3rd Edition
Applied Abstract Algebra with MapleTM and MATLAB®
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
Biography
Richard Klima, Appalachian State University, Boone, North Carolina, USA
Neil P. Sigmon, Radford University, Virginia, USA
Ernest Stitzinger, North Carolina State University, Raleigh, USA
