Computer Algebra: An Algorithm-Oriented Introduction

This textbook provides an algorithmic introduction to computer algebra, with hands-on tutorials and implementation-oriented approach using Mathematica, Maple, and Maxima. It covers number theory, modular arithmetic, coding theory, cryptography, polynomial arithmetic, algebraic numbers, and advanced topics, making it an essential resource for mathematics and computer science students.

Format: Paperback / softback
Length: 384 pages
Publication date: 13 July 2022
Publisher: Springer Nature Switzerland AG

This comprehensive textbook provides an algorithmic introduction to the field of computer algebra, authored by a renowned expert in the domain. It offers a hands-on approach, guiding readers through numerous practical tutorials aimed at developing essential skills and algorithmic thinking. With an implementation-oriented focus, the book equips readers with versatile tools that can be applied to enhance studies in mathematical theory, applications, and teaching. Presented using Mathematica code, the book is accompanied by downloadable sessions in Mathematica, Maple, and Maxima, ensuring comprehensive support.

The textbook begins by introducing computer algebra systems and the fundamentals of programming mathematical algorithms. It then delves into integer arithmetic, covering topics such as modular arithmetic and its applications in coding theory and cryptography. The focus shifts to polynomial arithmetic and algebraic numbers, where modern algorithms enable efficient factorization of polynomials. The final chapters explore advanced topics such as simplification and normal forms, power series, summation formulas, and integration.

Computer Algebra is an essential resource for mathematics and computer science students embarking on this field. Numerous examples illustrate algorithms and their implementation, with online support materials encouraging hands-on exploration. The book assumes a basic knowledge of calculus and linear algebra, making it accessible to a wide range of students. In addition to classroom use, its elementary approach and detailed index make it an invaluable reference for algorithms in computer algebra.

Weight: 751g
Dimension: 254 x 178 (mm)
ISBN-13: 9783030780197
Edition number: 1st ed. 2021