BN.com Gift Guide

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

Hardcover (Print)
Used and New from Other Sellers
Used and New from Other Sellers
from $49.95
Usually ships in 1-2 business days
(Save 58%)
Other sellers (Hardcover)
  • All (8) from $49.95   
  • New (5) from $104.59   
  • Used (3) from $49.95   

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

  • 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.

Read More Show Less

Editorial Reviews

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

Read More Show Less

Product Details

  • ISBN-13: 9781420071429
  • Publisher: Taylor & Francis
  • Publication date: 2/13/2009
  • Series: Discrete Mathematics and Its Applications Series
  • Edition description: New Edition
  • Edition number: 2
  • Pages: 424
  • Product dimensions: 6.30 (w) x 9.30 (h) x 1.00 (d)

Table of Contents

Preface

Integers and Computer Algebra

Integers

Computer Algebra vs. Numerical Analysis

Sums and Products

Mathematical Induction

Codes

Binary and Hexadecimal Codes

ASCII Code

Morse Code

Braille

Two-out-of-Five Code

Hollerith Codes

Euclidean Algorithm

The Mod Function

Greatest Common Divisors

Extended Euclidean Algorithm

The Fundamental Theorem of Arithmetic

Modular Arithmetic

Ciphers

Cryptography

Cryptanalysis

Substitution and Permutation Ciphers

Block Ciphers

The Playfair Cipher

Unbreakable Ciphers

Enigma Machine

Error-Control Codes

Weights and Hamming Distance

Bar Codes Based on Two-out-of-Five Code

Other Commercial Codes

Hamming (7, 4) Code

Chinese Remainder Theorem

Systems of Linear Equations Modulo n

Chinese Remainder Theorem

Extended Precision Arithmetic

Greatest Common Divisor of Polynomials

Hilbert Matrix

Theorems of Fermat and Euler

Wilson’s Theorem

Powers Modulo n

Fermat’s Little Theorem

Rabin’s Probabilistic Primality Test

Exponential Ciphers

Euler’s Theorem

Public Key Ciphers

The Rivest–Shamir–Adleman Cipher System

Electronic Signatures

A System for Exchanging Messages

Knapsack Ciphers

Digital Signature Standard

Finite Fields

The Galois Field GFp

The Ring GFp[x] of Polynomials

The Galois Field GF4

The Galois Fields GF8 and GF16

The Galois Field GFpn

The Multiplicative Group of GFpn

Random Number Generators

Error-Correcting Codes

BCH Codes

A BCH Decoder

Reed–Solomon Codes

Advanced Encryption Standard

Data Encryption Standard

The Galois Field GF256

The Rijndael Block Cipher

Polynomial Algorithms and Fast Fourier Transforms

Lagrange Interpolation Formula

Kronecker’s Algorithm

Neville’s Iterated Interpolation Algorithm

Secure Multiparty Protocols

Discrete Fourier Transforms

Fast Fourier Interpolation

Appendix A: Topics in Algebra and Number Theory

Number Theory

Groups

Rings and Polynomials

Fields

Linear Algebra and Matrices

Solutions to Odd Problems

Bibliography

Notation

Algorithms

Figures

Tables

Index

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)