Applied Algebra
eBook - PDF

Applied Algebra

Codes, Ciphers and Discrete Algorithms, Second Edition

  1. 410 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

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.

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Yes, you can access Applied Algebra by Darel W. Hardy,Fred Richman,Carol L. Walker in PDF and/or ePUB format, as well as other popular books in Computer Science & Cyber Security. We have over one million books available in our catalogue for you to explore.

Information

Table of contents

  1. Cover
  2. Title
  3. Copyright
  4. Contents
  5. Preface
  6. Chapter 1: Integers and Computer Algebra
  7. Chapter 2: Codes
  8. Chapter 3: Euclidean Algorithm
  9. Chapter 4: Ciphers
  10. Chapter 5: Error-Control Codes
  11. Chapter 6: Chinese Remainder Theorem
  12. Chapter 7: Theorems of Fermat and Euler
  13. Chapter 8: Public Key Ciphers
  14. Chapter 9: Finite Fields
  15. Chapter 10: Error-Correcting Codes
  16. Chapter 11: Advanced Encryption Standard
  17. Chapter 12: Polynomial Algorithms and Fast Fourier Transforms
  18. Appendix A: Topics in Algebra and Number Theory
  19. Solutions to Odd Problems
  20. Bibliography
  21. Notation
  22. Algorithms
  23. Figures
  24. Tables
  25. Index