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

by David Joyner

Overview

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.

Product Details

ISBN-13:	9780801897269
Publisher:	Johns Hopkins University Press
Publication date:	12/29/2008
Sold by:	Barnes & Noble
Format:	eBook
Pages:	328
File size:	27 MB
Note:	This product may take a few minutes to download.
Age Range:	18 Years

About the Author

David Joyner is a professor of mathematics at the U.S. Naval Academy. He is coauthor of Applied Abstract Algebra, also published by Johns Hopkins, and editor of Coding Theory and Cryptography: From Enigma and Geheimschreiber to Quantum Theory.

Table of Contents

Preface
Acknowledgments
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 directions
Bibliography
Index

Editorial Reviews

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

From the Publisher

"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

"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

"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