Richard Klima

Applied abstract algebra with Maple[TM] and MATLAB

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 Burnsides 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