## Adventures in group theory: Rubik's Cube, Merlin's machine, and other mathematical toysGroup theory deals with symmetry, in the most abstract form possible. It is a core part of the undergraduate math curriculum, and forms part of the training of theoretical physicists and chemical crystallographers. Group theory has tended to be very dry--until now. David Joyner uses mathematical toys (primarily the Rubik's Cube and its more modern cousins, the Megaminx, the Pyraminx, and so on) as well as other mathematical examples (e.g., bell ringing) to breathe new life into a time-honored subject. "Why," asks the author, "should two such different topics, mechanical puzzles and abstract group theory, be related? This book takes the reader on an intellectual trip to answer this curiosity." Adventures in Group Theory will not only appeal to all math enthusiasts and interested general readers but will also find use in the classroom as a wonderful supplementary text in any abstract algebra or group theory course. |

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

User Review - Andrea Frazier - GoodreadsI'd be interested in hearing from someone who used this in a second course in abstract algebra. Read full review

### Contents

Elementary my dear Watson | 1 |

And you do addition? | 11 |

A procession of permutation puzzles | 47 |

Copyright | |

11 other sections not shown

### Common terms and phrases

15 Puzzle 3-cycle algorithm basic moves belong to G bijection buttons called Cayley graph center facets chapter color column conjugate conservation of twists corner subcubes corresponding cosets cross group cycle notation defined Definition degree clockwise rotation denote the set disjoint dodecahedron edge subcube elements of G equivalence classes equivalence relation exactly example face finite field flips function G acts group G group of order group theory Hadamard matrix homomorphism icosahedron identity implies induction integers isomorphic ker(f label Lemma Let f Let G Let H linear Masterball mathematics Megaminx Merlin's Machine move g multiplication normal subgroup orbits orientation permutation group permutation matrix permutation puzzle pieces polynomial Ponderable proof prove Pyraminx real numbers resp Rubik's Cube group semi-direct product set of vertices Show Skewb slice square subgroup of G subset superflip surjective swaps symmetric group symmetry Theorem transpositions vector space vertex words wreath products