
Applied Algebra
Codes, Ciphers and Discrete Algorithms, Second Edition
- 410 pages
- English
- PDF
- Available on iOS & Android
Applied Algebra
Codes, Ciphers and Discrete Algorithms, Second Edition
About this book
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.
Frequently asked questions
- Essential is ideal for learners and professionals who enjoy exploring a wide range of subjects. Access the Essential Library with 800,000+ trusted titles and best-sellers across business, personal growth, and the humanities. Includes unlimited reading time and Standard Read Aloud voice.
- Complete: Perfect for advanced learners and researchers needing full, unrestricted access. Unlock 1.4M+ books across hundreds of subjects, including academic and specialized titles. The Complete Plan also includes advanced features like Premium Read Aloud and Research Assistant.
Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Information
Table of contents
- Cover
- Title
- Copyright
- Contents
- Preface
- Chapter 1: Integers and Computer Algebra
- Chapter 2: Codes
- Chapter 3: Euclidean Algorithm
- Chapter 4: Ciphers
- Chapter 5: Error-Control Codes
- Chapter 6: Chinese Remainder Theorem
- Chapter 7: Theorems of Fermat and Euler
- Chapter 8: Public Key Ciphers
- Chapter 9: Finite Fields
- Chapter 10: Error-Correcting Codes
- Chapter 11: Advanced Encryption Standard
- Chapter 12: Polynomial Algorithms and Fast Fourier Transforms
- Appendix A: Topics in Algebra and Number Theory
- Solutions to Odd Problems
- Bibliography
- Notation
- Algorithms
- Figures
- Tables
- Index