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| Nievergelt J., Farrar J.C., Reingold E.M. — Computer approaches to mathematical problems |
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| Предметный указатель |
Goedel number 237
Golden ratio 188
Golomb, S. 89
Gordon, G. 168
Gotlieb, C.C. 89
Grammar 6 10 38
Grammar, context-free 38
Graph 62—72 91 102 133 138
Graph theory 62 90—101
Graph, adjacency matrix for 63 68
Graph, algorithms 62—73 91
Graph, application to decision theory 91
Graph, branch of 62 see edges
Graph, circuit in 68
Graph, collapsed, in Shannon switching game 103
Graph, component of 103
Graph, connected component of 66
Graph, connectivity matrix of 66—67
Graph, definition 62
Graph, directed 62
Graph, distance between all pairs of nodes 67
Graph, distance matrix 68
Graph, dual 138
Graph, duality 105 138
Graph, edges of 62 102 103 134
Graph, fundamental circuit matrix of 95
Graph, incidence matrix 62
Graph, length of edge 68
Graph, length of path in 68
Graph, minimal cost spanning tree 68
Graph, minimal cost spanning tree, algorithms 69—71
Graph, nodes of 64 102—105
Graph, nodes of, merged in Shannon switching game 103
Graph, path 64 105
Graph, planar 138
Graph, self-loop in 62
Graph, shortest path in 64
Graph, spanning trees 63 68—72
Graph, Warshall's algorithm 63 67
Greenblatt, R. 98 136
Gregory, J. 200
Griego, R.J. 168
Gries, D. 38
Griswold, R.E. 39
Hadamard, J. 208
Hagedorn, R.K. 243
Hall, M. 88—89
Halting problem 239—240
Hammersley, J.M. 168
Handscomb, D.C. 168
Harary, F. 90
Harmonic equations 168
Harmonic functions 159 160
Hawkins, D. 219
Height of tree 85 88
Hein, P. 137
Herman, R. 169
Heron the Elder 218
Hersh, R. 168
Heuristic programming 99 138
Heuristic search of game tree 129 136
Heuristic value of position in game tree 129—130 132
Heuristics 98—99 131—132
Heuristics, game playing techniques 99
HEX 97 99 109—111 137
Hi-Q puzzle 93
Hollerith, H. 92
Hopcroft, J.E. 38
Hull, T.E. 167
Hurwitz, A. 210
ILLIAC 196 210
In-place sorting algorithm 78
Incidence matrix 51—52 62
Incidence matrix for block designs 51
Incidence matrix for graphs 62
Index of computable function 240 242
Infinite random sequence 143 193
Infix notation 11
Insertion sorting 76 81—84
Instant Insanity puzzle 92
Integration, Monte Carlo methods for 155 156
Integration, numerical 55—156
Interaction of random numbers with boundary of region 171
Interaction of simulation with real time event 165
Internal sorting 76
Interpretation 1—2 18—19
Interpretation of expression 18—19
Jeenel, J. 201
Jeffress, L.A. 244
Kakutani, S. 159
Kauffman, A. 91
Kendall, M.G. 167
Key 73 81 see
Key operator (in arithmetic expressions) 41
Keyword 228
Kirchhoffs First Law 58 see
Kleene, S.C. 245
Knock-out tournament 80—81
Knuth, D.E. 38 89 92 167 219
Koenig, D. 90
Kruskal, J.B. 167
Lal, M. 194 221
Large primes 208
Latin squares 52—55 90
Latin squares, definition 52
Latin squares, origin of name 55
Latin squares, orthogonal see "Orthogonal latin squares"
Law of Large Numbers 154 156
Lee, R.C.T. 138
Lehman, A. 137
Lehmer, D.H. 89 167 219
Leibnitz, G. 43 88
Limitations of machines 235 245
Lindeberg, J.W. 152
Linear congruential method see "Random number generator"
Linear convergence 181
Linear programming 118
Linear recurrence relation 187
Linear search 82
Linked linear list 75 82
Literal semantics 19—20
Liu, C.L. 88
Ljapunov, A. 152
Logical limitations of machines 235 245
Lucas test for primeness 210 223
Luce, R.D. 137
Lucky numbers 206 222
Lukasiewics, Jan 12
Mac Hack VI (a chess—playing program by R. Greenblatt) 98 136
Machin, J. 210
Machine intelligence see "Artificial intelligence"
Machine language 15
Machine thinking 98 225 244
Machines 224 232 234
Machines, logical limitations of 235 245
Magic square 54 94
Maisel, H. 168
Manipulation of expressions 10
Mann, H.B. 89
Marnie, L.G. 137
Martin, A. 192
Martin, F.F. 168
Martin, W.A. 92
Mathematical model 97
Mathematical puzzles 54 93
Maximal connected subgraph 66
Mcllroy, M.D. 92
Mean 151
Mean-value property 159
Mersenne primes 209 210 219
| Mersenne, M. 208 222
Metaexpression 4—5 8
Metasymbol 3—5
Meyer, H.A. 168
Millo, J. 245
Mind-machine problem 225 244
Minimal-cost spanning tree 63 68—71 95
Minimal-cost spanning tree, exchange algorithm for 69
Minimal-cost spanning tree, partition algorithms for 71
minimax 98 114—116 122 129—130
Minimax, backup procedure 132 133
Minimax, evaluation of game tree 122—124
Minimax, play, optimality of 114
Minimax, player 114—115
Minimax, strategy 114—116 124
Minimax, theorem (von Neumann) 115—116
Minsky, M. 244 245
Minty, G.J. 92
Monte Carlo methods 153
Monte Carlo methods for solving harmonic equations 168
Monte Carlo methods, applied to deterministic problems 153
Monte Carlo methods, applied to Dirichlet problem 159—160
Monte Carlo methods, Buffon needle problem 153
Monte Carlo methods, computation of pi 171
Monte Carlo methods, convergence of 153
Monte Carlo methods, example 157
Monte Carlo methods, generality of 160
Monte Carlo methods, interactions with boundaries 171
Monte Carlo methods, motivation for 156
Monte Carlo methods, multiple integration 155
Monte Carlo methods, origin of 153
Monte Carlo methods, potential theory 159
Monte Carlo methods, random walks 158
Moore, E.F. 91
Morgenstern, O. 111 137
Moser, L. 137
Moses, J. 38
Multiply-by-3-and-add-1 algorithm 211 219 223
Munro, J.I. 91
Mutually ofthogonal set of latin squares 55 94
Napier, J. 196
Nash, J. 137
Natural numbers 236 237
Naur, P. 38
Newman, J.R. 244
Newton's method 185—186 194
Nicholson, S.C. 201
NIM 99—102 138
Nim, game tree for 123
Nim, Niven, I. 167
Nim, safe and unsafe triples 100—101
Nim, strategy 99—100
Nodes of a graph 62—65
Nodes of game tree 121—129 135
Nodes of parsing tree 7
Nodes, distance between 64
Nonassociativity 177
Nonterminal node 7
Nonterminal symbol 3—5 7—8
Normal distribution 152 158
Normal distribution, approximation of 152
Normal number 167
Normalized floating point number 176
Notation 1—3 10—12
Notation, infix 11
Notation, Polish 11
Notation, prefix 11
Notation, suffix 12
Null string 4
Number theoretic problems 175 202 219
Numbering of procedures 240
Numerical analysis 174 175
Numerical computation 174
Numerical methods 21 187
Numerical methods, stability of 187
Odds, in game 105—106
Ohm's law 58 see
Omission of parentheses 11
Operand 11—15
Operations research 111 144
Operator 3 6 11—16 41 67 94 230
Operator, additive 3
Operator, AND- 67
Operator, binary 11
Operator, involving infinity symbol 68
Operator, key (in arithmetic expressions) 41
Operator, multiplicative 6
Operator, OR- 67 94
Optimal strategy 118 121
Oracle 105—109 139 246
Order of convergence 181 184
order of operations 11
Ordered tree 121
Ore, O. 90—91
Orthogonal Latin squares 53—55 90 93—94
Orthogonal latin squares, complete set of 55
Orthogonal latin squares, definition 54
Orthogonal latin squares, Euler's conjecture 55
Orthogonal latin squares, generating a magic square 54
OUGHTRED, W. 196
Overflow 176
Packing problems 56
Pairing function 246
Parentheses 11—30
Parentheses, omission of 11
Parentheses, redundant, in arithmetic expressions 19 23—30
Parentheses, redundant, in arithmetic expressions, removal of 24
Parenthesis notation 2 15
Parker, E.T. 90
Parsing 7
Parsing tree 7—13 26—33 39
Parsing tree, set of 10
Parsing tree, uniqueness of 8 10
Partition 69 76
Pascal, B. 111
Path 64
Pattern in random numbers 144 157
Pattern recognition 138
Patterns 144 157 208 212 214 216
Payoff 111 116—119 124 135
Payoff matrix 112 see
Pell equation 194
Planar graph 138
Poage, J. F. 39
Poisson distribution 170
Poker test see "Random number generator"
Polish expression, evaluation of 13—15
Polish notation 10—20 30 40
Polish notation, expressions in, recognition of 40
Polish notation, prefix 12
Polish notation, suffix 19 30 40
Polish notation, suffix, conversion from parenthesis notation 15
Polonsky, I.P. 39
Position in game 98 128—132
Position in game, dead 98
Position in game, quiescent 131—132
Position in game, value of 129 132
Post, E. 245
Potential theory 159
Pounder, J.R. 137
Pragmatic semantics 20
Pragmatic simplification 35
Precedence 7 11
PRECISION 175 191
Prefix notation 11
Prime number theorem 208
Prime numbers 203 208 219
Prime numbers, Lucas test 210
probability 106—109 111 121 127 148 154 158 162
Probability density function 151
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