Applications of Abstract Algebra with Maple and MATLAB, Second Edition

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CRC Press, Jul 12, 2006 - Mathematics - 528 pages
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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 MapleTM 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.
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    Contents

    Preliminary Mathematics
    1
    Block Designs
    29
    Error Correcting Codes
    53
    BCH Codes
    93
    ReedSolomon Codes
    135
    Algebraic Cryptography
    169
    Vigenere Ciphers
    219
    The RSA Cryptosystem
    259
    The Advanced Encryption Standard
    335
    Polya Theory
    389
    Graph Theory
    417
    Appendices
    445
    B UserWritten MATLAB Functions
    461
    Bibliography
    481
    Index
    493
    Copyright

    Elliptic Curve Cryptography
    293

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