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Joyner D. — Adventures in group theory: Rubik's cube, Merlin's machine, and other mathematical toys
Joyner D. — Adventures in group theory: Rubik's cube, Merlin's machine, and other mathematical toys

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Название: Adventures in group theory: Rubik's cube, Merlin's machine, and other mathematical toys

Автор: Joyner D.

Аннотация:

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.



Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 2008

Количество страниц: 332

Добавлена в каталог: 29.01.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Abel, Niels Henrik      90 180
Abelian      91
action      110
Adjacent vertices      144 151
Algorithm for conjugacy classes      109
Algorithm for elements of G      92
Algorithm for orbits      113
Algorithm, Dimino's      119
Alien Tiles      127 137
Alternating group      97
Arrangement      33
Assmus and Mattson Theorem      279
Associativity      88
Automorphism      170
Automorphism, code      275
Bandelow, Christoph      7
Base (of wreath product)      195
Basic move      69 79 81
Basic move, Skewb      253
Basic moves      78
Basic moves of the cube      8
Basic moves, Pyraminx      259
Basis      133
Bierce, Ambrose      2 181
Bijection      18
Binary code      274
Binary operation      83
Block design      279
Boolean addition      4
Boolean algebra      5
Boolean multiplication      4
Boolean value      1
Bryan, Jerry      100 149
Campanology      119
Cancellation law      89
Cardinality      7
Carroll, Lewis      13 43
Cartesian product      16
Catalog      294
Catalog of Masterball moves      292
Cauchy's theorem      93
Cauchy, Augustin      94
Cayley graph      146
Cayley, Arthur      20 146
Center      97
centralizer      114
Characteristic of a field      237
Characteristic polynomial      133
Check matrix      275
Chip firing games      127
Churchill, Winston      285
Class equation for groups      117
Clean moves      287 294
Code      274
Codeword      274
Codimension      133
Cofactor      25
Coloring      65
Combination      33
Commutative      91
Commutator      103
Commutator subgroup      104
Commutator subgroup of the cube group      228
Complement      192
Complete machine      128
composition      18
Conclusion      5
Conjugacy class      108
conjugate      105
Conjugation      112
Connected      144
Connective      1
Conservation of total flips      224
Conservation of total twists      224
Constant      6
Continuum Hypothesis      205
Conway, John      280
Corner 3-cycles      288
Corner orientations      221
Coset representative      118
Countable      18
Cross move      246
Cycle decomposition      50
Cycle structure      50
Cyclic      94
Cyclic code      275
Cyclic groups      85 209
Cyclic permutation      49
De Morgan's laws      5 10
De Morgan, A.      5 31
Decision algorithm      200
Degree      144
Dehn, Max      204
Derived series      104
Determinant      25
Diagonal entries      23
Diagonal matrix      23
Diameter      145
Digraph      144
Dihedral group      86 103 209
DIMENSION      133
Dimino's Algorithm      119
Direct product      16 184
Disjoint      10
Distance      145
Distance function      157
Dodecads      278
dodecahedron      78
Duad      163
Dyson, Freeman      83 247 298
Echelon form, row reduced      135
EDGE      143 144
Edge 3-cycle      288
Edge orientations      222
Eigenvalue      133
Eigenvector      133
Elementary matrix      132
Elementary row operation      134
Elements      7
Embed      170
Empty set      8
Equal sets      9
Equatorial      65
Euler's phi function      14
Even permutation      39
Existential quantifier      4
Fabel, K.      98
Face degree      155
Face turn metric      148
Facet      65
Feynmann, Richard      110
Fibonacci polynomial      131
Field      236
Field extension      239
Field isomorphism      236
Finite field      237
Finite-state machine      127
First fundamental cube theorem      186
First isomorphism theorem      182
fishing      286 291
Fractional linear transformation      241
Free group      201
Function      13
Galois' last dream      272
Galois, E.      91 105 143 182
Gardner, M.      7
Gauss Elimination Game      134
Gaussian elimination      134
General linear group of order      2 241
Generalized symmetric group      194
Generating matrix      274
Generating polynomial      107
Generator polynomial for code      275
Generators      92 207
God's algorithm      149 202
Golay code      276
Golay, Marcel      277
Gold — Turner theorem      253
Gordan game      94
Graph      143
Graph, directed      144
Graph, simple      143
Group      89
Group operation      84
Group, finitely presented      207
Hadamard conjecture      281
Hadamard determinant bound      281
Hadamard Jacques      281
Hadamard matrix      281
Hamilton, William R.      84 150
Hamiltonian circuit      150
Hockeypuck puzzle      63
Hoelder, Otto      175 181
Hoey, Dan      215
Hofstadter, Douglas      269
Holmes, Sherlock      7
Homomorphism      168
Homotopy group      152
Homotopy group of Square      1 263
Homotopy group of the 15 Puzzle      152
Icosahedral group      156
IDA      291
Identity      89
Identity matrix      23
Illegal Rubik's Cube group      196
Illegal Square 1 group      264
Image      168
INDEX      97
Information space      274
Injective      18
Inner automorphism      175
Inverse      89
Inverse function      20
Inverse matrix      24
Irreducible polynomial      239
ISBN code      278
Isometry      157
Isomorphism      170
Iterative deepening A*      291
Jordan, Camille      105 170
Kernel      178
Klein 4-group      209 249
Kociemba, Herbert      290
Lagrange's theorem      118
Langlands, Robert      251
Laplace cofactor expansion      25
Large      65
Latitudinal line      65
Laws of negation      5 10
Layer method      286
Left action      111
Left coset      115
Left equivalent      283
Left multiplication      112
Length      39 225
Length (of word)      201
Length, code      274
Lights Out      123 124 126
Lights Out, Cube      127
Lights Out, Deluxe      126
Lights Out, Keychain      126 141
Lights Out, solved      130
Linear fractional transformation      241
Logical argument      5
Longitudinal line      65
Longridge, Mark      191 296
Lower triangular entries      23
Loyd, Sam      62
Machine, complete      128
Machine, finite state      128
Machine, Mealy      128
Machine, Merlin's      128
Machine, Rubik's Cube      128
MAP      13
Masterball      64
Mathieu group $M_{12}$      270
Mathieu groups      273 277
Mathieu, Emile      270
Matrix      22
Matrix, history      20
Matrix, identity      23
Matrix, monomial      23
Matrix, permutation      23
Matrix, square      22
Mealy machine      127
Meffert, Uwe      68
Megaminx      78
Merlin's Machine      128
Merlin's Magic      123 125
middle      65
Middle slice      286
Minimum distance      275
Minor      25
Moebius transformations      241 271
Moebius, August      241
Moebius-superflip game      76
Monge, Gaspard      270
Mongean shuffie      270
Monomial matrix      23 194 275
Move      66
Neighboring      78
Neighboring vertices      144
Next state function      127
Non-singular matrix      25
NonAbelian      91
Noncommutative      91
Nonslice-superflip game      76
normal      178
Nullity      135
Octahedral group      156
Odd permutation      39
One-to-one      18
Onto      18
Operation      88
Orbit      113
Orbix      125 137
Order      42 93
Orientation preserving      157
Orientations      219
Orthogonal group      159
Outer automorphism      175
Output function      127
Paley, Raymond      282
Parity      224 252
Parity check matrix      275
Partial function      128
Partition      10
Pascal, Blaise      35
Path      144 152
Path, composition      152
Path, inverse      152
Path, simple      152
Pentad      163
Permutation      37
Permutation group      92
Permutation matrix      23 44
Plain Bob Minimus      119
Platonic groups      156
Poincare polynomial      201
polar      65
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