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

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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.

Johns Hopkins University Press

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Editorial Reviews


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.

American Scientist

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.


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.

MAA Online

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.

Zentralblatt Math

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.

Ian W. Knowles
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.
From The Critics
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 (
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Product Details

  • ISBN-13: 9780801890130
  • Publisher: Johns Hopkins University Press
  • Publication date: 12/5/2008
  • Edition description: second edition
  • Edition number: 2
  • Pages: 328
  • Sales rank: 785,178
  • Product dimensions: 5.90 (w) x 8.90 (h) x 0.90 (d)

Meet 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.

Johns Hopkins University Press

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Table of Contents

Where to begin ...
Ch. 1 Elementary my dear Watson 1
Ch. 2 'And you do addition?' 11
Ch. 3 Bell ringing and other permutations 29
Ch. 4 A procession of permutation puzzles 47
Ch. 5 What's commutative and purple? 65
Ch. 6 Welcome to the machine 99
Ch. 7 'God's algorithm' and graphs 115
Ch. 8 Symmetry and the Platonic solids 125
Ch. 9 The illegal cube group 135
Ch. 10 Words which move 161
Ch. 11 The (legal) Rubik's Cube group 177
Ch. 12 Squares, two-faces, and other subgroups 189
Ch. 13 Other Rubik-like puzzle groups 205
Ch. 14 Crossing the rubicon 223
Ch. 15 Some solution strategies 233
Ch. 16 Coda: questions and other directions 249
Bibliography 251
Index 257
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Customer Reviews

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