Applied Abstract Algebra with MapleTM and MATLAB(R) 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 Polya'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(R) 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.
Richard Klima, Appalachian State University, Boone, North Carolina, USA Neil P. Sigmon, Radford University, Virginia, USA Ernest Stitzinger, North Carolina State University, Raleigh, USA
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 Vigenere Ciphers Encryption and Decryption Cryptanalysis Vigenere Ciphers with Maple Vigenere 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 Polya 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
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- ID: 9781482248234
3rd Revised edition
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