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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 toysАвтор: 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: Рубрика: Математика /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Издание: 2-nd editionГод издания: 2008Количество страниц: 332Добавлена в каталог: 29.01.2014Операции: Положить на полку |
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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 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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