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


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Word Power Books

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

by John O. Kiltinen (Author)


Mixed media product

ISBN: 9780883857250


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Book and CD explaining how to apply group theory to solve a range of popular puzzles.

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.


ISBN 883857251
ISBN13 9780883857250
Publisher Mathematical Association of America
Format Mixed media product
Publication date 23/10/2003
Pages 322
Weight (grammes) 598
Published in United States
Height (mm) 253
Width (mm) 177

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.