
Adventures in Group Theory
Rubik's Cube, Merlin's Machine, and Other Mathematical Toys
- English
- ePUB (mobile friendly)
- Available on iOS & Android
About this book
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.
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Information
Table of contents
- Cover Page
- Title Page
- Copyright Page
- Dedication
- Contents
- Preface
- Acknowledgments
- Where to begin. . .
- Chapter 1 Elementary, my dear Watson
- Chapter 2 ‘And you do addition?’
- Chapter 3 Bell ringing and other permutations
- Chapter 4 A procession of permutation puzzles
- Chapter 5 What’s commutative and purple?
- Chapter 6 Welcome to the machine
- Chapter 7 ‘God’s algorithm’ and graphs
- Chapter 8 Symmetry and the Platonic solids
- Chapter 9 The illegal cube group
- Chapter 10 Words which move
- Chapter 11 The (legal) Rubik’s Cube group
- Chapter 12 Squares, two-faces, and other subgroups
- Chapter 13 Other Rubik-like puzzle groups
- Chapter 14 Crossing the Rubicon
- Chapter 15 Some solution strategies
- Chapter 16 Coda: Questions and other directions
- Bibliography
- Index