Applied Algebra: Codes, Ciphers and Discrete Algorithms, Second Edition / Edition 2

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

Overview

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

• Downloadable resources 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.

Product Details

ISBN-13:	9781420071429
Publisher:	Taylor & Francis
Publication date:	02/17/2009
Series:	Discrete Mathematics and Its Applications
Edition description:	New Edition
Pages:	424
Product dimensions:	6.30(w) x 9.30(h) x 1.00(d)

About the Author

Darel W. Hardy (Author) , Fred Richman (Author) , Carol L. Walker (Author)

Table of Contents

Preface. Integers and Computer Algebra. Codes. Euclidean Algorithm. Ciphers. Error-Control Codes. Chinese Remainder Theorem. Theorems of Fermat and Euler. Public Key Ciphers. Finite Fields. Error-Correcting Codes. Advanced Encryption Standard. Polynomial Algorithms and Fast Fourier Transforms. Appendix. Solutions to Odd Problems. Bibliography. Notation. Algorithms. Figures. Tables. Index.

What People are Saying About This

From the Publisher

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

Editorial Reviews

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

From the Publisher