Applied Abstract Algebra

Erscheinungsjahr 2004
ISBN: 978-0-8018-7822-0
Verlag: Johns Hopkins University Press

Buch, Englisch, 344 Seiten, Format (B × H): 182 mm x 262 mm, Gewicht: 880 g

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.

Autoren/Hrsg.

Joyner, David

Kreminski, Richard

Turisco, Joann

Inhaltsverzeichnis

Preface
Chapter 1. Some Elementary Number Theory
Chapter 2. Polynomials, Rings, and Fields
Chapter 3. Error-Correcting Codes
Chapter 4. Permutations
Chapter 5. An Introduction to Groups
Chapter 6. Special Projects: Codes
Chapter 7. Appendixes
Bibliography
Index

Über Autor(innen)

Joyner, David
David Joyner is a professor in the Mathematics Department at the U.S. Naval Academy. He is the author of Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys, also published by Johns Hopkins.

Turisco, Joann
JoAnn Turisco is an associate professor of mathematics at the United States Naval Academy.

Kreminski, Richard
Richard Kreminski is a professor and head of the mathematics department at Texas A & M University–Commerce.

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.