Applications of Abstract Algebra with Maple and MATLAB

Richard E. Klima, Neil P. Sigmon, Ernest Stitzinger - Collection Discrete Mathematics and Its Applications

528 pages, parution le 12/07/2006 (2^eme édition)

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Résumé

Eliminating the need for heavy number-crunching, sophisticated mathematical software packages open the door to areas like cryptography, coding theory, and combinatorics that are dependent on abstract algebra. Applications of Abstract Algebra with Maple and MATLAB, Second Edition explores these topics and shows how to apply the software programs to abstract algebra and its related fields.

Carefully integrating Maple® and MATLAB®, this book provides an in-depth introduction to real-world abstract algebraic problems. The first chapter offers a concise and comprehensive review of prerequisite advanced mathematics. The next several chapters examine block designs, coding theory, and cryptography while the final chapters cover counting techniques, including Pólya's and Burnside's theorems. Other topics discussed include the Rivest, Shamir, and Adleman (RSA) cryptosystem, digital signatures, primes for security, and elliptic curve cryptosystems.

New to the Second Edition

Three new chapters on Vigenère ciphers, the Advanced Encryption Standard (AES), and graph theory as well as new MATLAB and Maple sections
Expanded exercises and additional research exercises
Maple and MATLAB files and functions available for download online and from a CD-ROM

With the incorporation of MATLAB, this second edition further illuminates the topics discussed by eliminating extensive computations of abstract algebraic techniques. The clear organization of the book as well as the inclusion of two of the most respected mathematical software packages available make the book a useful tool for students, mathematicians, and computer scientists.

Sommaire

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
- Hints or Answers for Selected Exercises

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Chapman and Hall / CRC
Auteur(s)	Richard E. Klima, Neil P. Sigmon, Ernest Stitzinger
Collection	Discrete Mathematics and Its Applications
Parution	12/07/2006
Édition	2^eme édition
Nb. de pages	528
Format	16 x 24
Couverture	Relié
Poids	900g
Intérieur	Noir et Blanc
EAN13	9781584886105
ISBN13	978-1-58488-610-5