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

David Joyner (Author)

Book Description

Publication Date: December 1, 2008

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.

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." - MAA Online "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 "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." - American Scientist"

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.

(MAA Online )

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 2003)

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.

(American Scientist 2003)

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.

(Zentralblatt Math 2007)

See all Editorial Reviews

Product Details

• Paperback: 328 pages
• Publisher: The Johns Hopkins University Press; 2nd edition (December 1, 2008)
• Language: English
• ISBN-10: 0801890136
• ISBN-13: 978-0801890130
• Product Dimensions: 6 x 0.7 x 9 inches
• Shipping Weight: 15.2 ounces (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #1,044,527 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.

Most Helpful Customer Reviews

13 of 14 people found the following review helpful

3.0 out of 5 stars Frustrating reading experience February 9, 2012

By Illinois cyclist

Format:Paperback

I can't figure out who the intended audience is for this book. It's not a textbook; the subject is not developed in a systematic manner, nor are there useful problems sets. The reader exercises, referred to as 'Ponderables' in the book, can be extremely challenging and off-topic, beginning with the chess problems in the first chapter. It's also too technical to be a popularization, although it seems to be targeted as such. I was looking for friendly introduction to group theory, and the core concepts are there. However, a focus on the Rubik's cube and other similar games as primary examples of groups introduces a lot of complexity.

The book is written in an entertaining fashion with many historical references, quotes, puns and quips. I often found them to be a distraction.

The SAGE programming code provides quite a few examples but it is often not decipherable to a reader unfamiliar with this relatively obscure language based on Python; a little explanation would have gone a long way. Frequently terminology and notation are used before they are defined. Apparently this second edition cleaned up some errors, but there are still a number of typos and statements which are simply wrong. Theorems are stated imprecisely, and the proofs in the book are often hand-waving exercises rather than actual proofs. Important results are presented without justification or the proof left to the reader.

I don't intend to imply there is no value here. Parts of the book provide a relatively accessible introduction to group theory, but the reading experience can be very frustrating.

5.0 out of 5 stars absolutely fine April 13, 2013

By Marek Komorowski

Format:Paperback|Amazon Verified Purchase

This book is good, mathematical point of view , connections between rubic cube and other similar puzzles with the group theory, the seller is fine , I can recommend it.