodek, Bernard

2009-01-01

Educational programs for young children emerged reasonably early in the history of the United States of America. The movements of Child-Centered Education, the Nursery School, the Project Method, Curriculum Reform, and contemporary research have all influenced mathematics in early childhood education. The Froebelian kindergarten and the Montessori…

Math Exchanges: Guiding Young Mathematicians in Small-Group Meetings

ERIC Educational Resources Information Center

Wedekind, Kassia Omohundro

2011-01-01

Traditionally, small-group math instruction has been used as a format for reaching children who struggle to understand. Math coach Kassia Omohundro Wedekind uses small-group instruction as the centerpiece of her math workshop approach, engaging all students in rigorous "math exchanges." The key characteristics of these mathematical conversations…

The Triangles of Aristarchus

ERIC Educational Resources Information Center

Hirshfeld, Alan W.

2004-01-01

Greek philosopher mathematician, Aristarchus of Samos, in the third century B.C., proposed that the sun held in the central position, casting its light symmetrically outward on the other celestial bodies. He demonstrated the way in which a person could use simple observations and elementary geometry to measure on a cosmic scale.

Independent Events in Elementary Probability Theory

ERIC Educational Resources Information Center

Csenki, Attila

2011-01-01

In Probability and Statistics taught to mathematicians as a first introduction or to a non-mathematical audience, joint independence of events is introduced by requiring that the multiplication rule is satisfied. The following statement is usually tacitly assumed to hold (and, at best, intuitively motivated): If the n events E[subscript 1],…

Measurement, Mathematics, and Music.

ERIC Educational Resources Information Center

Blackburn, Katie; White, David

The Greek mathematician, Pythagoras, was among the first to undertake a mathematical study of music. His work, resulted in a scale of notes which can produce beautiful melodies and which is easily reproduced in the elementary classroom. In an age when teachers look for an interdisciplinary connection between various aspects of the curriculum, in a…

Values and Norms of Proof for Mathematicians and Students

ERIC Educational Resources Information Center

Dawkins, Paul Christian; Weber, Keith

2017-01-01

In this theoretical paper, we present a framework for conceptualizing proof in terms of mathematical values, as well as the norms that uphold those values. In particular, proofs adhere to the values of establishing a priori truth, employing decontextualized reasoning, increasing mathematical understanding, and maintaining consistent standards for…

The Changing Landscape of One Primary School's Mathematics Curriculum

ERIC Educational Resources Information Center

Dent, Wendy; McChesney, Jane

2016-01-01

This paper describes a period of substantial changes in the mathematics curriculum of one primary school in Christchurch. Using retrospective analysis, we identified two important conceptual themes: equity of mathematical learning and opportunities for all students to learn to be a mathematician. Access to research about these themes prompted two…

Predicting Student Achievement Using Measures of Teachers' Knowledge for Teaching Geometry

ERIC Educational Resources Information Center

Mohr-Schroeder, Margaret; Ronau, Robert N.; Peters, Susan; Lee, Carl W.; Bush, William S.

2017-01-01

This article describes the development and validation of two forms of the Geometry Assessments for Secondary Teachers (GAST), which were designed to assess teachers' knowledge for teaching geometry. Both forms were developed by teams of mathematicians, mathematics educators, psychometricians, and secondary classroom geometry teachers. Predictive…

Duoethnography: A New Research Methodology for Mathematics Education

ERIC Educational Resources Information Center

Rapke, Tina Kathleen

2014-01-01

I have developed an adaptation of the emerging duoethnography methodology that allows me to draw on my processes of creating mathematics, interpret these processes for what they might mean for classrooms, and explore/reconceptualize my complementary and competing perspectives as a mathematician and an educator. This article includes a…

The Shoemaker's Knife

ERIC Educational Resources Information Center

Thomson, Ian

2010-01-01

Archimedes, the famous Greek mathematician, lived from 287 BCE until approximately 212 BCE. He thought that the figure of two semi-circles on a straight line enclosed by a larger semi-circle resembled a shoemaker's knife. Archimedes called this figure an "arbelos" since arbelos is the Greek word for a shoemaker's knife. The author describes the…

Encouraging Example Generation: A Teaching Experiment in First-Semester Calculus

ERIC Educational Resources Information Center

Wagner, Elaine Rumsey; Orme, Susan Marla; Turner, Heidi Jean; Yopp, David

2017-01-01

Mathematicians use example generation to test and verify mathematical ideas; however, the processes through which undergraduates learn to productively generate examples are not well understood. We engaged calculus students in a teaching experiment designed to develop skills in productively generating examples to learn novel concepts. This article…

Journey into Problem Solving: A Gift from Polya

ERIC Educational Resources Information Center

Lederman, Eric

2009-01-01

In "How to Solve It", accomplished mathematician and skilled communicator George Polya describes a four-step universal solving technique designed to help students develop mathematical problem-solving skills. By providing a glimpse at the grace with which experts solve problems, Polya provides definable methods that are not exclusive to…

Content Area Literacy in the Mathematics Classroom

ERIC Educational Resources Information Center

Armstrong, Abbigail; Ming, Kavin; Helf, Shawnna

2018-01-01

Content area literacy has an important role in helping students understand content in specific disciplines, such as mathematics. Although the strategies are not unique to each individual content area, they are often adapted for use in a specific discipline. For example, mathematicians use mathematical language to make sense of new ideas and…

Challenging Students' Beliefs about Mathematics: The Use of Documentary to Alter Perceptions of Efficacy

ERIC Educational Resources Information Center

Hekimoglu, Serkan; Kittrell, Emily

2010-01-01

This study investigates whether seeing a documentary on how mathematicians do mathematics improves students' math "self-efficacy beliefs." The analysis of students' written reflections and classroom observations suggests that watching the documentary may help students' math anxiety decrease and positive self-efficacy toward learning mathematics…

Mathematical versus English Meaning in Implication and Disjunction

ERIC Educational Resources Information Center

Shipman, Barbara A.

2013-01-01

As mathematicians, we assign rigid meanings to words that may have a variety of interpretations in common language. This article considers meanings of "if" and "or" from everyday English that have caused students to misinterpret mathematical statements, and that are consistently overlooked by instructional materials in addressing students'…

Finding Fifths in Origami

ERIC Educational Resources Information Center

Hsiao, Joy

2015-01-01

Paper folding, or origami in Japanese, is a traditional craft that has been enjoyed by both children and adults for hundreds of years. Mathematicians have long studied the mathematics of paper folding. They use square papers to construct mathematical shapes (for example, folding an equilateral triangle from a square paper or trisecting an angle),…

The Effect of Authority on the Persuasiveness of Mathematical Arguments

ERIC Educational Resources Information Center

Inglis, Matthew; Mejia-Ramos, Juan Pablo

2009-01-01

Three experiments are reported that investigate the extent to which an authority figure influences the level of persuasion undergraduate students and research-active mathematicians invest in mathematical arguments. We demonstrate that, in some situations, both students and researchers rate arguments as being more persuasive when they are…

Euler Teaches a Class in Structural Steel Design

ERIC Educational Resources Information Center

Boyajian, David M.

2009-01-01

Even before steel was a topic of formal study for structural engineers, the brilliant eighteenth century Swiss mathematician and physicist, Leonhard Euler (1707-1783), investigated the theory governing the elastic behaviour of columns, the results of which are incorporated into the American Institute of Steel Construction's (AISC's) Bible: the…

Analogy and Intersubjectivity: Political Oratory, Scholarly Argument and Scientific Reports.

ERIC Educational Resources Information Center

Gross, Alan G.

1983-01-01

Focuses on the different ways political oratory, scholarly argument, and scientific reports use analogy. Specifically, analyzes intersubjective agreement in Franklin D. Roosevelt's First Inaugural address, the scholarly argument between Sir Karl Popper and Thomas S. Kuhn, and the scientific reports of various mathematicians and scientists. (PD)

New Languages of Possibility: Early Experiments in Education as Dissent

ERIC Educational Resources Information Center

Walsh, Brendan; Lalor, John

2015-01-01

This paper reviews the work of four early radical educators: the cultural nationalist Rabindranath Tagore (1861-1941), Asia's first Nobel Laureate; Bertrand Russell (1872-1970), Cambridge mathematician and philosopher; the Irish educationalist and insurgent Patrick Pearse (1879-1916) and Leonard Elmhirst (1893-1975), co-founder of Dartington Hall…

Solitary Pain: Bertrand Russell as Cognitive Therapist

ERIC Educational Resources Information Center

Overskeid, Geir

2004-01-01

Bertrand Russell was a prominent philosopher, mathematician, and political activist. It is less well known that Russell suffered from various psychological problems and developed his own method of dealing with them. Continuing a long philosophical tradition, Russell examined how faulty thinking may elicit painful emotions. Though seldom, if ever,…

Proof Construction and Evaluation Practices of Prospective Mathematics Educators

ERIC Educational Resources Information Center

Imamoglu, Yesim; Togrol, Aysenur Yontar

2015-01-01

This study was conducted with 93 freshmen and 82 senior prospective mathematicians and mathematics teachers in order to investigate how they construct and evaluate proofs and whether there are any significant differences in their proof construction (with respect to department and grade) and proof evaluation (with respect to department)…

Cramer's Rule Revisited

ERIC Educational Resources Information Center

Ayoub, Ayoub B.

2005-01-01

In 1750, the Swiss mathematician Gabriel Cramer published a well-written algebra book entitled "Introduction a l'Analyse des Lignes Courbes Algebriques." In the appendix to this book, Cramer gave, without proof, the rule named after him for solving a linear system of equations using determinants (Kosinki, 2001). Since then several derivations of…

The Mathematics of Sundials

ERIC Educational Resources Information Center

Vincent, Jill

2008-01-01

As early as 3500 years ago, shadows of sticks were used as a primitive instrument for indicating the passage of time through the day. The stick came to be called a "gnomon" or "one who knows." Early Babylonian obelisks were designed to determine noon. The development of trigonometry by Greek mathematicians meant that hour lines…

Introduction to this special issue on statistics for wildfire processes

Treesearch

Marcia Gumpertz

2009-01-01

This special issue on statistics for wildfire processes brings together foresters, wildfire ecologists, statisticians, mathematicians, and economists. All of these disciplines bring different interests, approaches and expertise to the modeling of wildfire processes. It is not necessarily easy, however, to communicate across disciplines or follow the developments in a...

Using magnetic charge to understand soft-magnetic materials

NASA Astrophysics Data System (ADS)

Arrott, Anthony S.; Templeton, Terry L.

2018-04-01

This is an overview of what the Landau-Lifshitz-Gilbert equations are doing in soft-magnetic materials with dimensions large compared to the exchange length. The surface magnetic charges try to cancel applied magnetic fields inside the soft magnetic material. The exchange energy tries to reach a minimum while meeting the boundary conditions set by the magnetic charges by using magnetization patterns that have a curl but no divergence. It can almost do this, but it still pays to add some divergence to further lower the exchange energy. There are then both positively and negatively charged regions in the bulk. The unlike charges attract one another, but do not annihilate because they are paid for by the reduction in exchange energy. The micromagnetics of soft magnetic materials is about how those charges rearrange themselves. The topology of magnetic charge distributions presents challenges for mathematicians. No one guessed that they like to form helical patterns of extended multiples of charge density.

Mathematics of Web science: structure, dynamics and incentives.

PubMed

Chayes, Jennifer

2013-03-28

Dr Chayes' talk described how, to a discrete mathematician, 'all the world's a graph, and all the people and domains merely vertices'. A graph is represented as a set of vertices V and a set of edges E, so that, for instance, in the World Wide Web, V is the set of pages and E the directed hyperlinks; in a social network, V is the people and E the set of relationships; and in the autonomous system Internet, V is the set of autonomous systems (such as AOL, Yahoo! and MSN) and E the set of connections. This means that mathematics can be used to study the Web (and other large graphs in the online world) in the following way: first, we can model online networks as large finite graphs; second, we can sample pieces of these graphs; third, we can understand and then control processes on these graphs; and fourth, we can develop algorithms for these graphs and apply them to improve the online experience.

Fractal Geometry in the Arts: AN Overview across the Different Cultures

NASA Astrophysics Data System (ADS)

Sala, Nicoletta

Fractal, in mathematics, is a geometric shape that is complex and detailed in structure at any level of magnification. The word "fractal" was coined less than thirty years ago by one of history's most creative and mathematicians, Benoit Mandelbrot, whose work, The Fractal Geometry of Nature, first introduced and explained concepts underlying this new vision of the geometry. Although other mathematical thinkers like Georg Cantor (1845-1918), Felix Hausdorff (1868-1942), Gaston Julia (1893-1978), Helge von Koch (1870-1924), Giuseppe Peano (1858-1932), Lewis Richardson (1891-1953), Waclaw Sierpinski (1882-1969) and others had attained isolated insights of fractal understanding, such ideas were largely ignored until Mandelbrot's genius forged them at a single blow into a gorgeously coherent and fascinating discipline. Fractal geometry is applied in different field now: engineering, physics, chemistry, biology, and architecture. The aim of this paper is to introduce an approach where the arts are analysed using a fractal point of view.

How Much Did Maine's Molocket and Metallak Know about Rapid Climate Change? Did They Utilize Psychological Strategies and Cover Stories to Conceal Their Impact Communities, Observational Sites and Data Collection?

NASA Astrophysics Data System (ADS)

Bates, Tiffany R.; Mc Leod, Roger D.; Mc Leod, David M.

2003-10-01

The Pequakets Molocket (adherent of God La[ngued]oc Christ Cathar Spirit-signal) and Metallak operated in NH and the western border area of ME, during the early 1800s. Molocket requested shelter in South Paris, ME during a powerful thunderstorm. Denied access, she cursed that area. Our interests have led us to recognize that there may be psychological reasons that deception is good strategic procedure for concealing valuable activities associated with impact power groups striving to protect their operating turf. Many sites associated with tradition-respecting Native Americans are quite electromagnetically responsive to climate change. Metallak (mathematician-applied astronomer God Spirit-signal) is purported to have driven off his son over purloined furs; that elder son then operated among the MiKmaw/Micmacs of ME and the Canadian Maritimes. They are purported to make the weather. Information protection and surreptitious data collection may indicate an impact groups concealed interests.

The Pulley: A Parable of Effort and Reward

NASA Astrophysics Data System (ADS)

Gluck, Paul

2012-11-01

The Alwood machine and various problems involving pulleys are sta(p)le diets of students when applying Newton's second law of motion. Interest in such problems can be increased and discussion enlivened by couching them in forms that have in them elements of suspense (sic!) or competition. Two didactic papers have suggested versions in this vein.1,2 Here we should like to present a discussion that contrasts models and theoretical constructs with a reallife situation. A mathematician N and a physicist P having identical masses m sit at the same height at the ends of a rope passing over a pulley, as in Fig. 1(a). They decide on a race to climb up the rope, the first one to reach the pulley wins. Which one of them will be the winner? Is it prudent to work hard, or does the indolent get there first by mere force of thought? The following qualitative discussion could be of interest when introducing the class to the Atwood machine.

Is Learning Data in the Right Shape?

ERIC Educational Resources Information Center

Kelly, Anthony E.

2017-01-01

In this short thought-piece, I attempt to capture the type of freewheeling discussions I had with our late colleague, Mika Seppälä, a research mathematician from Helsinki. Mika, not being a psychometrician or learning scientist, was blissfully free from the design constraints that experts sometimes ingest, unwittingly. I also draw on delightful…

Master's Students' Perceptions of Microsoft Word for Mathematical Typesetting

ERIC Educational Resources Information Center

Loch, Birgit; Lowe, Tim W.; Mestel, Ben D.

2015-01-01

It is widely recognized that mathematical typesetting is more difficult than typesetting in most other disciplines due to the need for specialized mathematical notation and symbols. While most mathematicians type mathematical documents using LaTeX, with varying levels of proficiency, students often use other options or handwrite mathematics. Here,…

Pi Division and Addition

ERIC Educational Resources Information Center

Scott, Paul

2008-01-01

The number Pi (approximately 3.14159) is defined to be the ratio C/d of the circumference (C) to the diameter (d) of any given circle. In particular, Pi measures the circumference of a circle of diameter d = 1. Historically, the Greek mathematician Archimedes found good approximations for Pi by inscribing and circumscribing many-sided polygons…

Educators' Expectations and Aspirations around Young Children's Mathematical Knowledge

ERIC Educational Resources Information Center

Perry, Bob; MacDonald, Amy

2015-01-01

Let's Count is a mathematics professional learning programme for preschool educators in Australia, managed by a prominent non-government organisation and sponsored by industry. It has been implemented in both face-to-face and online modes over 2013/14. Let's Count is based on the constructs that all young children are powerful mathematicians and…

A Description of a Family of Heron Quadrilaterals

ERIC Educational Resources Information Center

Sastry, K. R. S.

2005-01-01

Mathematical historians place Heron in the first century. Right-angled triangles with integer sides and area had been determined before Heron, but he discovered such a "non" right-angled triangle, viz 13, 14, 15; 84. In view of this, triangles with integer sides and area are named "Heron triangles." The Indian mathematician Brahmagupta, born in…

Opening Real Science: Evaluation of an Online Module on Statistical Literacy for Pre-Service Primary Teachers

ERIC Educational Resources Information Center

Bilgin, Ayse Aysin Bombaci; Date-Huxtable, Elizabeth; Coady, Carmel; Geiger, Vincent; Cavanagh, Michael; Mulligan, Joanne; Petocz, Peter

2017-01-01

Opening Real Science (ORS) is a three-year government initiative developed as part of the Mathematics and Science Teachers program. It is a collaboration across universities involving teacher educators, scientists, mathematicians, statisticians and educational designers aimed at improving primary and secondary pre-service teachers' competence and…

The Mathematics of High School Physics: Models, Symbols, Algorithmic Operations and Meaning

ERIC Educational Resources Information Center

Kanderakis, Nikos

2016-01-01

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…

Creating Mathematicians and Scientists: Disciplinary Literacy in the Early Childhood Classroom

ERIC Educational Resources Information Center

Mongillo, Maria Boeke

2017-01-01

Disciplinary literacy focuses on the specific ways a content area thinks, uses language, and shares information. While much of the literature on disciplinary literacy suggests it is an advanced language strategy to be taught to secondary students, early childhood classrooms may be the ideal environment in which to introduce this type of…

Castelli, Benedetto (1578-1643)

NASA Astrophysics Data System (ADS)

Murdin, P.

2000-11-01

Mathematician, born in Brescia, Italy, Benedictine monk, professor at Padua. GALILEO's closest scientific collaborator, he defended, and edited Galileo, he helped his sunspot research, inventing the method of projection so as to view safely the Sun's image with a telescope. His book on hydraulics, Della Misura dell'Acque Correnti, or On the Measurement of Running Waters, founded modern hydrodynam...

An Evaluation of Student Team Teaching in Sophomore Physics Classes. Final Report.

ERIC Educational Resources Information Center

Thrasher, Paul H.

In the present document the effectiveness of a student team teaching technique is evaluated in comparison with the lecture method. The team teaching technique, previously used for upper division and graduate physics courses, was, for this study, used in a sophomore physics, electricity and magnetism course for engineers, mathematicians, chemists,…

Educated in Romance. Women, Achievement, and College Culture.

ERIC Educational Resources Information Center

Holland, Dorothy C.; Eisenhart, Margaret A.

This ethnographic study investigated why so few women become scientists or mathematicians. The study followed the lives of two groups of women, one black and one white, all with strong academic records, who were attending two southern U.S. universities, one predominantly black and the other predominantly white. The study was initiated in 1979 when…

Selected Issues Facing U.S. Graduate Education.

ERIC Educational Resources Information Center

Neal, Homer A.

Three issues are discussed that relate to (1) the need for the United States to become more technologically competitive and more daring in ways to produce, nurture and encourage high quality research and (2) the state of the talent pool that must produce the scientists, mathematicians and engineers to do this research. The first issue concerns…

Designing Online Learning for Developing Pre-Service Teachers' Capabilities in Mathematical Modelling and Applications

ERIC Educational Resources Information Center

Geiger, Vince; Date-Huxtable, Liz; Ahlip, Rehez; Herberstein, Marie; Jones, D. Heath; May, E. Julian; Rylands, Leanne; Wright, Ian; Mulligan, Joanne

2016-01-01

The purpose of this paper is to describe the processes utilised to develop an online learning module within the Opening Real Science (ORS) project--"Modelling the present: Predicting the future." The module was realised through an interdisciplinary collaboration, among mathematicians, scientists and mathematics and science educators that…

A Combinatorics Course with One Goal: Authentic Mathematical Inquiry

ERIC Educational Resources Information Center

Storm, Christopher

2017-01-01

This article shares an example of a course in Combinatorics, taught at Adelphi University in Fall 2012, designed with a primary goal of engaging students in pursuing mathematics as mathematicians do. The course went beyond usual applications of inquiry-based learning in that students were also charged with the responsibility of posing the…

Learning to Teach--Gill's Story

ERIC Educational Resources Information Center

Hatch, Gill; Rowland, Tim

2006-01-01

Gill Hatch was a very fine mathematician. Indeed, following her undergraduate studies in Cambridge in the late 1950s, she was one of the elite who went on to the notoriously difficult Part III of the Mathematical Tripos. In this article, the author describes the autobiographical accounts of Hatch during her teaching career in teacher education, as…

Thinking in Patterns to Solve Multiplication, Division, and Fraction Problems in Second Grade

ERIC Educational Resources Information Center

Stokes, Patricia D.

2016-01-01

Experts think in patterns and structures using the specific "language" of their domains. For mathematicians, these patterns and structures are represented by numbers, symbols and their relationships (Stokes, 2014a). To determine whether elementary students in the United States could learn to think in mathematical patterns to solve…

Typology of Perfectionism in a Group of Mathematically Gifted Czech Adolescents over One Decade

ERIC Educational Resources Information Center

Portešová, Šárka; Urbánek, Tomáš

2013-01-01

This study assessed differences in Parker's typology of perfectionism (healthy perfectionist, unhealthy perfectionist, and nonperfectionist). We compared the results from previous research with follow-up 2005 and 2010 data collected from highly gifted Czech mathematicians aged 12 to 16 years. The study examined whether the same three…

A Moving Tale

ERIC Educational Resources Information Center

Science Teacher, 2005

2005-01-01

Massachusetts Institute of Technology (MIT) mathematicians have discovered how certain insects can climb what to them are steep, slippery slopes in the water's surface without moving their limbs, and do it at high speed. Welcome to the world of the tiny creatures that live on the surface of ponds, lakes, and other standing bodies of water. For the…

Playing around in Lewis Carroll's "Alice" Books

ERIC Educational Resources Information Center

Susina, Jan

2010-01-01

Mathematician Charles Dodgson's love of play and his need for rules came together in his use of popular games as part of the structure of the two famous children's books, "Alice in Wonderland" and "Through the Looking-Glass," he wrote under the pseudonym Lewis Carroll. The author of this article looks at the interplay between…

Centenary Birth Anniversary of E. W. Beth (1908-1964)

ERIC Educational Resources Information Center

Bagni, Giorgio T.

2008-01-01

Evert Willem Beth (1908-1964) was a Dutch logician, mathematician and philosopher, whose work mainly concerned the foundations of mathematics. Beth was among the founders of the Commission Internationale pour l'Etude et l'Amelioration de l'Enseignement des Mathematiques and was a member of the Central Committee of the International Commission on…

The Geometric Construction Abilities of Gifted Students in Solving Real-World Problems: A Case from Turkey

ERIC Educational Resources Information Center

Yildiz, Avni

2016-01-01

Geometric constructions have already been of interest to mathematicians. However, studies on geometric construction are not adequate in the relevant literature. Moreover, these studies generally focus on how secondary school gifted students solve non-routine mathematical problems. The present study aims to examine the geometric construction…

Ghosts of Mathematicians Past: Bharati Krishna and Gabriel Cramer

ERIC Educational Resources Information Center

Fitzherbert, John

2017-01-01

Jagadguru Shankaracharya Swami Bharati Krishna Tirtha (commonly abbreviated to Bharati Krishna) was a scholar who studied ancient Indian Veda texts and between 1911 and 1918 (vedicmaths.org, n.d.) and wrote a collection of 16 major rules and a number of minor rules which have collectively become known as the "sutras of Vedic…

Ghosts of Mathematicians Past: Paolo Ruffini

ERIC Educational Resources Information Center

Fitzherbert, John

2016-01-01

Paolo Ruffini (1765-1822) may be something of an unknown in high school mathematics; however his contributions to the world of mathematics are a rich source of inspiration. Ruffini's rule (often known as "synthetic division") is an efficient method of dividing a polynomial by a linear factor, with or without a remainder. The process can…

Triple Play: From De Morgan to Stirling to Euler to Maclaurin to Stirling

ERIC Educational Resources Information Center

Kolpas, Sid

2011-01-01

Augustus De Morgan (1806-1871) was a significant Victorian Mathematician who made contributions to mathematics history, mathematical recreations, mathematical logic, calculus, and probability and statistics. He was an inspiring mathematics professor who influenced many of his students to join the profession. One of De Morgan's significant books…

Case Studies of the Urban Mathematics Collaborative Project: Program Report 91-3.

ERIC Educational Resources Information Center

Popkewitz, Thomas S.; Myrdal, Sigurjon

The Urban Mathematics Collaborative (UMC) project has the goal of contributing to the improvement of mathematics education in the inner-city schools by identifying models to enhance the professional lives of teachers and encouraging the entry of high school mathematics teachers into a larger mathematics community including mathematicians from…

Let's Keep the College in Our Community Colleges: Mathematics for College Transfer.

ERIC Educational Resources Information Center

Curnutt, Larry

Preparing students for transfer to four-year colleges remains a significant part of the mission of most community college mathematicians. For some 30 years, calculus has been synonymous with entry-level college mathematics. Recent educational and technological changes, however, demand that the definition of college-level work in mathematics be…

The National Defense Education Act, Current STEM Initiative, and the Gifted

ERIC Educational Resources Information Center

Jolly, Jennifer L.

2009-01-01

During the past several years, much discussion has focused on developing America's future scientists, technologists, engineers, and mathematicians (STEM) in order to remain viable and competitive in a growing global economy. In retrospect, America has had a long-standing involvement with STEM issues that dates back to the establishment of West…

Mathematics Undergraduates' Responses to Semantic Abbreviations, 'Geometric' Images and Multi-Level Abstractions in Group Theory.

ERIC Educational Resources Information Center

Nardi, Elena

2000-01-01

Identifies and explores the difficulties in the novice mathematician's encounter with mathematical abstraction. Observes 20 first-year mathematics undergraduates and extracts sets of episodes from the transcripts of the tutorials and interviews within five topics in pure mathematics. Discusses issues related to the learning of one mathematical…

The Nature of Mathematics: A Heuristic Inquiry

ERIC Educational Resources Information Center

Pair, Jeffrey David

2017-01-01

What is mathematics? What does it mean to be a mathematician? What should students understand about the nature of mathematical knowledge and inquiry? Research in the field of mathematics education has found that students often have naive views about the nature of mathematics. Some believe that mathematics is a body of unchanging knowledge, a…

The Remarkable Number "1"

ERIC Educational Resources Information Center

Allen, G. Donald

2014-01-01

In human history, the origin of the numbers came from definite practical needs. Indeed, there is strong evidence that numbers were created before writing. The number "1", dating back at least 20,000 years, was found as a counting symbol on a bone. The famous statement by the German mathematician Leopold Kronecker (1823-1891), "God…

A Geometric Puzzle That Leads To Fibonacci Sequences.

ERIC Educational Resources Information Center

Rulf, Benjamin

1998-01-01

Illustrates how mathematicians work and do mathematical research through the use of a puzzle. Demonstrates how general rules, then theorems develop from special cases. This approach may be used as a research project in high school classrooms or math club settings with the teacher helping to formulate questions, set goals, and avoid becoming…

[Georg Joachim Rhetikus, between Paracelsus and Copernicus].

PubMed

Burmeister, K H

2000-01-01

At first the author presents the familial background of Rheticus, then his education, his friendships and scientific contacts. Rheticus was professor of university in Wittenberg and Leipzig. Most interesting were his contacts with Paracelsus and Copernicus. Last two decades of life Rheticus spent in Cracow working as a physician and mathematician. He died in Kosice.

An Assessment of Ada’s Suitability in General Purpose Programming Applications.

DTIC Science & Technology

1985-09-01

selected to honor the mathematician Lady Augusta Ada Byron (1815-1852), Countess of Lovelace. The Countess worked with Charles Babbage on his difference...stray from our research objectives. We would also like to thank Dr. Charles Richard for the assistance he gave us while learning the Ada language

David Gale: Restless Pioneer

ERIC Educational Resources Information Center

Meyer, Walter

2006-01-01

David Gale was one of the mathematicians responsible for the modern form of the theory of duality in linear programming and the associated proof of the minimax theorem in the theory of games. He is a member of the National Academy of Sciences and is Professor Emeritus of Mathematics and Operations Research at the University of California at…

Scientists and Mathematicians Collaborating to Build Quantitative Skills in Undergraduate Science

ERIC Educational Resources Information Center

Rylands, Leanne; Simbag, Vilma; Matthews, Kelly E.; Coady, Carmel; Belward, Shaun

2013-01-01

There is general agreement in Australia and beyond that quantitative skills (QS) in science, the ability to use mathematics and statistics in context, are important for science. QS in the life sciences are becoming ever more important as these sciences become more quantitative. Consequently, undergraduates studying the life sciences require better…

Mathematical History: Activities, Puzzles, Stories, and Games.

ERIC Educational Resources Information Center

Mitchell, Merle

Based on the history of mathematics, these materials have been planned to enrich the teaching of mathematics in grades four, five, and six. Puzzles and games are based on stories about topics such as famous mathematicians, numerals of ancient peoples, and numerology. The sheets are arranged by grade level and are designed for easy duplication.…

Creativity from Two Perspectives: Prospective Mathematics Teachers and Mathematician

ERIC Educational Resources Information Center

Yazgan-Sag, Gönül; Emre-Akdogan, Elçin

2016-01-01

Although creativity plays a critical role in mathematics, it remains underestimated in the context of a mathematics classroom. This study aims to explore the views and differences creativity displays in prospective teachers and one of their lecturers with respect to the characteristics and practices of creative teachers and the characteristics of…

Art-Integration through Making Dioramas of Women Mathematicians' Lives Enhances Creativity and Motivation

ERIC Educational Resources Information Center

Rule, Audrey C.; Atwood-Blaine, Dana; Edwards, Clayton M.; Gordon, Mindy M.

2016-01-01

Creativity is essential for solving problems in the workplace, natural environment, and everyday life, necessitating that creativity be nurtured in schools. Identification of factors that intrinsically motivate students to learn difficult or initially unappealing content is also important. This project, in which 24 racially diverse fifth grade…

Mathematics Education in Rural Communities: A Mathematician's View. Working Paper Series.

ERIC Educational Resources Information Center

Mahoney, Carolyn R.

Elizabeth City State University (ECSU) serves the 21 counties of rural northeastern North Carolina. In Fall 2000 ECSU administrators met with educators in area school districts to discuss their professional development needs. This paper reports on those expressed needs relevant to mathematics education and discusses ways to help achieve excellence…

A Phenomenological Exploration of Mathematical Engagement: Approaching an Old Metaphor Anew.

ERIC Educational Resources Information Center

Handa, Yuichi

2003-01-01

Investigates the heart of the experience of mathematical engagement and the meaning derived from such activities. Analyzes dialogue between five people, two of whom are professional mathematicians, another two who are graduate students in either engineering or education, and one who lacks advanced mathematical training but maintains a positive…

Estimating Earth's Circumference with an App

ERIC Educational Resources Information Center

Cooper, Linda; Dennis, Emily

2016-01-01

More than 2,200 years ago, Eratosthenes, who was a Greek astronomer, geographer, and mathematician, used a simple proportion involving the distance between two ancient cities and measures of shadows cast in those cities during a summer solstice to estimate the circumference of Earth (Nicastro 2008, 25-28). Today, middle school students can use…

Imagining Complex Numbers by Generating, Interpreting and Representing Them

ERIC Educational Resources Information Center

Vozzo, Enzo

2017-01-01

Ever since their serendipitous discovery by Italian mathematicians trying to solve cubic equations in the 16th century, imaginary and complex numbers have been difficult topics to understand. Here the word complex is used to describe something consisting of a number of interconnecting parts. The different parts of a complex number are the…

Integrating Literacy, Math, and Science to Make Learning Come Alive

ERIC Educational Resources Information Center

Bintz, William P.; Moore, Sara D.; Hayhurst, Elaine; Jones, Rubin; Tuttle, Sherry

2006-01-01

In this article, the authors who are an interdisciplinary team of middle school educators collaboratively developed and implemented an interdisciplinary unit designed to help middle school students: (1) think like mathematicians and scientists; (2) develop specific areas of expertise in math and science; and (3) use literature as a tool to learn…

Basic and Advanced Numerical Performances Relate to Mathematical Expertise but Are Fully Mediated by Visuospatial Skills

ERIC Educational Resources Information Center

Sella, Francesco; Sader, Elie; Lolliot, Simon; Cohen Kadosh, Roi

2016-01-01

Recent studies have highlighted the potential role of basic numerical processing in the acquisition of numerical and mathematical competences. However, it is debated whether high-level numerical skills and mathematics depends specifically on basic numerical representations. In this study mathematicians and nonmathematicians performed a basic…

Decisions, Decisions, Decisions: What Determines the Path Taken in Lectures?

ERIC Educational Resources Information Center

Paterson, Judy; Thomas, Mike; Taylor, Steve

2011-01-01

A group of mathematicians and mathematics educators are collaborating in the fine-grained examination of selected "slices" of video recordings of lectures, drawing on Schoenfeld's Resources, Orientations and Goals framework of teaching-in-context. In the larger project, we are exploring ways in which this model can be extended to examine…

Inventing (in) Early Geometry, or How Creativity Inheres in the Doing of Mathematics

ERIC Educational Resources Information Center

Maheux, Jean-François; Roth, Wolf-Michael

2015-01-01

Inventing is fundamental to mathematical activity, should one be a professional mathematician or a primary school student. Research on mathematical creativity generally is organized along three axes according to its focus on the final product, the overall process, or the individual person. Through these conceptualizations, however, research rarely…

Mathematicians in Schools: Uncovering Maths' Beautiful Secrets

ERIC Educational Resources Information Center

Welch, Bronwyn

2016-01-01

Mathematics professionals are working with teachers revealing the reality and beauty that happens in the world of math and to show that this is essentially a "human endeavour," embedded in much of what people do and the ways in which they think. In this article, the author shares vignettes of primary classes working with mathematicians…

The Common Core State Standards for Mathematics and College Readiness

ERIC Educational Resources Information Center

Kamin, David C.

2016-01-01

The Common Core State Standards were created with college and career readiness in mind to help prepare students to succeed upon graduation from high school. In this article, I examine college readiness as it has been described by both university mathematicians and educational researchers to precisely discern what will foster success in collegiate…

Mathematical Foresight: Thinking in the Future to Work in the Present

ERIC Educational Resources Information Center

Maciejewski, Wes; Barton, Bill

2016-01-01

Originating from interviews with mathematics colleagues, written accounts of mathematicians engaging with mathematics, and Wes's reflections on his own mathematical work, we describe a process that we call mathematical foresight: the imagining of a resolution to a mathematical situation and a path to that resolution. In a sense, mathematical…

Analysing the Mathematical Experience: Posing the "What Is Mathematics?" Question

ERIC Educational Resources Information Center

Padula, Janice

2011-01-01

In this paper, different schools of thought are discussed and compared to encourage lively classroom discussion and interest in mathematics for high achieving Form 12 students and first (or higher) year university students enrolled in a mathematics degree program. In particular the work and views of two mathematicians, Kurt Godel (1931) and Ian…

A Mathematician Learns the Basics of Writing Instruction: An Immersion Experience with Long-Term Benefits

ERIC Educational Resources Information Center

Doty, Lynne L.

2012-01-01

Initially designed to be an interdisciplinary experiment that would change attitudes about mathematics, the semester-long collaboration between a writing instructor and a mathematics instructor yielded unexpected long-term results. The collaboration served as an immersion in methods and techniques used by writing instructors. Description of…

Accommodation in the Formal World of Mathematical Thinking

ERIC Educational Resources Information Center

Stewart, Sepideh; Schmidt, Ralf

2017-01-01

In this study, we examined a mathematician and one of his students' teaching journals and thought processes concurrently as the class was moving towards the proof of the Fundamental Theorem of Galois Theory. We employed Tall's framework of three worlds of mathematical thinking as well as Piaget's notion of accommodation to theoretically study the…

Integral Students' Experiences: Measuring Instructional Quality and Instructors' Challenges in Calculus 1 Lessons

ERIC Educational Resources Information Center

Hong, Dae S.; Choi, Kyong Mi; Hwang, Jihyun; Runnalls, Cristina

2017-01-01

In this study, we examined 10 integral lessons to understand students' opportunities to learn cognitively challenging tasks and maintain cognitive demand during integral lessons. Our findings reveal issues with implemented tasks as well as the way these tasks were presented to students. We also examined mathematicians' reasons behind their…

What Is "Repeated Reasoning" in MP 8?

ERIC Educational Resources Information Center

Goldenberg, E. Paul; Carter, Cynthia J.; Mark, June; Nikula, Johannah; Spencer, Deborah B.

2017-01-01

The Common Core State Standards (CCSSI 2010) for Mathematical Practice have relevance even for those not in CCSS states because they describe the habits of mind that mathematicians--professionals as well as proficient school-age learners--use when doing mathematics. They provide a language to discuss aspects of mathematical practice that are of…

Women in Mathematics: A Nested Approach

ERIC Educational Resources Information Center

Köse, Emek; Johnson, Angela C.

2016-01-01

In this article, we present a case study of a course called Women in Mathematics. Students in the course studied the lives and the mathematical contributions of women mathematicians throughout history, as well as current gender equity issues in the study of mathematics and in mathematical careers. They also mentored 20 middle school girls…

Fractals and Chaos

DTIC Science & Technology

1991-06-01

22 C. AFFINE TRANSFORMATIONS OF THE PLANE ........................... 25 D. CONTRACTION MAPPINGS OF THE SPACE gi(X...Henri Poincare (1854-1912) knew about chaos in dynamical systems in the late nineteenth century. Additionally, the French mathematicians Pierre Fatou...portion) are presented in the Euclidean plane , with a brief mention of more abstract spaces where applicable. Mathematical proofs that can be

Latin and Cross Latin Squares

ERIC Educational Resources Information Center

Emanouilidis, Emanuel

2008-01-01

Latin squares were first introduced and studied by the famous mathematician Leonhard Euler in the 1700s. Through the years, Latin squares have been used in areas such as statistics, graph theory, coding theory, the generation of random numbers as well as in the design and analysis of experiments. Recently, with the international popularity of…

Emphasizing Language and Visualization in Teaching Linear Algebra

ERIC Educational Resources Information Center

Hannah, John; Stewart, Sepideh; Thomas, Mike

2013-01-01

Linear algebra with its rich theoretical nature is a first step towards advanced mathematical thinking for many undergraduate students. In this paper, we consider the teaching approach of an experienced mathematician as he attempts to engage his students with the key ideas embedded in a second-year course in linear algebra. We describe his…

Solving Cubic Equations by Polynomial Decomposition

ERIC Educational Resources Information Center

Kulkarni, Raghavendra G.

2011-01-01

Several mathematicians struggled to solve cubic equations, and in 1515 Scipione del Ferro reportedly solved the cubic while participating in a local mathematical contest, but did not bother to publish his method. Then it was Cardano (1539) who first published the solution to the general cubic equation in his book "The Great Art, or, The Rules of…

Paul Erdos

ERIC Educational Resources Information Center

Monroe, Helen; Scott, Paul

2004-01-01

This article presents a brief biography of Paul Erdos, who focused on problem-solving, particularly in the areas of number theory, combinatorics and graph theory. During his life he had no property, no family and no fixed address. He buttered his first piece of bread at age 21. He never cooked, nor ever drove a car. Another mathematician, Ron…

Conference Board of the Mathematical Sciences Newsletter, Volume 8, Number 4.

ERIC Educational Resources Information Center

Botts, Truman, Ed.

Among the articles in this newsletter are discussions concerning the employment of mathematicians in industry and questioning the necessity of some of the present doctoral programs in the mathematical sciences. Other articles include details of the organization and the members of the Policy Council of the National Institute of Education and a…

Loving and Loathing: Portrayals of School Mathematics in Young Adult Fiction

ERIC Educational Resources Information Center

Darragh, Lisa

2018-01-01

Images of mathematics and mathematicians are often negative and stereotyped. These portrayals may work to construct our impressions of mathematics and influence students' identity with and future participation in the subject. This study examined young adult fiction as a context in which school mathematics is portrayed and constructed. I used…

Investigation of Probability Distributions Using Dice Rolling Simulation

ERIC Educational Resources Information Center

Lukac, Stanislav; Engel, Radovan

2010-01-01

Dice are considered one of the oldest gambling devices and thus many mathematicians have been interested in various dice gambling games in the past. Dice have been used to teach probability, and dice rolls can be effectively simulated using technology. The National Council of Teachers of Mathematics (NCTM) recommends that teachers use simulations…

Number Wonders: 171 Activities to Meet Math Standards & Inspire Students

ERIC Educational Resources Information Center

Kuhns, Catherine Jones

2006-01-01

In this book, author Catherine Jones Kuhns introduces student- and teacher-friendly math activities designed to get students thinking like mathematicians and loving mathematics, while addressing content standards through grade 2. She also shows how to make math fun for students, get children actively engaged in learning, create a student-centered…

Romance of a Mathematician: Celebrating St Valentine's Day in a Mathematics Class

ERIC Educational Resources Information Center

Hekimoglu, Serkan

2005-01-01

Mathematics should not be studied simply because it is useful; mathematics should be also studied because it nurtures both the mind and soul with its beauty. By completing the four activities described in this paper, students will appreciate mathematical ideas both rationally and emotionally. Since students' appreciation of mathematical ideas…

Bell-Boole Inequality: Nonlocality or Probabilistic Incompatibility of Random Variables?

NASA Astrophysics Data System (ADS)

Khrennikov, Andrei

2008-06-01

The main aim of this report is to inform the quantum information community about investigations on the problem of probabilistic compatibility of a family of random variables: a possibility to realize such a family on the basis of a single probability measure (to construct a single Kolmogorov probability space). These investigations were started hundred of years ago by J. Boole (who invented Boolean algebras). The complete solution of the problem was obtained by Soviet mathematician Vorobjev in 60th. Surprisingly probabilists and statisticians obtained inequalities for probabilities and correlations among which one can find the famous Bell’s inequality and its generalizations. Such inequalities appeared simply as constraints for probabilistic compatibility. In this framework one can not see a priori any link to such problems as nonlocality and “death of reality” which are typically linked to Bell’s type inequalities in physical literature. We analyze the difference between positions of mathematicians and quantum physicists. In particular, we found that one of the most reasonable explanations of probabilistic incompatibility is mixing in Bell’s type inequalities statistical data from a number of experiments performed under different experimental contexts.

GeoGebra: A Global Platform for Teaching and Learning Math Together and Using the Synergy of Mathematicians

NASA Astrophysics Data System (ADS)

Kllogjeri, Pellumb

In present age we are witnesses and practioners of computer-based education which is highly speed progressing. The computer-based education allows educators and students to use educational programming language and e-tutors to teach and learn, to interact with one another and share together the results of their work. The computer-based education is done possible by special electronic tools among which the most important are the mathematical programmes. There are many mathematical programmes, but one which is being embraced and used by a daily increasing number of users throughout the world is GeoGebra. The recently published software GeoGebra by Markus Hohenwater (2004) explicitly links geometry and algebra. GeoGebra affords a bidirectional combination of geometry and algebra that differs from earlier software forms. The bidirectional combination means that, for instance, by typing in an equation in the algebra window, the graph of the equation will be shown in the dynamic and graphic window. This programme is so much preferred because of its three main features: the double representation of the mathematical object(geometric and algebraic), there are not strong requirements as to the age and the knowledge in using it(the students of the elementary school can use it as well) and, it is offered free of charge(simply by downloading it). In this paper we are concentrating in the double representation of the mathematical object and its advantages in explaining and forming mathematical concepts and performing operations, in the global opportunities for using GeoGebra and the benefits of using it by cooperating and sharing experiences.

Langley Centennial Celebration Highlights Hidden Figures on This Week @NASA – December 2, 2016

NASA Image and Video Library

2016-12-02

On Dec. 1, NASA Administrator Charlie Bolden helped kick off a yearlong centennial celebration for the agency’s Langley Research Center in Hampton, Virginia with several events highlighting the work of the African American women of Langley’s West Computing Unit. These mathematicians performed critical calculations for several historic NASA space missions in the early days of America’s space program, and their story is told in the book, “Hidden Figures,” by author Margot Lee Shetterly and the upcoming 20th Century Fox movie of the same name. It was also discussed during a NASA education event at Langley featuring Bolden, the film’s director Ted Melfi, NASA’s Chief Historian Bill Barry, and Langley electro-optics engineer Julie Williams-Byrd – a modern-day NASA figure using science, technology, engineering and mathematics, or STEM -- skills to make an impact. Later that evening, a VIP social and screenings of the film took place at nearby Virginia Air & Space Center. The women featured in Hidden Figures – Katherine Johnson, Mary Jackson and Dorothy Vaughan – known as “human computers,” helped put John Glenn in orbit, and helped Neil Armstrong and other astronauts land on the moon. Also, Cassini’s Ring-Grazing Orbit around Saturn, Next Space Station Crew Previews Mission, and Russian Cargo Ship Experiences Anomaly after Launch!

Mathematics and biology: The interface, challenges and opportunities

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

Levin, S.A.

1992-06-01

The interface between mathematics and biology has long been a rich area of research, with mutual benefit to each supporting discipline. Traditional areas of investigation, such as population genetics, ecology, neurobiology, and 3-D reconstructions, have flourished, despite a rather meager environment for the funding of such work. In the past twenty years, the kind and scope of such interactions between mathematicians and biologists have changed dramatically, reaching out to encompass areas of both biology and mathematics that previously had not benefited. At the same time, with the closer integration of theory and experiment, and the increased reliance on high-speed computation,more » the costs of such research grew, though not the opportunities for funding. The perception became reinforced, both within the research community and at funding agencies, that although these interactions were expanding, they were not doing so at the rate necessary to meet the opportunities and needs. A workshop was held in Washington, DC, between April 28 and May 3, 1990 which drew together a broadly based group of researchers to synthesize conclusions from a group of working papers and extended discussions. The result is the report presented here, which we hope will provide a guide and stimulus to research in mathematical and computational biology for at least the next decade. The report identifies a number of grand challenges, representing a broad consensus among the participants.« less

The Role of Mathematical Models in Understanding Pattern Formation in Developmental Biology

PubMed Central

Umulis, David M.

2016-01-01

In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics—whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: “It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations.” This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, “The laws of Nature are written in the language of mathematics…the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word.” Mathematics has moved beyond the geometry-based model of Galileo’s time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837–838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades—that of how organisms can scale in size. Mathematical analysis alone cannot “solve” these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology. PMID:25280665

Nanotechnology: A Vast Field for the Creative Mind

NASA Technical Reports Server (NTRS)

Benavides, Jeannette

2003-01-01

Nanotechnology is a rapidly developing field worldwide. Nanotechnology is the development of smart systems for many different applications by building from the molecular level up. Current research, sponsored by The National Nanotechnology Alliance in the US will be described. Future needs in manpower of different disciplines will be discussed. Nanotechnology is a field of research that could allow developing countries to establish a technological infrastructure. The nature of nanotechnology requires professionals in many areas, such as engineers, chemists, physicists, mathematicians, computer scientists, materials scientists, etc. One of the materials that provide unique properties for nanotechnology is carbon nanotubes. At Goddard we have develop a process to produce nanotubes at lower costs and without metal catalysts which will be of great importance for the development of new materials for space applications and others outside NASA. Nanotechnology in general is a very broad and exciting field that will provide the technologies of tomorrow including biomedical applications for the betterment of mankind. There is room in this area for many researchers all over the world. The key is collaboration, nationally and internationally.

Macmillan Encyclopedia of Chemistry (edited by Joseph J. Lagowski)

NASA Astrophysics Data System (ADS)

Kauffman, George B.

1998-11-01

Macmillan: New York, 1997. Four volumes. Figs., tables. lxxi + 1696 pp. 22.0 x 28.5 cm. $400. ISBN 0-02-897225-2. This latest addition to Macmillan's series of comprehensive core science encyclopedias (previous sets dealt with physics and earth sciences) will be of particular interest to readers of this Journal, for it is edited by longtime Journal of Chemical Education editor Joe Lagowski, assisted by a board of five distinguished associate editors. The attractively priced set offers clear explanations of the phenomena and concepts of chemistry and its materials, whether found in industry, the laboratory, or the natural world. It is intended for a broad spectrum of readers-professionals whose work draws on chemical concepts and knowledge (e.g., material scientists, engineers, health workers, biotechnologists, mathematicians, and computer programmers), science teachers at all levels from kindergarten to high school, high school and college students interested in medicine or the sciences, college and university professors, and laypersons desiring information on practical aspects of chemistry (e.g., household cleaning products, food and food additives, manufactured materials, herbicides, the human body, sweeteners, and animal communication).

"Machine" consciousness and "artificial" thought: an operational architectonics model guided approach.

PubMed

Fingelkurts, Andrew A; Fingelkurts, Alexander A; Neves, Carlos F H

2012-01-05

Instead of using low-level neurophysiology mimicking and exploratory programming methods commonly used in the machine consciousness field, the hierarchical operational architectonics (OA) framework of brain and mind functioning proposes an alternative conceptual-theoretical framework as a new direction in the area of model-driven machine (robot) consciousness engineering. The unified brain-mind theoretical OA model explicitly captures (though in an informal way) the basic essence of brain functional architecture, which indeed constitutes a theory of consciousness. The OA describes the neurophysiological basis of the phenomenal level of brain organization. In this context the problem of producing man-made "machine" consciousness and "artificial" thought is a matter of duplicating all levels of the operational architectonics hierarchy (with its inherent rules and mechanisms) found in the brain electromagnetic field. We hope that the conceptual-theoretical framework described in this paper will stimulate the interest of mathematicians and/or computer scientists to abstract and formalize principles of hierarchy of brain operations which are the building blocks for phenomenal consciousness and thought. Copyright © 2010 Elsevier B.V. All rights reserved.

Magellan 3D perspective of Venus surface in western Eistla Regio

NASA Technical Reports Server (NTRS)

1991-01-01

Magellan synthetic aperture radar data was used to create this three- dimensional (3D) perspective view of Venus' western Eistla Regio. This viewpoint is located at 1,310 kilometers (812 miles) southwest of Gula Mons at an elevation of 0.178 kilometers (0.48 miles). The view is of the northeast with Gula Mons appearing on the horizon. Gula Mons, a 3 kilometer (1.86 mile) high volcano, is located at approximately 22 degrees north latitude, 359 degrees east longitude. The impact crater Cunitz, named for the astronomer and mathematician Maria Cunitz, is visible in the center of the image. The crater is 48.5 kilometers (30 miles) in diameter and is 215 kilometers (133 miles) from the viewer's position. Magellan synthetic aperture radar data is combined with radar altimetry to develop a 3D map of the surface. Rays cast in a computer intersect the surface to create a 3D view. Simulated color and a digital elevation map developed by the United States (U.S.) Geological Survey is used to enhanc

ISMB/ECCB 2009 Stockholm

PubMed Central

Sagot, Marie-France; McKay, B.J. Morrison; Myers, Gene

2009-01-01

The International Society for Computational Biology (ISCB; http://www.iscb.org) presents the Seventeenth Annual International Conference on Intelligent Systems for Molecular Biology (ISMB), organized jointly with the Eighth Annual European Conference on Computational Biology (ECCB; http://bioinf.mpi-inf.mpg.de/conferences/eccb/eccb.htm), in Stockholm, Sweden, 27 June to 2 July 2009. The organizers are putting the finishing touches on the year's premier computational biology conference, with an expected attendance of 1400 computer scientists, mathematicians, statisticians, biologists and scientists from other disciplines related to and reliant on this multi-disciplinary science. ISMB/ECCB 2009 (http://www.iscb.org/ismbeccb2009/) follows the framework introduced at the ISMB/ECCB 2007 (http://www.iscb.org/ismbeccb2007/) in Vienna, and further refined at the ISMB 2008 (http://www.iscb.org/ismb2008/) in Toronto; a framework developed to specifically encourage increased participation from often under-represented disciplines at conferences on computational biology. During the main ISMB conference dates of 29 June to 2 July, keynote talks from highly regarded scientists, including ISCB Award winners, are the featured presentations that bring all attendees together twice a day. The remainder of each day offers a carefully balanced selection of parallel sessions to choose from: proceedings papers, special sessions on emerging topics, highlights of the past year's published research, special interest group meetings, technology demonstrations, workshops and several unique sessions of value to the broad audience of students, faculty and industry researchers. Several hundred posters displayed for the duration of the conference has become a standard of the ISMB and ECCB conference series, and an extensive commercial exhibition showcases the latest bioinformatics publications, software, hardware and services available on the market today. The main conference is preceded by 2 days of Special Interest Group (SIG) and Satellite meetings running in parallel to the fifth Student Council Symposium on 27 June, and in parallel to Tutorials on 28 June. All scientific sessions take place at the Stockholmsmässan/Stockholm International Fairs conference and exposition facility. Contact: bj@iscb.org PMID:19447790

A Short History of the Fibonacci and Golden Numbers with Their Applications

ERIC Educational Resources Information Center

Debnath, Lokenath

2011-01-01

This article deals with a brief history of Fibonacci's life and career. It includes Fibonacci's major mathematical discoveries to establish that he was undoubtedly one of the most brilliant mathematicians of the Medieval Period. Special attention is given to the Fibonacci numbers, the golden number and the Lucas numbers and their fundamental…

Euler and His Contribution Number Theory

ERIC Educational Resources Information Center

Len, Amy; Scott, Paul

2004-01-01

Born in 1707, Leonhard Euler was the son of a Protestant minister from the vicinity of Basel, Switzerland. With the aim of pursuing a career in theology, Euler entered the University of Basel at the age of thirteen, where he was tutored in mathematics by Johann Bernoulli (of the famous Bernoulli family of mathematicians). He developed an interest…

A Different Perspective of the Teaching Philosophy of RL Moore

ERIC Educational Resources Information Center

Jones, Stephen L.

2017-01-01

Dr RL Moore was undoubtedly one of the finest mathematics teachers ever. He developed a unique teaching method designed to teach his students to think like mathematicians. His method was not designed to convey any particular mathematical knowledge. Instead, it was designed to teach his students to think. Today, his method has been modified to…

Some Cosine Relations and the Regular Heptagon

ERIC Educational Resources Information Center

Osler, Thomas J.; Heng, Phongthong

2007-01-01

The ancient Greek mathematicians sought to construct, by use of straight edge and compass only, all regular polygons. They had no difficulty with regular polygons having 3, 4, 5 and 6 sides, but the 7-sided heptagon eluded all their attempts. In this article, the authors discuss some cosine relations and the regular heptagon. (Contains 1 figure.)

TEACHING OF ADVANCED MATHEMATICAL CONCEPTS TO CULTURALLY DISADVANTAGED ELEMENTARY SCHOOL CHILDREN.

ERIC Educational Resources Information Center

RUPLEY, WILLIAM H.

THE SUCCESS OF DISCOVERY MATHEMATICS TEACHING IN THE ELEMENTARY SCHOOL WAS TESTED OVER A 1-YEAR PERIOD. THE PROJECT WAS INTENDED TO SEE IF A TRAINED MATHEMATICIAN WORKING AT AN ELEMENTARY SCHOOL WITH DISADVANTAGED CHILDREN COULD (1) MOTIVATE THE CHILDREN TO BE INTERESTED IN SCHOOL WORK BY INTERESTING THEM IN MATHEMATICS AND (2) COMMUNICATE WITH…

Cross National Comparisons of Excellence in University Mathematics Instructors

ERIC Educational Resources Information Center

Grant, Frida

2014-01-01

Mathematicians have, historically, not been overly successful in their approach to teaching and much research has looked in to why this is so. Teaching mathematics is based on a solid understanding of the subject; however, instructors also need to be able to efficiently communicate the subject to their students. The purpose of this study was to…

Mathematical Discovery and "Affect": The "Effect" of Aha! Experiences on Undergraduate Mathematics Students

ERIC Educational Resources Information Center

Liljedahl, Peter G.

2005-01-01

The AHA! experience-the moment of illumination on the heels of lengthy, and seemingly fruitless, intentional effort-has long been the basis for lore in mathematics. Unfortunately, such lore is often restricted to the discussion of these phenomena in the context of great mathematicians and great mathematical advancement. But are such experiences…

Problem Solvers: MathLab's Design Brings Professional Learning into the Classroom

ERIC Educational Resources Information Center

Morales, Sara; Sainz, Terri

2017-01-01

Imagine teachers, administrators, and university mathematicians and staff learning together in a lab setting where students are excited about attending a week-long summer math event because they are at the forefront of the experience. Piloted in three New Mexico classrooms during summer 2014, MathLab expanded into 17 lab settings over six…

Educating the Young Mathematician: A Historical Perspective through the Nineteenth Century

ERIC Educational Resources Information Center

Saracho, Olivia N.; Spodek, Bernard

2009-01-01

Educational programs for young children emerged reasonably early in the history of the United States of America. Its theoretical foundation was based on the thoughts and principles of various early European scholars who differed from one another in their educational theories and how they viewed experiences that would impact on young children's…

Mathematics and Physics: The Idea of a Pre-Established Harmony

ERIC Educational Resources Information Center

Kragh, Helge

2015-01-01

For more than a century the notion of a pre-established harmony between the mathematical and physical sciences has played an important role not only in the rhetoric of mathematicians and theoretical physicists, but also as a doctrine guiding much of their research. Strongly mathematized branches of physics, such as the vortex theory of atoms…

Mathematics: Teaching and Learning. Pennsylvania Council of Teachers of Mathematics 1986 Yearbook.

ERIC Educational Resources Information Center

Nicely, Robert F., Jr., Ed.; Sigmund, Thomas F., Ed.

One of the strengths of the Pennsylvania Council of Teachers of Mathematics (PCTM) is that it gives mathematicians and mathematics educators the opportunity to exchange and contribute to each other's professional growth. The topic for each yearbook is chosen to coincide with the annual PCTM meeting. This 1986 yearbook contains 17 articles related…

An English Professor Considers Mathematics.

ERIC Educational Resources Information Center

Duncan, Noreen L.

There is a common belief that people have limited mental capabilities in that they are either good at English or mathematics, but not both. There is also a myth that men are naturally good at math, while women are not. But there are many good mathematicians who also write well. Also, good students appear to be good students, regardless of the…

Being a Girl Mathematician: Diversity of Positive Mathematical Identities in a Secondary Classroom

ERIC Educational Resources Information Center

Radovic, Darinka; Black, Laura; Salas, Christian E.; Williams, Julian

2017-01-01

The construction of positive mathematical identities (MIs) is a complex and central issue in school mathematics, where girls are usually "counted out" of the field. This study explores positive MIs (high achiever and positive relationship with mathematics) of 3 girls. We employed a nested model of identity based on a case study approach…

More, All Gone, Empty, Full: Math Talk Every Day in Every Way

ERIC Educational Resources Information Center

Greenberg, Jan

2012-01-01

Math is everywhere! Mathematics is "a way of describing the world--a way of thinking, knowing, and problem-solving" (Virginia's Early Childhood Development Alignment Project 2008, 83). Infants and toddlers are natural mathematicians. Even without adult support, infants and toddlers use math concepts to make sense of their world. An important role…

Did Jean Condorcet (1743-1794) commit suicide?

PubMed

Olry, Régis; Dupont, Geneviève

2006-08-01

Condorcet was a famous French mathematician, philosopher and revolutionary. In circumstances that are still unclear, he died in a cell of the Bourg-Egalité prison on 29 March 1794. Most historians of the French Revolution accept suicide as the most likely cause of death but we cannot rule out the possibility that he died of stroke or exhaustion.

On the Nature of Mathematical Thought and Inquiry: A Prelusive Suggestion

ERIC Educational Resources Information Center

McLoughlin, M. Padraig M. M.

2004-01-01

The author of this paper submits that humans have a natural inquisitiveness; hence, mathematicians (as well as other humans) must be active in learning. Thus, we must commit to conjecture and prove or disprove said conjecture. Ergo, the purpose of the paper is to submit the thesis that learning requires doing; only through inquiry is learning…

Becoming Mathematicians: Women and Students of Color Choosing and Leaving Doctoral Mathematics

ERIC Educational Resources Information Center

Herzig, Abbe H.

2004-01-01

Few women and even fewer African Americans, Latinos, and Native Americans complete doctoral degrees in mathematics in the United States. This article proposes a framework for understanding the small numbers of women and students of color who persist in doctoral mathematics based on the notion that academic and social integration are critical to…

Using Phun to Study "Perpetual Motion" Machines

ERIC Educational Resources Information Center

Kores, Jaroslav

2012-01-01

The concept of "perpetual motion" has a long history. The Indian astronomer and mathematician Bhaskara II (12th century) was the first person to describe a perpetual motion (PM) machine. An example of a 13th-century PM machine is shown in Fig. 1. Although the law of conservation of energy clearly implies the impossibility of PM construction, over…

First Graders Outwit a Famous Mathematician

ERIC Educational Resources Information Center

Bishop, Jessica Pierson; Lamb, Lisa L. C.; Philipp, Randolph A.; Schappelle, Bonnie P.; Whitacre, Ian

2011-01-01

In the third century, Diophantus, the "Father of Algebra" no less, described equations of the form x + 20 = 4 as "absurd." The absurdity stemmed from the fact that the result of four is obviously less than the addend of twenty. And more than 1300 years later, Pascal argued that subtracting four from zero leaves zero because of the impossibility of…

One Is Not Born a Mathematician: In Conversation with Vasily Davydov

ERIC Educational Resources Information Center

Fellus, Osnat; Biton, Yaniv

2017-01-01

That mathematics education has been one of the central concerns of educational systems worldwide is no secret. It is also an established consensus that as far back as eighty years ago, Russian psychologists such as Vygotsky, Luria, Meshcheryakov, and Davydov have pioneered work that contributed to the understanding of teaching and learning and…

An Empirical Introduction to the Concept of Chemical Element Based on Van Hiele's Theory of Level Transitions

ERIC Educational Resources Information Center

Vogelezang, Michiel; Van Berkel, Berry; Verdonk, Adri

2015-01-01

Between 1970 and 1990, the Dutch working group "Empirical Introduction to Chemistry" developed a secondary school chemistry education curriculum based on the educational vision of the mathematicians van Hiele and van Hiele-Geldof. This approach viewed learning as a process in which students must go through discontinuous level transitions…

The education of Ehrenfried Walther von Tschirnhaus (1651-1708).

PubMed

Adler, Jacob

2015-02-01

Ehrenfried Walther von Tschirnhaus, mathematician, inventor, and correspondent of Spinoza, is often thought to have studied medicine at Leiden, though documentation of this fact has been lacking. Tschirnhaus' medical education is here documented, along with the nature of his medical practice. © The Author(s) 2013 Reprints and permissions: sagepub.co.uk/journalsPermissions.nav.

Just Do It: Flipped Lecture, Determinants and Debate

ERIC Educational Resources Information Center

Kensington-Miller, Barbara; Novak, Julia; Evans, Tanya

2016-01-01

This paper describes a case study of two pure mathematicians who flipped their lecture to teach matrix determinants in two large mathematics service courses (one at Stage I and the other at Stage II). The purpose of the study was to transform the passive lecture into an active learning opportunity and to introduce valuable mathematical skills,…

Mathematics and Mathematicians at Sapienza University in Rome (XVII-XVIII Century)

ERIC Educational Resources Information Center

Favino, Federica

2006-01-01

This article introduces some data regarding the teaching of mathematics in "La Sapienza" in the 17th century, with particular reference to the discipline's role in the statutes, the lecturers, the courses' programmes, the interest that Popes took in it. Specifically, it will focus on the changes that occured at the end of the 17th…

A New View of Mathematics Will Help Mathematics Teachers

ERIC Educational Resources Information Center

Maasz, Juergen

2005-01-01

For many people mathematics is something like a very huge and impressive building. It has a given structure with lots of levels and rooms. For many people this structure and therefore mathematics itself is independent from society, culture and history. It exists and mathematicians try to recover (not: to construct!) new parts of it. From this…

Descartes, René (1596-1650)

NASA Astrophysics Data System (ADS)

Murdin, P.

2000-11-01

Mathematician and philosopher, born in La Haye (now Descartes), Touraine, France, settled in Holland. His work, La Géométrie, formulated geometry in terms of algebra, from which comes the concept of Cartesian coordinates. Studied Aristotelian philosophy and was attracted to mathematics, and the purely logical analysis of practically everything. Wrote Discours de la Méthode pour bien Conduire sa R...

Where's Spot? Finding STEM Opportunities for Young Children in Moments of Dramatic Tension

ERIC Educational Resources Information Center

McClure, Elisabeth; Guernsey, Lisa; Ashbrook, Peggy

2017-01-01

The potential for integrated science, technology, engineering, and math (STEM) learning really is all around us. The moments of intense drama children experience when they test out a new design are the engines that drive STEM practices; it's what keeps scientists, programmers, engineers, and mathematicians up at night, wanting to try "just…

Wren, Sir Christopher (1632-1723)

NASA Astrophysics Data System (ADS)

Murdin, P.

2000-11-01

Architect and astronomer, born in East Knoyle, Wiltshire, became professor of astronomy at Gresham College, and Savilian Professor of Astronomy at Oxford. He rebuilt London after the fire of 1666, planning the entire city and rebuilding 51 churches, including St Paul's Cathedral. Newton acknowledges Wren as a mathematician in the Principia. Wren independently proved KEPLER's third law and formula...

An Interdisciplinary Approach to Designing Online Learning: Fostering Pre-Service Mathematics Teachers' Capabilities in Mathematical Modelling

ERIC Educational Resources Information Center

Geiger, Vince; Mulligan, Joanne; Date-Huxtable, Liz; Ahlip, Rehez; Jones, D. Heath; May, E. Julian; Rylands, Leanne; Wright, Ian

2018-01-01

In this article we describe and evaluate processes utilized to develop an online learning module on mathematical modelling for pre-service teachers. The module development process involved a range of professionals working within the STEM disciplines including mathematics and science educators, mathematicians, scientists, in-service and pre-service…

The Mathematics Curriculum: Issues and Perspectives. Pennsylvania Council of Teachers of Mathematics 1987 Yearbook.

ERIC Educational Resources Information Center

Nicely, Robert F., Jr., Ed.; Sigmund, Thomas F., Ed.

One of the strengths of the Pennsylvania Council of Teachers of Mathematics (PCTM) is that it gives mathematicians and mathematics educators the opportunity to exchange and contribute to each other's professional growth. The topic for each yearbook is chosen to coincide with the annual PCTM meeting. This 1987 yearbook contains 14 articles which…

Mathematics for the Class of 2000. Pennsylvania Council of Teachers of Mathematics 1988 Yearbook.

ERIC Educational Resources Information Center

Nicely, Robert F., Jr., Ed.; Sigmund, Thomas F., Ed.

One of the strengths of the Pennsylvania Council of Teachers of Mathematics (PCTM) is that it gives mathematicians and mathematics educators the opportunity to exchange and contribute to each other's professional growth. The topic for each yearbook is chosen to coincide with the annual PCTM meeting. This 1988 yearbook contains 27 articles which…

Gregory [Gregorie], James (1638-75)

NASA Astrophysics Data System (ADS)

Murdin, P.

2000-11-01

Scottish mathematician and optician, born in Aberdeen. Gregory described in Optica Promota a design (which he never realized) for the first practical reflecting telescope in which a perforated primary concave parabolic mirror converges the light to the focus of a concave ellipsoidal secondary mirror. The light is reflected back to the ellipsoid's second focus behind the main mirror. A real image ...

No Humble Pie: The Origins and Usage of a Statistical Chart

ERIC Educational Resources Information Center

Spence, Ian

2005-01-01

William Playfair's pie chart is more than 200 years old and yet its intellectual origins remain obscure. The inspiration likely derived from the logic diagrams of Llull, Bruno, Leibniz, and Euler, which were familiar to William because of the instruction of his mathematician brother John. The pie chart is broadly popular but--despite its common…

Transactions of the Twenty-Seventh Conference of Army Mathematicians.

DTIC Science & Technology

1982-01-01

Mixtures," Phil . Trans. R. Soc., London, 292, 45-99 (1979). 26. G. Tsatsaronis, "Prediction of Propagating Laminar Flames in Methane, Oxygen, Nitrogen...work of E. J. Haug and his coworkers; the work of M. A. Chace, N. Orlandea, J. J. Uicker, etc; Beckett , R. E., Pan, K. C., and Chu, S. C., J. Engg. Ind

Writing for Mathematics Discovery-Learning: A Model for Composition Courses.

ERIC Educational Resources Information Center

Weaver, Laura H.

Focusing on how expert writers in various disciplines convey complex ideas, this paper shows how the techniques used by the mathematician, Clark Kimberling, in various writings can (1) be transferred to other disciplines, (2) show learning taking place, and (3) provide models for students to re-enact learning in all subject areas. The paper…

Aspiring Mathematicians: Students' Views regarding What It Takes to Be Successful in Mathematics

ERIC Educational Resources Information Center

Ampadu, Ernest

2013-01-01

This article explores junior high school students' views regarding what it takes to be successful in mathematics. Qualitative and quantitative methods were employed to collect and analyse data, describe and interpret junior high school students (12-14 years) perceptions about what it takes to be successful in mathematics. 22 students from four…

Moving beyond Solving for "x": Teaching Abstract Algebra in a Liberal Arts Mathematics Course

ERIC Educational Resources Information Center

Cook, John Paul

2015-01-01

This paper details an inquiry-based approach for teaching the basic notions of rings and fields to liberal arts mathematics students. The task sequence seeks to encourage students to identify and comprehend core concepts of introductory abstract algebra by thinking like mathematicians; that is, by investigating an open-ended mathematical context,…