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

David Joyner (Author)

Book Description

Publication Date: June 6, 2002 | ISBN-10: 0801869471 | ISBN-13: 978-0801869471

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.

Editorial Reviews

Review

"Adventures in Group Theory is a tour through the algebra of several 'permutation puzzles'... If you like puzzles, this is a somewhat fun book. If you like algebra, this is a fun book. If you like puzzles and algebra, this is a really fun book." -- Donald L. Vestal

"Joyner has collated all the Rubik lore and integrated it with a self-contained introduction to group theory that equals or, more likely, exceeds what is available in typical dedicated elementary texts." -- Choice

"The book begins with some lecture notes of discrete mathematics and group theory. These theoretical notions are very nicely applied to some practical problems, e.g.: Rubik's cube, Rubik-like puzzle groups, crossing the rubicon, God's algorithm and graphs. The work ends with a rich bibliography and index." -- Cristinel Mortici, Zentralblatt Math

"Joyner does convey some of the excitement and adventure in picking up knowledge of group theory by trying to understand Rubik's Cube. Enthusiastic students will learn a lot of mathematics from this book." -- David Singmaster, American Scientist

"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." -- Charles Ashbacher

"This is a book on group theory that lives outside the usual rather dry regime of typical mathematics texts. In setting the book squarely among these puzzles, the underlying mathematics comes alive in quite spectacular fashion. The author achieves this goal admirably here. The text is well organized and written in an interesting and very readable manner." -- Ian W. Knowles, University of Alabama, Birmingham

Review

"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." -- Charles Ashbacher

--This text refers to an out of print or unavailable edition of this title.

See all Editorial Reviews

Product Details

• Paperback: 288 pages
• Publisher: The Johns Hopkins University Press (June 6, 2002)
• Language: English
• ISBN-10: 0801869471
• ISBN-13: 978-0801869471
• Product Dimensions: 9.2 x 6.7 x 1 inches
• Shipping Weight: 13.6 ounces
• Average Customer Review: 3.0 out of 5 stars  See all reviews (3 customer reviews)
• Amazon Best Sellers Rank: #1,516,965 in Books (See Top 100 in Books)

More About the Author

I'm a math professor and enjoy writing about mathematics and related topics. Not all my books are listed in the Amazon author's page (and at least one that is was not written by me), so feel free to use the search feature if you don't find something.

Customer Reviews

Most Helpful Customer Reviews

33 of 36 people found the following review helpful:

3.0 out of 5 stars Riddled with errors, but ---, May 31, 2003

By 

Bobby R. Treat "DrMajorBob" (Round Rock, TX United States) - See all my reviews
(REAL NAME)   

This review is from: Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys (Paperback)

I have never seen so many typos, omissions, and errors in a published book. Many of the examples are poorly introduced, theorems are mentioned that don't exist in the book, etc. Other than Rubik's cube, most of the other puzzles are presented in a completely incomprehensible manner. It's very annoying, in a book that's otherwise just what I want. It does give a good quick and dirty intro to the group theory needed, however.

19 of 26 people found the following review helpful:

5.0 out of 5 stars In depth group theory via games and puzzles, April 3, 2003

By 

Charles Ashbacher (Marion, Iowa United States) - See all my reviews
(TOP 500 REVIEWER)    (VINE VOICE)    (HALL OF FAME REVIEWER)   

This review is from: Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys (Paperback)

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.

9 of 41 people found the following review helpful:

1.0 out of 5 stars Why bother fixing typos?, March 17, 2006

By 

Cranky (London, England) - See all my reviews

This review is from: Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys (Paperback)

I was thinking of buying this book, but when I read that it is riddled with typos, I declined. Perhaps publishers will get the message that not doing proper editing results in lost sales.