Adventures in Group Theory : Rubik's Cube,

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.

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.

Preface	p. ix
Acknowledgments	p. xi
Where to begin...	p. xiii
Elementary, my dear Watson	p. 1
'And you do addition?'	p. 13
Bell ringing and other permutations	p. 37
A procession of permutation puzzles	p. 61
What's commutative and purple?	p. 83
Welcome to the machine	p. 123
'God's algorithm' and graphs	p. 143
Symmetry and the Platonic solids	p. 155
The illegal cube group	p. 167
Words which move	p. 199
The (legal) Rubik's Cube group	p. 219
Squares, two-faces, and other subgroups	p. 233
Other Rubik-like puzzle groups	p. 251
Crossing the Rubicon	p. 269
Some solution strategies	p. 285
Coda: Questions and other directions	p. 297
Bibliography	p. 299
Index	p. 305
Table of Contents provided by Ingram. All Rights Reserved.

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

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