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Oval Track and Other Permutation Puzzles: And Just Enough Group Theory to Solve Them by John O. Kiltinen at Abbey's Bookshop,

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

John O. Kiltinen


Cambridge University Pres

Mathematics & Sciences;
Groups & group theory


324 pages

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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.

By:   John O. Kiltinen
Imprint:   Cambridge University Pres
Country of Publication:   United States
Volume:   No. 2
Dimensions:   Height: 253mm,  Width: 177mm,  Spine: 19mm
Weight:   598g
ISBN:   9780883857250
ISBN 10:   0883857251
Series:   Classroom Resource Materials
Pages:   324
Publication Date:   April 2004
Audience:   General/trade ,  College/higher education ,  ELT Advanced ,  Primary
Format:   Paperback
Publisher's Status:   Active

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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