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

David Joyner, "Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys"
The Johns Hopkins University Press | 2008 | ISBN: 0801890136, 0801890128 | 328 pages | Djvu | 2,6 MB
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.

David Joyner, "Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys"
The Johns Hopkins University Press | 2008 | ISBN: 0801890136, 0801890128 | 328 pages | Djvu | 2,6 MB
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.


From the preface:
This book grew out of a combined fascination with games and mathematics, from a desire to marry 'play' with 'work' in a sense. It pursues playing with mathematics and working with games. In particular, abstract algebra is developed and used to study certain toys and games from a mathematical modeling perspective. All the abstract algebra needed to understand the mathematics behind the Rubik's Cube, Lights Out, and many other games is developed here.
If you believe in the quote by von Neumann on a previous page, I hope you will enjoy getting used to the mathematics developed here. Why is it that these games, developed for amusement by non-mathematicians,
can be described so well using mathematics? To some extent, I believe it is because many aspects of our experience are universal, crossing cultural boundaries. One can view the games considered in this book, the Rubik's Cube, Lights Out, etc., to be universal in this sense Mathematics provides a collection of universal analytical methods, which is, I believe, why it works so well to model these games.
This book began as some lecture notes designed to teach discrete mathematics and group theory to students who, though certainly capable of learning the material, had more immediate pressures in their lives than the long-term discipline required to struggle with the abstract concepts involved. My strategy, to tempt them with something irresistible such as the Rubik's Cube, worked and students loved it. Based on my correspondence, my students were not the only ones to enjoy the notes, which have been expanded considerably. I've tried to write the book to be interesting to people with a wider variety of backgrounds, but at the same time I've tried to make it useful as a reference.
This book was truly a labor of love in the sense that I enjoyed every minute of it. I hope the reader derives some fun from it too.


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