Applied Algebra: Codes, Ciphers and Discrete Algorithms, Second Edition (Discrete Mathematics and Its Applications) - Hardcover

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

Hardcover

ISBN 10: 1420071424 ISBN 13: 9781420071429

Publisher: Chapman and Hall/CRC, 2009

Synopsis

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.

About this title

About the Author

Colorado State University, Fort Collins, USA Florida Atlantic University, Boca Raton, USA New Mexico State University, Las Cruces, USA Monmouth University, Middletown, New Jersey, USA

Review

This book attempts to show the power of algebra in a relatively simple setting.
―Mathematical Reviews, 2010

... The book supports learning by doing. In each section we can find many examples which clarify the mathematics introduced in the section and each section is followed by a series of exercises of which approximately half are solved in the end of the book. Additional the book comes with a CD-ROM containing an interactive version of the book powered by the computer algebra system Scientific Notebook. ... the mathematics in the book are developed as needed and the focus of the book lies clearly on learning by examples and exercises. ... the book gives good insight on how algebra can be used in coding and cryptography ... The strength of the book is clearly the number of examples ...
―IACR book reviews, January 2010

Edition details

• Publisher: Chapman and Hall/CRC
• Publication date: 2009
• ISBN 10: 1420071424
• ISBN 13: 9781420071429
• Binding: Hardcover
• Language: English
• Edition number: 2
• Number of pages: 424