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Oval Track and Other Permutation Puzzles: And Just Enough Group Theory to Solve Them
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Oval Track and Other Permutation Puzzles: And Just Enough Group Theory to Solve Them

by John O. Kiltinen, William Watkins
 

ISBN-10: 0883857251

ISBN-13: 9780883857250

Pub. Date: 10/28/2002

Publisher: Mathematical Association of America

Popular puzzles such as the Rubik's cube and so-called oval track puzzles give a concrete representation to the theory of permutation groups. They are relatively simple to describe in group theoretic terms, yet present a challenge to anyone trying to solve them. John Kiltinen shows how the theory of permutation groups can be used to solve a range of puzzles. There

Overview

Popular puzzles such as the Rubik's cube and so-called oval track puzzles give a concrete representation to the theory of permutation groups. They are relatively simple to describe in group theoretic terms, yet present a challenge to anyone trying to solve them. John Kiltinen shows how the theory of permutation groups can be used to solve a range of puzzles. There is also an accompanying CD that can be used to reduce the need for carrying out long calculations and memorising difficult sequences of moves. This book will prove useful as supplemental material for students taking abstract algebra courses. It provides a real application of the theory and methods of permutation groups, one of the standard topics. It will also be of interest to anyone with an interest in puzzles and a basic grounding in mathematics. The author has provided plenty of exercises and examples to aid study.

Product Details

ISBN-13:
9780883857250
Publisher:
Mathematical Association of America
Publication date:
10/28/2002
Series:
Classroom Resource Materials Ser.
Edition description:
New Edition
Pages:
304
Product dimensions:
6.96(w) x 10.00(h) x 0.70(d)

Table of Contents

1. An overview of oval tracks; 2. The transpose puzzle: an introductory tour; 3. The slide puzzle: an introductory tour; 4. The Hungarian puzzle: an introductory tour; 5. Permutation groups: just enough definitions and notation; 6. Permutation groups: just enough theory; 7. Cycles and transpositions; 8. The parity theorem; 9. The role of conjugates; 10. The role of commutators; 11. Mastering the oval track puzzle; 12. Transferring knowledge between puzzles; 13. What a difference a disk makes!: changing the number of disks, and using Maple or GAP; 14. Mastering the slide puzzle; 15. Mastering the Hungarian rings with numbers; 16. Mastering the Hungarian rings with colours; 17. Advanced challenges.

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