## Applied Abstract AlgebraWith the advent of computers that can handle symbolic manipulations, abstract algebra can now be applied. In this book David Joyner, Richard Kreminski, and Joann Turisco introduce a wide range of abstract algebra with relevant and interesting applications, from error-correcting codes to cryptography to the group theory of Rubik's cube. They cover basic topics such as the Euclidean algorithm, encryption, and permutations. Hamming codes and Reed-Solomon codes used on today's CDs are also discussed. The authors present examples as diverse as "Rotation," available on the Nokia 7160 cell phone, bell ringing, and the game of NIM. In place of the standard treatment of group theory, which emphasizes the classification of groups, the authors highlight examples and computations. Cyclic groups, the general linear group With its clear writing style and wealth of examples, |

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### Contents

Some Elementary Number Theory 1 | 26 |

Polynomials Rings and Fields | 67 |

ErrorCorrecting Codes | 135 |

Permutations | 185 |

An Introduction to Groups | 217 |

Codes | 269 |

Appendixes by David Joyner | 295 |

319 | |