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

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 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 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 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 " 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." "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." "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." "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." 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.