Exploring mathematics with CAS assistance : topics in geometry, algebra, univariate calculus, and probability

著者

    • Novozhilova, Lydia S.
    • Dolan, Robert D. (Robert Domenic)

書誌事項

Exploring mathematics with CAS assistance : topics in geometry, algebra, univariate calculus, and probability

Lydia S. Novozhilova, Robert D. Dolan

（Classroom resource materials, v. 69）

MAA Press, an imprint of the American Mathematical Society, c2022

  • : pbk

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注記

Includes bibliographical references and index

内容説明・目次

内容説明

Exploring Mathematics with CAS Assistance is designed as a textbook for an innovative mathematics major course in using a computer-algebra system (CAS) to investigate, explore, and apply mathematical ideas and techniques in problem solving. The book is designed modularly with student investigations and projects in number theory, geometry, algebra, single-variable calculus, and probability. The goal is to provoke an inquiry mindset in students and to arm them with the CAS tools to investigate low-entry, open-ended questions in a variety of mathematical arenas. Because of the modular design, the individual chapters could also be used selectively to design student projects in a number of upper-division mathematics courses. These projects could, in fact, lead into undergraduate research projects. The existence of powerful computer-algebra systems has changed the way mathematicians perform research; this book enables instructors to put some of those new methods and approaches into their undergraduate instruction. Prerequisites include a basic working knowledge of discrete mathematics and single-variable calculus. Programming experience and some basic familiarity with elementary probability and statistics are beneficial but not required. The book takes a software-agnostic approach and emphasizes algorithmic structure of solution methods by systematically providing their step-by-step verbal descriptions or suitable pseudocode that can be implemented in any CAS.

目次

Part 1 Algebra & Geometry: Computer algebra systems and elements of algorithmics Topics in classical geometry More topics in classical geometry Topics in elementary number theory Topics in algebra: Solving univariate algebraic equations Topics in algebra: Bivariate systems of polynomial equations Part 2 Calculus and numerics: Derivatives Definite integrals Approximating zeros of functions by iteration methods Polynomial approximations Trigonometric approximation Fourier analysis in music and signal processing Part 3 Probability and statistics: Probability and statistics basics Computer simulation of statistical sampling Simple random walks Data for lab 17 in chapter 14 Bibliography Index

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