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Nievergelt J., Farrar J.C., Reingold E.M. — Computer approaches to mathematical problems
Nievergelt J., Farrar J.C., Reingold E.M. — Computer approaches to mathematical problems

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Название: Computer approaches to mathematical problems

Авторы: Nievergelt J., Farrar J.C., Reingold E.M.

Аннотация:

This book is intended as a text for an intermediate course in computer science or mathematics which focuses on the relation between computers and mathematics in formulating and solving problems. In such a course a wide variety of problems would be discussed, the underlying connection being that all of the problems require mathematical concepts for their formulation, and computer techniques for their practical solution.


Язык: en

Рубрика: Computer science/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1974

Количество страниц: 267

Добавлена в каталог: 24.02.2015

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\alpha$-cutoff      124 126
$\alpha$-value      124
$\beta$-cutoff      124 126 see
$\beta$—value      124 see
$\pi$      21 171 191—192 198 218 222
$\pi$, computation of      171 198 218
$\sqrt{2}$, computation of      191 192
::=(symbol used in productions)      3
< > metasymbol (e.g., operator )      3 12
Adjacency matrix      63 66—68 94
Akers, S.B.      91
Algebra word problems      229
Algol      60 38
Algorithm      1 10 16 19 23
Algorithm, backtrack      47
Algorithm, existence, decidability      241—243
Algorithm, fictitious play      118—119 137
Algorithm, formal differentiation      23
Algorithm, graph      62—73
Algorithm, graph, computation of distance matrix      68
Algorithm, graph, decomposition type      63 72—73
Algorithm, graph, exchange (for minimal cost spanning tree)      69
Algorithm, graph, generating all spanning trees      72
Algorithm, graph, minimal cost spanning tree      69—70
Algorithm, graph, propagation type      63
Algorithm, graph, shortest path      63—64
Algorithm, graph, Warshall's      63 67
Algorithm, minimax evaluation of game tree      122
Algorithm, multiply-by-3-and-add-l      212
Algorithm, random number generator      144—145
Algorithm, sorting      75—83
Algorithm, sorting, bubble sort      77—78
Algorithm, sorting, insertion sorting      81
Algorithm, sorting, Quicksort      78
Algorithm, sorting, tournament-selection sort      81 95
Algorithm, syntax—directed      10 16 38
Algorithmic computation      236
Algorithmic meaning      19—24 29 41 see algorithmic"
Algorithmic semantics      20 41
Alpha-beta pruning      122—128 140
Ambiguity      4 11
Ambiguous grammar      39
Anderson, A.R.      244
Andree, R.V.      218
Apter, M.J.      244
Archimedes      198 222
Arithmetic      1 175 217
arithmetic expressions      1—42
Arithmetic expressions, class of all      2
Arithmetic expressions, definition      5
Arithmetic expressions, differentiation of      22
Arithmetic expressions, key operator in      41
Arithmetic expressions, language of      2—7
Arithmetic expressions, meaning of      7 see
Arithmetic expressions, Polish representation for      12
Arithmetic expressions, recognition of      39
Arithmetic expressions, reduction of      36
Arithmetic expressions, semantics      2—20
Arithmetic expressions, set of      10
Arithmetic expressions, syntax      36
Arithmetic, floating point      176 220
Arithmetical progression      205 222
Artificial intelligence, contribution of game playing programs      99
Ashton, W.D.      168
Association for Computing Machinery      98
Associative laws      31
Asymptotic error constant      181 184
Automata      232—236
Babington-Smith, B.      167
Backtrack      44—50 72 89 93 98 203
Backtrack, algorithm      44—47
Backtrack, applied to tilings      90
Backtrack, contrasted with heuristic tree search      98
Backup procedure      132—133 140
Backup procedure, comparison of several      140
Backup procedure, m and n      132
Backup procedure, minimax      124 132
Backus — Naur Form (Backus Normal Form)      36
Balanced incomplete block design      50—52
Balanced tree      83 85—86 96
Baumert, L.      89
Beckenbach, E.F.      88
Beckmann, P.      219
Berge, C.      90
Bernoulli, J.      154
Binary representation of numbers, applied to analysis of Nim      100
Binary search      82—84 95
Binary search tree      83—85
Binet's formula      188
Block designs      50—52 89
BNF      see "Backus — Naur Form"
Bobrow, D.G.      231 244
Boorman, J.M.      192
Branch and bound algorithm      46
Bratley, P.      245
Brouncker, Lord William      200
Brown, G.W.      118 138
Brown, R.      158
Bubble sort      77—78
Buffon Needle Problem      153 170
Burks, A.W.      245
Calling the largest number      105—109 137 139
Calling the largest number and dynamic storage allocation      137
Calling the largest number, analysis of      106—109
Calling the largest number, variations on      139
Campbell, J.A.      137
Cantor, G.      239
Cayley, A.      72
Central-limit theorem      152
CHARACTER      2—5
character string      4 7 15 19 238
Chase, S.M.      137
Checker-playing program      99 136
Checking long computations      197 211
Chess      98 117—118 132 136
Chess automation      243
Chess-playing programs      136 225
Chi-square, applied to random number generator      149
Chi-square, statistic      148 169
Chi-square, test      146 222
Chomsky, N.      38
Church's thesis      236
Church, A.      236 245
CIR(e,T) (circuit function on spanning trees)      69—70 95
Circuit, in graph      68
Cohn, J.H.E.      219
Coin tosses      142 148
Combinatorial computing      43—96
Combinatorial mathematics      43 89
Combinatorial problems      43—44 47 191
Commutative laws      30
Complete tiled rectangle      61
complexity      232
Compound-interest law      195
Computability      236 245
Computable function      234 239
Computation of constants to high precision      191
Computer arithmetic      175 217
Computer chess tournament      98
Computer conversation      227—228
Connected component of a graph      66 69
Connectivity matrix      66—67 91 94
Constal, R.      192
Constant      4 191
Constraints in combinatorial problems      47
Context—free grammar      38
Convergence      138 179
Convergence, rate of      181 see
Conversational programs      226 246
Cost of spanning tree      69
Crocker, S.      136
Csima, J.      89
Current flow in electrical network      56
Cutoff depth, criterion for halting variable-depth search      133
Cut—player      102 see
D<X,5>, formal derivative of an arithmetic expression      22 40
Dahse, Z.      200
Data structure      13 75
Davis, M.      245
de la Valine Poussin, C.J.      208
De Lagny, F.      200
Decision procedure      239
Decision theory      91
decision-making      97 137
Depth—first search      46 see
Derivation      1 5—8 11
Derivation tree (parsing tree)      7 39
Derivation, immediate      5
Derivative      22 195
Derivative of arithmetic expression, formal      22
Descendant, nodes in game tree      124 130
Descriptions of machines      234—235
Design of statistical experiments      50—51
Diagonalization      239 246
Dichampt, M.      201
Directed graph (digraph)      62
Dirichlet problem      159—160
Distance between pairs of nodes in a graph      67
Distance matrix      68 94
Distribution of primes, asymptotic      208 210
Distribution of random numbers      148 151 152 170
Distribution of random numbers, exponential      170
Distribution of random numbers, normal      152
Distribution of random numbers, Poisson      170
Distribution of random numbers, transformation of      151
Distribution of random numbers, uniform      151
Distributivity      32
Dobell, A.R.      167
DOCTOR      227
Dual graph      138
Duality, in graph theory      105 138
Dutka, J.      194 218 222
Dynamic storage allocation      137
Dynkin, E.B.      137
e      191 192 195 218 222
E(p,q), expected payoff in two-person zero-sum game      115—116
Eastlake, R.      136
Edge-disjoint spanning trees      139
Edges      62 65 73 135
Edges of a graph, directed      62
Effective numbering of procedures      240 242
Effectiveness      1 240
Eight-queens problem      44—48 92
Electrical networks      56—59 72 90 94
Electrical networks, correspondence with tiled rectangles      59
Electrical networks, current flow in      56
Electrical networks, Kirchhoff s First Law      58
Electrical networks, Ohm's Law      58
Electrical networks, planar      57
Electrical networks, resistance of branch      57
Electrical networks, solution of      58
Electrical networks, system of equations for      59
ELIZA      227—228 244
ENIAC      196 201
Equivalence of arithmetic expressions      18 35
Equivalence of procedures      241
Equivalence problem      241
Equivalence-preserving transformation      27—30
Eratosthenes, sieve of      203
Errors      175 187 189 211 217
Errors in long computer runs      211
Essential parentheses      26
Euclid      208
Euler's conjecture (on orthogonal latin squares)      55
Euler, L.      55 196 202
Evaluation of expressions      13
Evaluation of game tree, fixed—depth search      128 130
Evaluation of game tree, minimax      122
Evaluation of game tree, variable depth search      132—133
Evaluation of random number generators      146 149 167
Evaluation of random number generators, frequency test      146
Evaluation of random number generators, gap test      167
Evaluation of random number generators, poker test      150 170
Exchange algorithm (for min-cost spanning tree)      69 95
Exclusive-OR      100
Exhaustive search      98 128 202 see
expected payoff      116 119
Exponential distribution      170
exponentiation      39
Expression      1—10 16—24 see
Expression, interpretation      18—19
Expression, manipulation      10 21
Expression, rational      21
External sorting      76
Factor      6 26
Fibonacci numbers      86 187 206 219
Fibonacci squares      206 219 222
Fictitious play for evaluating game      118—121 137—139
Field axioms      30
FILE      73 76
Fillatoire      201
Finite affine plane      55 see
Finney, D.J.      89
Fixed—depth search, for evaluating game trees      130—131
Fletcher, J.G.      90
floating-point      175—176 178 217 220
Foliow-the-leader theory      168
Formal differentiation      22
Formal language      1—4 10 235
FORTRAN      21
Fox, J.H.Jr.      137
Frequency test for random numbers      146
Friedlander, G.G.      169
Froeberg, C.E.      217
Function      11 18—19
Function computed by a procedure      237 241
Functional equivalence      35
Functional semantics      18—20
Fundamental circuit matrix      95
Game      97
Game theory      98 111—119 137
Game tree      121—136 140
Game tree and number of strategies      140
Game tree, evaluation of      121—136
Game tree, heuristic search of      129—133
Game tree, illustrated for Nim      123
Game tree, labeling of nonterminal nodes      124
Game tree, levels of      122
Game tree, ordering of nodes      126
Game, calling largest number      105—109
Game, complete information in      105
Game, examples      99—111
Game, Game as model for decision and conflict situation      111
Game, game-playing programs      97 118
Game, Hex      109—111
Game, Nim      99—102
Game, position in      98 131—132
Game, Shannon switching      102
Game, two-person zero—sum      98 112—118
Game, value of      112—121 137
Game-playing program      98—99 118—122 129—130 140
Gap test, for random numbers      169
Gardelo, K.      169
Gardner, M.      90 137
Gauss's identity      202
Gauss, K.F.      202 208
Genuys, F.      201
Gillies, D.B.      196 210 218 219
Gilloud, J.      201
Gnugnoli, G.      168
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