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Full Description
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.
Contents
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
