finelybook
Computer Algebra: An Algorithm-Oriented Introduction ( Undergraduate Texts in Mathematics and Technology)
by 作者: Wolfram Koepf
Publisher Finelybook 出版社: ; 1st ed. 2021 edition (July 12,2021)
Language 语言: English
pages 页数: 396 pages
ISBN-10 书号: 3030780163
ISBN-13 书号: 9783030780166
Book Description
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.
