$Handbook of Cubik Math - Alexander H. Jr Frey$

Handbook of Cubik Math

By: Alexander H. Jr Frey, David Singmaster

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Paperback | 29 July 2010

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The Handbook of Cubic Math unveils the theory involved in Rubik's Cube's solution, the potential applications of that theory to other similar puzzles, and how the cube provides a physical example for many concepts in mathematics where such examples are difficult to find. Nonetheless, the authors have been able to cover and explain these topics in a way which is easily understandable to the layman, suitable for a junior-high-school or high-school course in math, and appropriate for a college course in modern algebra. This manual will satisfy the experts' curiosity about the moves that lead to the solution of the cube and will offer a useful supplementary teaching aid to the beginners.

Industry Reviews

"The best book yet written - or likely to be written - on the wonders and the dark, unsolved mysteries of the cube" Martin Gardiner "Frey and Singmaster give a nicely blended discussion of specific algorithms for the cube together with some underlying theoretical concepts from group theory. Thus, cubists will be able to cure their insomnia by reading Chapter 3, and then perhaps satisfy their aroused curiosity about what is really going on by reading further" David M. Goldschmidt, Professor of Mathematics, University of California, Berkeley "Frey and Singmaster masterfully use the Rubik's cube to give a very tangible and tactile feel to the abstract concept of a group ... the book remains the definitive source for cube mathematics and presents an interesting and accessible introduction to group theory." David A. Reimann, in Mathematical Reviews, Issue 2012d

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You Can Find This Book In

Non-Fiction Mathematics Algebra Groups & Group Theory

Preface	p. vi
Introduction	p. 1
A Cubik Orientation	p. 3
Cubies and Cubicles	p. 3
Orientation Based On the Center Facelets	p. 8
Notation for Abbreviations	p. 11
Restoring the Cube	p. 20
The Down-Face Edge Cubies	p. 25
Three Down-Face Corner Cubies	p. 30
Three Middle-Layer Edge Cubies	p. 35
The Remaining Five Edge Cubies	p. 36
Placing the Final Corners	p. 45
Untwisting the Final Corners	p. 51
Cubik Games	p. 58
The What, Why, and How of Cube Movements	p. 60
Processes and Permutations	p. 61
Equivalent Processes	p. 68
Identities and Inverses	p. 69
Cyclic Order of a Permutation	p. 72
Finding Useful Processes	p. 75
Commutativity and Commutators	p. 77
Conjugates: Building New Processes from Old	p. 82
Improved Restoration Processes	p. 87
The Down-Face Edges	p. 87
Three Down-Face Corners	p. 88
Middle-Layer Edges	p. 90
Final Up-Face Edges	p. 90
Restoring Corners Untwisted	p. 92
Conjugates Help Orient the Final Corners	p. 93
Untwisting Corners	p. 96
The Cube Group and Subgroups	p. 98
The Permutations of the Cube form a Group	p. 99
Generators of a Group	p. 101
The Two-Squares Group	p. 104
The Slice Group	p. 105
The Two-Generator Group	p. 108
Other Subgroups of the Cube	p. 108
The Supergroup and Other Larger Groups	p. 113
Permutation Structures & the Order of Groups	p. 116
Permutations Are Odd or Even	p. 116
Parity of Permutations on the Cube	p. 118
The Parity of Flips and Twists	p. 121
The Order of the Cube Group	p. 125
The Order of the Two-Generator Group	p. 127
The Orders of Other Groups	p. 129
Advanced Restoration Methods	p. 132
Nested Subgroups	p. 132
Cosets of Subgroups	p. 136
Normal Subgroups and Isomorphisms	p. 140
Epilogue	p. 147
A Small Catalogue of Processes	p. 149
Solutions to Exercises	p. 155
Index	p. 177
Table of Contents provided by Ingram. All Rights Reserved.

Handbook of Cubik Math

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