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Applied Abstract Algebra with MapleTM and MATLAB® provides an in-depth introduction to real-world abstract algebraic problems. This popular textbook covers a variety of topics including block designs, coding theory, cryptography, and counting techniques, including Pólya´s and Burnside´s theorems. The book also includes a concise review of all prerequisite advanced mathematics.

The use of sophisticated mathematical software packages such as MapleTM and MATLAB® allows students to work though realistic examples without having to struggle with extensive computations.

Notable additions to the third edition include expanded contemporary applications, coverage of the two-message problem, and a full chapter on symmetry in Western music. Several other parts of the book were also updated, including some MATLAB sections due to their adoption of the MuPAD computer algebra system since the last edition. This edition also contains more than 100 new exercises.

This new edition includes the two most widely used mathematical software packages. It builds upon the successful previous editions, favored by instructors and students alike.



Preliminary Mathematics

Permutation Groups

Cosets and Quotient Groups

Rings and Euclidean Domains

Finite Fields

Finite Fields with Maple

Finite Fields with MATLAB

The Euclidean Algorithm

Exercises

Block Designs

General Properties

Hadamard Matrices

Hadamard Matrices with Maple

Hadamard Matrices with MATLAB

Difference Sets

Difference Sets with Maple

Difference Sets with MATLAB

Exercises


Error-Correcting Codes

General Properties

Hadamard Codes

Reed-Muller Codes

Reed-Muller Codes with Maple

Reed-Muller Codes with MATLAB

Linear Codes

Hamming Codes with Maple

Hamming Codes with MATLAB

Exercises


BCH Codes

Construction

Error Correction

BCH Codes with Maple

BCH Codes with MATLAB

Exercises

Reed-Solomon Codes

Construction

Error Correction

Error Correction Method Proof

Reed-Solomon Codes with Maple

Reed-Solomon Codes with MATLAB

Reed-Solomon Codes in Voyager 2

Exercises

Algebraic Cryptography

Two Elementary Cryptosystems

Shift and Affine Ciphers with Maple

Shift and Affine Ciphers with MATLAB

Hill Ciphers

Hill Ciphers with Maple

Hill Ciphers with MATLAB

The Two-Message Problem

Exercises


Vigenère Ciphers

Encryption and Decryption

Cryptanalysis

Vigenère Ciphers with Maple

Vigenère Ciphers with MATLAB

Exercises


RSA Ciphers

Preliminary Mathematics

Encryption and Decryption

RSA Ciphers with Maple

RSA Ciphers with MATLAB

Efficiency and Security Issues

The Diffie-Hellman Key Exchange with RSA

Discrete Logarithms with Maple

Discrete Logarithms with MATLAB

Exercises


Elliptic Curve Cryptography

ElGamal Ciphers

ElGamal Ciphers with Maple

ElGamal Ciphers with MATLAB

Elliptic Curves

Elliptic Curves with Maple

Elliptic Curves with MATLAB

Elliptic Curve Cryptography

Elliptic Curve Cryptography with Maple

Elliptic Curve Cryptography with MATLAB

Exercises

The Advanced Encryption Standard

Text Setup

The S-Box

Key Generation

Encryption

The AES Layers

Decryption

AES with Maple

AES with MATLAB

Exercises


Pólya Theory

Group Actions

Burnside's Theorem

The Cycle Index

The Pattern Inventory

The Pattern Inventory with Maple

The Pattern Inventory with MATLAB

Switching Functions

Exercises


Graph Theory

The Cycle Index of Sn

The Cycle Index of Sn with Maple

The Cycle Index of Sn with MATLAB

Counting Undirected Graphs

Counting Undirected Graphs with Maple

Counting Undirected Graphs with MATLAB

Exercises


Symmetry in Western Music

Introduction

Group Actions and Scales

Group Actions and Chords

Group Actions and Chords with Maple

Group Actions and Chords with MATLAB

Cayley Graphs for Z12

Twelve-Tone Rows

Twelve-Tone Rows with Maple

Twelve-Tone Rows with MATLAB

Exercises


Bibliography