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Applications of Abstract Algebra with MAPLE and MATLAB

Richard E. Klima, Neil P. Sigmon, and Ernest L. Stitzinger
Publisher: 
Chapman & Hall/CRC
Publication Date: 
2007
Number of Pages: 
505
Format: 
Hardcover with CDROM
Edition: 
2
Series: 
Discrete Mathematics and Its Applications 40
Price: 
89.95
ISBN: 
1584886102
Category: 
Textbook
We do not plan to review this book.

 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
BLOCK DESIGNS
General Properties
Hadamard Matrices
Hadamard Matrices with Maple
Hadamard Matrices with MATLAB
Difference Sets
Difference Sets with Maple
Difference Sets with MATLAB
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
BCH CODES
Construction
Error Correction
BCH Codes with Maple
BCH Codes with MATLAB
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
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
VIGENÈRE CIPHERS
Encryption and Decryption
Cryptanalysis
Vigenère Ciphers with Maple
Vigenère Ciphers with MATLAB
THE RSA CRYPTOSYSTEM
Preliminary Mathematics
Encryption and Decryption
The RSA Cryptosystem with Maple
The RSA Cryptosystem with MATLAB
A Note on Modular Exponentiation
A Note on Primality Testing
A Note on Integer Factorization
A Note on Digital Signatures
The Diffie-Hellman Key Exchange
Discrete Logarithms with Maple
Discrete Logarithms with MATLAB
ELLIPTIC CURVE CRYPTOGRAPHY
The ElGamal Cryptosystem
The ElGamal Cryptosystem with Maple
The ElGamal Cryptosystem 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
THE ADVANCED ENCRYPTION STANDARD
Alphabet Assignment and Text Setup
The S-Box
Key Generation
Encryption
The AES Layers
Decryption
A Note on Security
AES with Maple
AES with MATLAB
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
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
Appendix A
Appendix B
Bibliography
Hints or Answers for Selected Exercises
Index

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