Computers in Science and Mathematics

Author: Robert Plotkin

Publisher: N.A

ISBN: 9780816077571

Category: Computers

Page: 168

View: 9560

Explores how computers have enhanced the study of science and mathematics by improving calculation speeds in such areas as simulation, weather, and cryptography.

Phase Change

The Computer Revolution in Science and Mathematics

Author: Douglas S. Robertson

Publisher: Oxford University Press, USA

ISBN: 9780195157482

Category: Computers

Page: 190

View: 5853

Robertson's earlier work, The New Renaissance projected the likely future impact of computers in changing our culture. Phase Change builds on and deepens his assessment of the role of the computer as a tool driving profound change by examining the role of computers in changing the face of the sciences and mathematics. He shows that paradigm shifts in understanding in science have generally been triggered by the availability of new tools, allowing the investigator a new way of seeing into questions that had not earlier been amenable to scientific probing.

Computers in Science and Mathematics

Computers, Internet, and Society Series

Author: Boris Waxweiler

Publisher: N.A

ISBN: 9781681178493


Page: 400

View: 7463

"Computation provides new sources of unfolding and investigating scientific and mathematical systems. The field of computer science studies the nature of computation and its uses, among other things. Simulation by computer may be the only way to predict how certain complicated systems develop. Scientific laws give algorithms, or procedures, for determining how systems behave. The computer program is a medium in which the algorithms can be expressed and applied. Physical objects and mathematical structures can be represented as numbers and symbols in a computer, and a program can be written to manipulate them according to the algorithms. When the computer program is executed, it causes the numbers and symbols to be modified in the way specified by the scientific laws. It thereby allows the consequences of the laws to be deduced. Executing a computer program is much like performing an experiment. Unlike the physical objects in a conventional experiment, however, the objects in a computer experiment are not bound by the laws of nature. Instead they follow the laws embodied in the computer program, which can be of any consistent form. Computation thus extends the realm of experimental science: it allows experiments to be performed in a hypothetical universe. Computation also extends theoretical science. It is important for our society of the near future that every educated person understand some of the principles on which computers operate; and second, that there is an important relationship between mathematics education and computers, both in the sense that the mathematics curriculum can contribute significantly towards teaching students about computers, as well as in the sense that computers have a role to play in mathematics education. This book Computers in Science and Mathematics provides an overview of the latest research in these areas and assessment of the role of the computer as a tool driving profound change by examining the role of computers in changing the face of the sciences and mathematics. It is the only periodical devoted specifically to using information technology in the teaching of mathematics and science. It provides a medium of exchange for those engaged in fields where there exists a non-trivial interplay between mathematics and computers. This book shows scientists and engineers how Mathematics can be used to do scientific computations."

Modeling and Simulation in Science and Mathematics Education

Author: Wallace Feurzeig,Nancy Roberts

Publisher: Springer Science & Business Media

ISBN: 1461214149

Category: Computers

Page: 334

View: 7348

This book/software package brings the tools and excitement of modeling to pre-college teachers, to researchers involved in curriculum development, and to software developers interested in the pre-college market.

Computer Science with MATHEMATICA ®

Theory and Practice for Science, Mathematics, and Engineering

Author: Roman E. Maeder

Publisher: Cambridge University Press

ISBN: 9780521663953

Category: Computers

Page: 389

View: 4591

This introductory course shows scientists and engineers how Mathematica can be used to do scientific computations.

Science, Computers, and People

From the Tree of Mathematics

Author: ULAM

Publisher: Springer Science & Business Media

ISBN: 1461598192

Category: Mathematics

Page: 266

View: 5941

STANISLAW MARCIN ULAM, or Stan as his friends called him, was one of those great creative mathematicians whose interests ranged not only over all fields of mathematics, but over the physical and biological sciences as well. Like his good friend "Johnny" von Neumann, and unlike so many of his peers, Ulam is unclassifiable as a pure or applied mathematician. He never ceased to find as much beauty and excitement in the applications of mathematics as in working in those rarefied regions where there is a total un concern with practical problems. In his Adventures of a Mathematician Ulam recalls playing on an oriental carpet when he was four. The curious patterns fascinated him. When his father smiled, Ulam remembers thinking: "He smiles because he thinks I am childish, but I know these are curious patterns. I know something my father does not know." The incident goes to the heart of Ulam's genius. He could see quickly, in flashes of brilliant insight, curious patterns that other mathematicians could not see. "I am the type that likes to start new things rather than improve or elaborate," he wrote. "I cannot claim that I know much of the technical material of mathematics.

Geometric Methods and Applications

For Computer Science and Engineering

Author: Jean Gallier

Publisher: Springer Science & Business Media

ISBN: 1461301378

Category: Mathematics

Page: 566

View: 5072

As an introduction to fundamental geometric concepts and tools needed for solving problems of a geometric nature using a computer, this book fills the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, or robotics that do not cover the underlying geometric concepts in detail. Gallier offers an introduction to affine, projective, computational, and Euclidean geometry, basics of differential geometry and Lie groups, and explores many of the practical applications of geometry. Some of these include computer vision, efficient communication, error correcting codes, cryptography, motion interpolation, and robot kinematics. This comprehensive text covers most of the geometric background needed for conducting research in computer graphics, geometric modeling, computer vision, and robotics and as such will be of interest to a wide audience including computer scientists, mathematicians, and engineers.

Mathematical Principles for Scientific Computing and Visualization

Author: Gerald Farin,Dianne Hansford

Publisher: CRC Press

ISBN: 156881321X

Category: Mathematics

Page: 280

View: 6591

This non-traditional introduction to the mathematics of scientific computation describes the principles behind the major methods, from statistics, applied mathematics, scientific visualization, and elsewhere, in a way that is accessible to a large part of the scientific community. Introductory material includes computational basics, a review of coordinate systems, an introduction to facets (planes and triangle meshes) and an introduction to computer graphics. The scientific computing part of the book covers topics in numerical linear algebra (basics, solving linear system, eigen-problems, SVD, and PCA) and numerical calculus (basics, data fitting, dynamic processes, root finding, and multivariate functions). The visualization component of the book is separated into three parts: empirical data, scalar values over 2D data, and volumes.

Mathematics for Electronics and Computers

Author: Nigel P. Cook

Publisher: N.A

ISBN: 9780130811622

Category: Computer science

Page: 747

View: 6959

With 12 textbooks; 23 editions, and 20 years of front-line education experience, best-selling author Nigel Cook has written this text as a complete math course for high school, community college, or vocational/technical college students seeking a career in electronics and computer technology. This finely tuned, carefully tested, and accuracy checked volume is organized into three parts: *PART A: Basic Math *Fractions; Decimal Numbers; Positive and Negative Numbers; Exponents and the Metric System; Algebra, Equations, and Formulas; Geometry and Trigonometry; and Logarithms and Graphs *PART B: Electronics Math *Current and Voltage; Resistance and Power; Series DC Circuits; Parallel DC Circuits; Series-Parallel DC Circuits and Theorems; Alternating Current (AC); Capacitors; Inductors and Transformers; RLC Circuits and Complex Numbers; and Diodes and Transistors *PART C: Computer Math *Analog to Digital; Number Systems and Codes; Logic Gates; Boolean Expressions and Algebra; Binary Arithmetic; and Introduction to Computer Programming Text Features As with any topic to be learned, the method of presentation can make a big difference between clear comprehension and complete confusion. all math topics with extensive applications to show the student the value of math as a tool. Therefore, if the need for math is instantly demonstrated, the tool is retained. Some additional features include: *Student-friendly writing style *Integrated math applications *Section self-test evaluation points *Circuit analysis tables *Extensive end-of-chapter test bank *Humanistic vignettes *Worked-out examples *Calculator sequence examples *Proto-board pictorials *Margin term definitions

Learning from Computers: Mathematics Education and Technology

Author: Christine Keitel-Kreidt,Kenneth Ruthven

Publisher: Springer Science & Business Media

ISBN: 3642785425

Category: Education

Page: 332

View: 6852

The NATO Advanced Research Workshop on Mathematics Education and Technology was held in Villard-de-Lans, France, between May 6 and 11, 1993. Organised on the initiative of the BaCoMET (Basic Components of Mathematics Education for Teachers) group (Christiansen, Howson and Otte 1986; Bishop, Mellin-Olsen and van Dormolen 1991), the workshop formed part of a larger NATO programme on Advanced Educational Technology. Some workshop members had already participated in earlier events in this series and were able to contribute insights from them: similarly some members were to take part in later events. The problematic for the workshop drew attention to important speculative developments in the applications of advanced information technology in mathematics education over the last decade, notably intelligent tutoring, geometric construction, symbolic algebra and statistical analysis. Over the same period, more elementary forms of information technology had started to have a significant influence on teaching approaches and curriculum content: notably arithmetic and graphic calculators; standard computer tools, such as spreadsheets and databases; and computer-assisted learning packages and computer microworlds specially designed for educational purposes.

Brains, Machines, and Mathematics

Author: Michael A. Arbib

Publisher: Springer Science & Business Media

ISBN: 1461247829

Category: Computers

Page: 202

View: 7689

This is a book whose time has come-again. The first edition (published by McGraw-Hill in 1964) was written in 1962, and it celebrated a number of approaches to developing an automata theory that could provide insights into the processing of information in brainlike machines, making it accessible to readers with no more than a college freshman's knowledge of mathematics. The book introduced many readers to aspects of cybernetics-the study of computation and control in animal and machine. But by the mid-1960s, many workers abandoned the integrated study of brains and machines to pursue artificial intelligence (AI) as an end in itself-the programming of computers to exhibit some aspects of human intelligence, but with the emphasis on achieving some benchmark of performance rather than on capturing the mechanisms by which humans were themselves intelligent. Some workers tried to use concepts from AI to model human cognition using computer programs, but were so dominated by the metaphor "the mind is a computer" that many argued that the mind must share with the computers of the 1960s the property of being serial, of executing a series of operations one at a time. As the 1960s became the 1970s, this trend continued. Meanwhile, experi mental neuroscience saw an exploration of new data on the anatomy and physiology of neural circuitry, but little of this research placed these circuits in the context of overall behavior, and little was informed by theoretical con cepts beyond feedback mechanisms and feature detectors.

Applications of Mathematics and Informatics in Military Science

Author: Nicholas Daras

Publisher: Springer Science & Business Media

ISBN: 1461441099

Category: Computers

Page: 248

View: 7889

Analysis, assessment, and data management are core tools required for operation research analysts. The April 2011 conference held at the Helenic Military Academy addressed these issues with efforts to collect valuable recommendations for improving analysts’ capabilities to assess and communicate the necessary qualitative data to military leaders. This unique volume is an outgrowth of the April conference and comprises of contributions from the fields of science, mathematics, and the military, bringing Greek research findings to the world. Topics cover a wide variety of mathematical methods used with application to defense and security. Each contribution considers directions and pursuits of scientists that pertain to the military as well as the theoretical background required for methods, algorithms, and techniques used in military applications. The direction of theoretical results in these applications is conveyed and open problems and future areas of focus are highlighted. A foreword will be composed by a member of N.A.T.O. or a ranking member of the armed forces. Topics covered include: applied OR and military applications, signal processing, scattering, scientific computing and applications, combat simulation and statistical modeling, satellite remote sensing, and applied informatics – cryptography and coding. The contents of this volume will be of interest to a diverse audience including military operations research analysts, the military community at large, and practitioners working with mathematical methods and applications to informatics and military science.​

Exploiting Mental Imagery with Computers in Mathematics Education

Author: Rosamund Sutherland,John Mason

Publisher: Springer Science & Business Media

ISBN: 3642577717

Category: Computers

Page: 326

View: 7001

The advent of fast and sophisticated computer graphics has brought dynamic and interactive images under the control of professional mathematicians and mathematics teachers. This volume in the NATO Special Programme on Advanced Educational Technology takes a comprehensive and critical look at how the computer can support the use of visual images in mathematical problem solving. The contributions are written by researchers and teachers from a variety of disciplines including computer science, mathematics, mathematics education, psychology, and design. Some focus on the use of external visual images and others on the development of individual mental imagery. The book is the first collected volume in a research area that is developing rapidly, and the authors pose some challenging new questions.

A Primer on Scientific Programming with Python

Author: Hans Petter Langtangen

Publisher: Springer

ISBN: 3662498871

Category: Computers

Page: 922

View: 2332

The book serves as a first introduction to computer programming of scientific applications, using the high-level Python language. The exposition is example and problem-oriented, where the applications are taken from mathematics, numerical calculus, statistics, physics, biology and finance. The book teaches "Matlab-style" and procedural programming as well as object-oriented programming. High school mathematics is a required background and it is advantageous to study classical and numerical one-variable calculus in parallel with reading this book. Besides learning how to program computers, the reader will also learn how to solve mathematical problems, arising in various branches of science and engineering, with the aid of numerical methods and programming. By blending programming, mathematics and scientific applications, the book lays a solid foundation for practicing computational science. From the reviews: Langtangen ... does an excellent job of introducing programming as a set of skills in problem solving. He guides the reader into thinking properly about producing program logic and data structures for modeling real-world problems using objects and functions and embracing the object-oriented paradigm. ... Summing Up: Highly recommended. F. H. Wild III, Choice, Vol. 47 (8), April 2010 Those of us who have learned scientific programming in Python ‘on the streets’ could be a little jealous of students who have the opportunity to take a course out of Langtangen’s Primer.” John D. Cook, The Mathematical Association of America, September 2011 This book goes through Python in particular, and programming in general, via tasks that scientists will likely perform. It contains valuable information for students new to scientific computing and would be the perfect bridge between an introduction to programming and an advanced course on numerical methods or computational science. Alex Small, IEEE, CiSE Vol. 14 (2), March /April 2012 “This fourth edition is a wonderful, inclusive textbook that covers pretty much everything one needs to know to go from zero to fairly sophisticated scientific programming in Python...” Joan Horvath, Computing Reviews, March 2015

Responsive Teaching in Science and Mathematics

Author: Amy D. Robertson,Rachel Scherr,David Hammer

Publisher: Routledge

ISBN: 1317423747

Category: Education

Page: 216

View: 1720

Answering calls in recent reform documents to shape instruction in response to students’ ideas while integrating key concepts and scientific and/or mathematical practices, this text presents the concept of responsive teaching, synthesizes existing research, and examines implications for both research and teaching. Case studies across the curriculum from elementary school through adult education illustrate the variety of forms this approach to instruction and learning can take, what is common among them, and how teachers and students experience it. The cases include intellectual products of students’ work in responsive classrooms and address assessment methods and issues. Many of the cases are supplemented with online resources ( including classroom video and extensive transcripts, providing readers with additional opportunities to immerse themselves in responsive classrooms and to see for themselves what these environments look and feel like.

Calculated Bets

Computers, Gambling, and Mathematical Modeling to Win

Author: Steven S. Skiena

Publisher: Cambridge University Press

ISBN: 9780521009621

Category: Computers

Page: 232

View: 8438

A story of using computer simulations and mathematical modeling techniques to predict the outcome of jai-alai matches and bet on them successfully.