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Springer Undergraduate Texts in Mathematics and Technology
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Computer Algebra

An Algorithm-Oriented Introduction

Authors: Koepf, Wolfram

  • 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
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Buy this book

eBook $54.99
price for USA in USD
  • ISBN 978-3-030-78017-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.99
price for USA in USD
  • ISBN 978-3-030-78016-6
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
About this Textbook

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.

About the authors

Wolfram Koepf is Professor of Mathematics (retired) at the University of Kassel. He is a leading expert in computer algebra. Between 2002 and 2010 he was the Chairman of the Fachgruppe Computeralgebra, the largest computer algebra group worldwide. He has organized numerous conferences and workshops around the world, including the International Symposium on Symbolic and Algebraic Computation (ISSAC) 2010 as general chair, and a cooperation with the African Institute of Mathematical Sciences Cameroon in 2017 and 2018. In addition to his prolific research and organizational activities, he has a strong interest in education and teacher preparation. He is also a member of the executive committee of the German Mathematical Union (DMV).

Table of contents (12 chapters)

Table of contents (12 chapters)
  • Introduction to Computer Algebra

    Pages 1-20

    Koepf, Wolfram

  • Programming in Computer Algebra Systems

    Pages 21-38

    Koepf, Wolfram

  • Number Systems and Integer Arithmetic

    Pages 39-64

    Koepf, Wolfram

  • Modular Arithmetic

    Pages 65-89

    Koepf, Wolfram

  • Coding Theory and Cryptography

    Pages 91-112

    Koepf, Wolfram

Buy this book

eBook $54.99
price for USA in USD
  • ISBN 978-3-030-78017-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $69.99
price for USA in USD
  • ISBN 978-3-030-78016-6
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Computer Algebra
Book Subtitle
An Algorithm-Oriented Introduction
Authors
Series Title
Springer Undergraduate Texts in Mathematics and Technology
Copyright
2021
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-78017-3
DOI
10.1007/978-3-030-78017-3
Hardcover ISBN
978-3-030-78016-6
Series ISSN
1867-5506
Edition Number
1
Number of Pages
XII, 384
Number of Illustrations
1 b/w illustrations, 26 illustrations in colour
Topics