Overview
- Balances theoretical and practical aspects with an implementation-oriented approach
- Guides readers through numerous hands-on tutorials to build practical skills and algorithmic thinking
- Supports three computer algebra systems with downloadable resources in Mathematica, Maple, and Maxima
Part of the book series: Springer Undergraduate Texts in Mathematics and Technology (SUMAT)
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Table of contents(12 chapters)
Keywords
- Computer algebra textbook
- Computer algebra reference
- Maple algebra
- Mathematica algebra
- Maxima algebra
- Coding theory computer algebra
- Cryptography computer algebra
- Computer algebra programming
- Computer algebra algorithms
- Polynomial multiplication fast algorithm
- Efficient factorization in polynomial rings
- Algorithmic summation
- Algorithmic integration
- Computer algebra for high school teachers
About this book
This textbook offers an algorithmic introduction to the field of computer algebra. A leading expert in the field, the author guides readers through numerous hands-on tutorials designed to build practical skills and algorithmic thinking. This implementation-oriented approach equips readers with versatile tools that can be used to enhance studies in mathematical theory, applications, or teaching. Presented using Mathematica code, the book is fully supported by downloadable sessions in Mathematica, Maple, and Maxima.
Opening with an introduction to computer algebra systems and the basics of programming mathematical algorithms, the book goes on to explore integer arithmetic. A chapter on modular arithmetic completes the number-theoretic foundations, which are then applied to coding theory and cryptography. From here, the focus shifts to polynomial arithmetic and algebraic numbers, with modern algorithms allowing the efficient factorization of polynomials. The final chapters offer extensions into more advanced topics: simplification and normal forms, power series, summation formulas, and integration.
Computer Algebra is an indispensable resource for mathematics and computer science students new to the field. Numerous examples illustrate algorithms and their implementation throughout, with online support materials to encourage hands-on exploration. Prerequisites are minimal, with only a knowledge of calculus and linear algebra assumed. In addition to classroom use, the elementary approach and detailed index make this book an ideal reference for algorithms in computer algebra.
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Authors and Affiliations
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Institut für Mathematik, Universität Kassel, Kassel, Germany
Wolfram Koepf
About the author
Bibliographic Information
Book Title: Computer Algebra
Book Subtitle: An Algorithm-Oriented Introduction
Authors: Wolfram Koepf
Series Title: Springer Undergraduate Texts in Mathematics and Technology
DOI: https://doi.org/10.1007/978-3-030-78017-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2021
Hardcover ISBN: 978-3-030-78016-6Published: 12 July 2021
Softcover ISBN: 978-3-030-78019-7Published: 13 July 2022
eBook ISBN: 978-3-030-78017-3Published: 11 July 2021
Series ISSN: 1867-5506
Series E-ISSN: 1867-5514
Edition Number: 1
Number of Pages: XII, 384
Number of Illustrations: 1 b/w illustrations, 26 illustrations in colour
Topics: Algebra, Symbolic and Algebraic Manipulation, Algorithms, Mathematical Software