Adventures in Group Theory
Rubik's Cube, Merlin's Machine, and Other Mathematical Toys
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.
"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, reviewing a previous edition or volume
"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, reviewing a previous edition or volume
"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, reviewing a previous edition or volume
"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, reviewing a previous edition or volume
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.Related Links:
David Joyner's USNA webpage
Permutation Puzzles
Related Books:
Likelihood, expanded edition
A. W. F. Edwards
Matrix Computations, third edition
Gene H. Golub and Charles F. Van Loan
