Applications of Abstract Algebra with Maple and MATLAB, Second Edition - Rilegato

Klima, Richard; Sigmon, Neil; Stitzinger, Ernest

 
9781584886105: Applications of Abstract Algebra with Maple and MATLAB, Second Edition
Rilegato
ISBN 10: 1584886102 ISBN 13: 9781584886105
Casa editrice: Chapman and Hall/CRC, 2006

Sinossi

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.

    • Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

    Contenuti

    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

    Each chapter contains Computer and Research Exercises.

    APPENDIX A: USER-WRITTEN MAPLE FUNCTIONS
    APPENDIX B: USER-WRITTEN MATLAB FUNCTIONS
    BIBLIOGRAPHY
    HINTS OR ANSWERS FOR SELECTED EXERCISES
    INDEX

    Product Description

    Book by Klima Richard E Sigmon Neil Stitzinger Ernest

    Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

    Editore
    Chapman and Hall/CRC
    Data di pubblicazione
    2006
    Lingua
    Inglese
    ISBN 10 
    1584886102
    ISBN 13 
    9781584886105
    Rilegatura
    Copertina rigida
    Numero edizione
    2
    Numero di pagine
    522
    Contatto del produttore
    non disponibile
    Persona responsabile
    non disponibile