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Oval Track and Other Permutation Puzzles: And Just Enough Group Theory to Solve Them (Classroom Resource Materials) [Paperback]

John O. Kiltinen
5.0 out of 5 stars  See all reviews (1 customer review)


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Book Description

July 2003 0521619742 978-0521619745
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.

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Book Description

Popular puzzles such as the Rubik's cube and so-called oval track puzzles give a concrete representation to abstract mathematics. This book and CD show how the theory of permutation groups can be used to solve a range of puzzles. Ideal for students of algebra or anyone with an interest in puzzles.

About the Author

John O. Kiltinen is a native of Marquette,Michigan. He earned his Bachelor of Arts degree at Northern MichiganUniversity in 1963 and his Doctor of Philosophy in mathematics at DukeUniversity in 1967. After teaching at the University of Minnesota for four years, he returned in 1971 to his undergraduate alma mater, where he has been a faculty member ever since. He was a visiting professor during1978-79 in Finland, spending half of the year at the University of Joensuu,and half at the Tampere University of Technology. For the first half ofhis year in Finland, he held a Fulbright Lectureship.

Product Details

  • Series: Classroom Resource Materials
  • Paperback: 304 pages
  • Publisher: The Mathematical Association of America (July 2003)
  • Language: English
  • ISBN-10: 0521619742
  • ISBN-13: 978-0521619745
  • ASIN: 0883857251
  • Product Dimensions: 0.8 x 9.8 x 6.7 inches
  • Shipping Weight: 1.3 pounds
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #2,558,839 in Books (See Top 100 in Books)

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1 of 1 people found the following review helpful
5.0 out of 5 stars Permutation puzzle challenges that never end October 9, 2008
Format:Paperback
This package of book and software presents three fundamental puzzles that can be solved using permutations. The first is called the "Oval Tracks" puzzles and consists of an oval-shaped track that contains numbered disks. There are two fundamental operations that can be performed on the disks:

*) All can be rotated around the track a certain number of positions in either direction. This movement will maintain the fundamental order of the disks.
*) A certain set of permutations can be performed on a small number of the disks.

The second category of puzzle is the "slide puzzles." In this case there is a rectangular grid where each cell of the grid contains a single disk. There is an empty cell and the disks are moved one at a time into the unoccupied cell, creating a different unoccupied cell. Variations of this puzzle have cells marked with an X that are rigid and cannot be moved.
The third category of puzzles is called the "Hungarian Rings." In this case, the puzzle is constructed from two interlocking rings of disks that are either numbered or colored. The disks share two locations and are separately movable so the only operations are rotating the disks.
In all cases, the player is given start and final configurations and the goal is to move from the start to the final state. The software can be used to execute a random rearrangement of the disks at the start of the game. Undo buttons and the ability to create complex macro operations are available.
Using the fundamentals of group theory as it is applied to permutation groups, you can solve all of these games. Therefore, after the initial descriptions of the games, there is an introduction to group theory and permutations.
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