## Applications of abstract algebra with Maple and MATLAB, Volume 1Eliminating 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. |

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### Contents

Preliminary Mathematics OOBIII1 | 1 |

Block Designs | 29 |

Error Correcting Codes | 53 |

Copyright | |

13 other sections not shown

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### Common terms and phrases

AES encryption process affine cipher BCH code beads block design CD-ROM Chapter ciphertext codewords colleague column com/e_products/downloads/download complete summary compute construct contains convert cosets crcpress ctext cycle index cycles of length decrypt the ciphertext deﬁned determine downloaded encrypt the message encryption exponent entering the following entries error correction Euclidean algorithm ﬁeld elements ﬁnal ﬁnd ﬁndings ﬁnite ﬁeld ﬁve found in Appendix group G Hadamard Hadamard matrix Hamming code Hill cipher index of coincidence initial key initial round input parameter insecure line intruder key matrix keyword linear code M-ﬁle Maple session MATLAB MATLAB session modulo necklace nonzero elements ordered pairs output partition pattern inventory permutation plaintext positive integer preceding command prime primitive polynomial ptext Reed-Muller code RSA cryptosystem S-box satisﬁes session and saved shift cipher Speciﬁcally Suppose Theorem undirected graphs user-written function variable vertices Vigenere cipher write a complete written separately