Applied Abstract Algebra

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JHU Press, 2004 - Mathematics - 329 pages
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With 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 GL(n), and the symmetric groups are emphasized.

With its clear writing style and wealth of examples, Applied Abstract Algebra will be welcomed by mathematicians, computer scientists, and students alike. Each chapter includes exercises in GAP (a free computer algebra system) and MAGMA (a noncommercial computer algebra system), which are especially helpful in giving students a grasp of practical 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
Bibliography
319
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About the author (2004)

David Joyner is a professor of mathematics at the United States Naval Academy. He is the author of Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys, also available from Johns Hopkins. Richard Kreminski is a professor and head of the mathematics department at Texas A & M University-Commerce. JoAnn Turisco is an associate professor of mathematics at the United States Naval Academy.

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