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

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JHU Press, 2002 - Mathematics - 262 pages
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Group theory deals with symmetry, in the most abstract form possible. It is a core part of the undergraduate math curriculum, and forms part of the training of theoretical physicists and chemical crystallographers. Group theory has tended to be very dry -- until now. David Joyner uses mathematical toys (primarily the Rubik's Cube and its more modern cousins, the Megaminx, the Pyraminx, and so on) as well as other mathematical examples (e.g., bell ringing) to breathe new life into a time-honored subject.

"Why," asks the author, "should two such different topics, mechanical puzzles and abstract group theory, be related? This book takes the reader on an intellectual trip to answer this curiosity." Adventures in Group Theory will not only appeal to all math enthusiasts and interested general readers but will also find use in the classroom as a wonderful supplementary text in any abstract algebra or group theory course.

 

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This is an excellent, beautiful little book, which I am happy to be the first reviewer to provide a well-deserved 5-star rating for. It provides the concrete examples that really flesh out the bare theorems that one typically gains from an undergraduate course or text in algebra. It is a joy to read, and every time I pick it up I get something new from it. Great for building intuition, the kind of stuff that can really open things up for gaining insight and "aha" moments.  

Contents

Elementary my dear Watson
1
And you do addition?
11
Bell ringing and other permutations
29
A procession of permutation puzzles
47
Whats commutative and purple?
65
Welcome to the machine
99
Gods algorithm and graphs
115
Symmetry and the Platonic solids
125
The legal Rubiks Cube group
177
Squares twofaces and other subgroups
189
Other Rubiklike puzzle groups
205
Crossing the Rubicon
223
Some solution strategies
233
Coda Questions and other directions
249
Bibliography
251
Index
257

The illegal cube group
135
Words which move
161

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