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

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

by David Joyner


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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.

Product Details

ISBN-13: 9780801869471
Publisher: Johns Hopkins University Press
Publication date: 06/28/2002
Pages: 280
Product dimensions: 6.30(w) x 9.18(h) x 0.64(d)

About the Author

David Joyner is a professor of mathematics at the U.S. Naval Academy. He is coauthor of Linear Algebra with Applications and editor of Coding Theory and Cryptography: From Enigma and Geheimschreiber to Quantum Theory.

Table of Contents



Where to begin... 1. Elementary, my dear Watson

2. 'And you do addition?'

3. Bell ringing and other permutations

4. A procession of permutation puzzles

5. What's commutative and purple?

6. Welcome to the machine

7. 'God's algorithm' and graphs

8. Symmetry and the Platonic solids

9. The illegal cube group

10. Words which move

11. The (legal) Rubik's cube group

12. Squares, two-faces, and other subgroups

13. Other Rubik-like puzzle groups

14. Crossing the Rubicon

15. Some solution strategies

16. Coda: Questions and other directionsBibliography


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