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

By David Joyner

Book Overview

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.

• Format: Paperback
• Language: English
• ISBN: 0801869471
• ISBN13: 9780801869471
• Release Date: June 2002
• Publisher: Johns Hopkins University Press
• Length: 288 Pages
• Weight: 1.04 lbs.
• Dimensions: 0.6" x 6.3" x 9.2"

Customer Reviews

In depth group theory via games and puzzles

I am old enough to remember the original appearance of the Rubik's cube puzzle. I examined it a few times while in a store, but never put any effort into it. Later, I looked at some of the literature that explained how "easy" it was to solve the puzzle. The solution involves the use of some advanced topics in group theory, so it is a puzzle with a mathematical twist. However, that is not the only application of group theory, there are many ways in which it can be used. Joyner shows us many of them, and provides the foundation before he tackles the problems. This is an excellent book that can be used to either refresh your understanding of group theory or teach it to advanced undergraduates. The objects being manipulated are easy to understand, sometimes easy to build or acquire and the explanations are easy to follow. They are also different from those found in the standard group theory text. Puzzles are an area that fascinates many people, so it is often an advantage to present mathematical instruction in the form of a puzzle rather than in the standard sequence of background notation, theorem and then proof. Finally, the author is to be commended for donating all of the profits from the book to the Earth Island Institute. It is a non-profit organization dedicated to environmental projects throughout the world. Therefore, not only can a purchase of this book do your mathematical skills some good, it can also improve the quality of life for everyone on the planet. Published in the recreational mathematics newsletter, reprinted with permission.