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

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:	9780801890130
Publisher:	Johns Hopkins University Press
Publication date:	12/29/2008
Edition description:	second edition
Pages:	328
Product dimensions:	5.90(w) x 8.90(h) x 0.90(d)
Age Range:	18 Years

About the Author

David Joyner is a professor in the Mathematics Department at the U.S. Naval Academy. He is the author of Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys, also published by Johns Hopkins.

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

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

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

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

Joyner's text grew out of lecture notes designed to teach discrete mathematics and group theory to university students in an engaging, creative way. The text develops the basics of group theory and creates group-theoretical models of Rubik's Cube-like puzzles. The solution strategy for the Rubik's Cube is covered in some detail; solution strategies for similar puzzles (the 15 Puzzle, the Rubik Tetrahedron, the Rubik Dodecahedron, the Skewb, the Hockeypuck, and the Masterball) are discussed in less detail. Earlier chapters will be accessible to high school students with a strong mathematics background; later chapters are more advanced. The author's specific credentials are not given. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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