Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical ToysThis 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. |
Contents
| 1 | |
Chapter 2 And you do addition? | 13 |
Chapter 3 Bell ringing and other permutations | 37 |
Chapter 4 A procession of permutation puzzles | 61 |
Chapter 5 Whats commutative and purple? | 83 |
Chapter 6 Welcome to the machine | 123 |
Chapter 7 Gods algorithm and graphs | 143 |
Chapter 8 Symmetry and the Platonic solids | 155 |
Chapter 11 The legal Rubiks Cube group | 219 |
Chapter 12 Squares twofaces and other subgroups | 233 |
Chapter 13 Other Rubiklike puzzle groups | 251 |
Chapter 14 Crossing the Rubicon | 269 |
Chapter 15 Some solution strategies | 285 |
Questions and other directions | 297 |
| 299 | |
| 305 | |
Other editions - View all
Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other ... David Joyner Limited preview - 2008 |
Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other ... David Joyner Limited preview - 2002 |