Applied Algebra: Codes, Ciphers and Discrete Algorithms, Second Edition

Darel W. Hardy, Fred Richman, Carol L. Walker

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February 17, 2009 by Chapman and Hall/CRC
Textbook - 424 Pages - 32 B/W Illustrations
ISBN 9781420071429 - CAT# C7142
Series: Discrete Mathematics and Its Applications

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Features

  • Covers topics from algebra, cryptography, and number theory
  • Includes algorithms that offer common-sense approaches to problems, such as computing large powers
  • Provides complete coverage on error-correcting codes
  • Explains the Rijndael algorithm to help students understand the data encryption standard
    Solutions manual available for qualifying instructors

CD-ROM Features

  • Links that make it easy to find topics and navigate page-by-page, chapter-by-chapter, or by keywords
  • Interactive examples
  • Computing hints
  • Self-tests
  • Some details of problem solutions beyond those in the printed text

Summary

Using mathematical tools from number theory and finite fields, Applied Algebra: Codes, Ciphers, and Discrete Algorithms, Second Edition presents practical methods for solving problems in data security and data integrity. It is designed for an applied algebra course for students who have had prior classes in abstract or linear algebra. While the content has been reworked and improved, this edition continues to cover many algorithms that arise in cryptography and error-control codes.

New to the Second Edition

  • A CD-ROM containing an interactive version of the book that is powered by Scientific Notebook®, a mathematical word processor and easy-to-use computer algebra system
  • New appendix that reviews prerequisite topics in algebra and number theory
  • Double the number of exercises

Instead of a general study on finite groups, the book considers finite groups of permutations and develops just enough of the theory of finite fields to facilitate construction of the fields used for error-control codes and the Advanced Encryption Standard. It also deals with integers and polynomials. Explaining the mathematics as needed, this text thoroughly explores how mathematical techniques can be used to solve practical problems.

About the Authors
Darel W. Hardy is Professor Emeritus in the Department of Mathematics at Colorado State University. His research interests include applied algebra and semigroups.

Fred Richman is a professor in the Department of Mathematical Sciences at Florida Atlantic University. His research interests include Abelian group theory and constructive mathematics.

Carol L. Walker is Associate Dean Emeritus in the Department of Mathematical Sciences at New Mexico State University. Her research interests include Abelian group theory, applications of homological algebra and category theory, and the mathematics of fuzzy sets and fuzzy logic.