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Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys 2nd Edition

by David Joyner (Author)

4.6 17 ratings

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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.

ISBN-10

0801890136
ISBN-13

978-0801890130
Edition

2nd
Publisher

Johns Hopkins University Press
Publication date

December 29, 2008
Language

English
Dimensions

6 x 0.74 x 9 inches
Print length

328 pages
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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 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

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.
--Zentralblatt Math

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

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

Product details

Publisher ‏ : ‎ Johns Hopkins University Press; 2nd edition (December 29, 2008)
Language ‏ : ‎ English
Paperback ‏ : ‎ 328 pages
ISBN-10 ‏ : ‎ 0801890136
ISBN-13 ‏ : ‎ 978-0801890130
Reading age ‏ : ‎ 18 years and up
Item Weight ‏ : ‎ 1.12 pounds
Dimensions ‏ : ‎ 6 x 0.74 x 9 inches

Best Sellers Rank: #1,822,410 in Books (See Top 100 in Books)
- #185 in Group Theory (Books)
- #189 in Abstract Algebra (Books)
- #1,007 in Math Games

Customer Reviews:
4.6 17 ratings

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David Joyner

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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.

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4.6 out of 5

17 global ratings

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Marek Komorowski

absolutely fine

Reviewed in the United States on April 13, 2013

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.

4 people found this helpful

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Raul Antonio Ferraz

Five Stars

Reviewed in the United States on November 29, 2017

Verified Purchase

Very interesting book!

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The item blew off the porch and onto a neighbours lawn … it was found a week later … so all is good. Amazon Customer

A great book.

Reviewed in the United States on January 21, 2017

Verified Purchase

A great book... a bit advanced though... not as much Rubiks Cube as I had hoped! Foolishly ~ my bad!

One person found this helpful

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Illinois cyclist

Frustrating reading experience

Reviewed in the United States on February 9, 2012

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.

31 people found this helpful

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