Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys / Edition 2

Adventures in Group Theory: Rubik's Cube, Merlin's Machine, and Other Mathematical Toys / Edition 2

4.0 2
by David Joyner
     
 

ISBN-10: 0801890136

ISBN-13: 9780801890130

Pub. Date: 12/01/2008

Publisher: Johns Hopkins University Press

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

Overview

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.

Product Details

ISBN-13:
9780801890130
Publisher:
Johns Hopkins University Press
Publication date:
12/01/2008
Edition description:
second edition
Pages:
328
Sales rank:
752,097
Product dimensions:
5.90(w) x 8.90(h) x 0.90(d)
Age Range:
18 Years

Table of Contents

Preface ix

Acknowledgments xi

Where to begin... xiii

Chapter 1 Elementary, my dear Watson 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 What's commutative and purple? 83

Chapter 6 Welcome to the machine 123

Chapter 7 'God's algorithm' and graphs 143

Chapter 8 Symmetry and the Platonic solids 155

Chapter 9 The illegal cube group 167

Chapter 10 Words which move 199

Chapter 11 The (legal) Rubik's Cube group 219

Chapter 12 Squares, two-faces, and other subgroups 233

Chapter 13 Other Rubik-like puzzle groups 251

Chapter 14 Crossing the Rubicon 269

Chapter 15 Some solution strategies 285

Chapter 16 Coda: Questions and other directions 297

Bibliography 299

Index 305

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