Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys

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JHU Press, Dec 5, 2008 - Mathematics - 328 pages
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This updated and revised edition of David Joyner’s entertaining "hands-on" tour of group theory and abstract algebra brings life, levity, and practicality to the topics through mathematical toys.

Joyner uses permutation puzzles such as the Rubik’s Cube and its variants, the 15 puzzle, the Rainbow Masterball, Merlin’s Machine, the Pyraminx, and the Skewb to explain the basics of introductory algebra and group theory. Subjects covered include the Cayley graphs, symmetries, isomorphisms, wreath products, free groups, and finite fields of group theory, as well as algebraic matrices, combinatorics, and permutations.

Featuring strategies for solving the puzzles and computations illustrated using the SAGE open-source computer algebra system, the second edition of Adventures in Group Theory is perfect for mathematics enthusiasts and for use as a supplementary textbook.

 

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Contents

Chapter 1 Elementary my dear Watson
1
Chapter 2 And you do addition?
13
Chapter 3 Bell ringing and other permutations
37
Chapter 4 A procession of permutation puzzles
61
Chapter 5 Whats commutative and purple?
83
Chapter 6 Welcome to the machine
123
Chapter 7 Gods algorithm and graphs
143
Chapter 8 Symmetry and the Platonic solids
155
Chapter 11 The legal Rubiks Cube group
219
Chapter 12 Squares twofaces and other subgroups
233
Chapter 13 Other Rubiklike puzzle groups
251
Chapter 14 Crossing the Rubicon
269
Chapter 15 Some solution strategies
285
Questions and other directions
297
Bibliography
299
Index
305

Chapter 9 The illegal cube group
167
Chapter 10 Words which move
199

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About the author (2008)

David Joyner is a professor of mathematics at the U.S. Naval Academy. He is coauthor of Applied Abstract Algebra, also published by Johns Hopkins, and editor of Coding Theory and Cryptography: From Enigma and Geheimschreiber to Quantum Theory.

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