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| Kemeny T., Snell J.L., Thompson G. — Introduction to finite mathematics |
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| Предметный указатель |
Absorbing Markov chain 214
Absorbing Markov chain, canonical form 215
Absorbing Markov chain, fundamental matrix of 216
Arguments, fallacy 32
Arguments, valid 31
Aristotle 3
BASIC 226 229
Basic variable 344
BASIC, nine-word 241
Bayes’s probability 110
Bayes’s probability, theorem 110
Biconditional 12
Binomial coefficients 65
Binomial coefficients, properties of 69
Binomial coefficients, theorem 71
Birthday problem 93
Boole, George 3
Branch-and-bound method 473
Canonical form 436 437
Canonical form for transition matrix 215
Central limit theorem 277
Combinatorial decision problems 72
Combinatorial decision problems, knapsack problem 473
Combinatorial decision problems, sequencing problem 476
Communication, equivalence classes 432 433
Communication, matrix 423
Communication, network 423
Communication, one- and two-stage 426
Complement of a set 50
Complementary slackness 343 358
Complete set of alternatives 98
Components of a vector 153
compound statement 3
Compound statement, biconditional 12
Compound statement, conditional 11
Compound statement, conjunction 6
Compound statement, disjunction 6 7
Compound statement, equivalent 9 27
Compound statement, inconsistent 28
Compound statement, logically false 18
Compound statement, logically true 18
Compound statement, negation 7
Computer programming 224
Computer programs 225
Computer programs, BACK 243
Computer programs, BINOMC 246
Computer programs, BINOMPR 247
Computer programs, BIRTH2 240
Computer programs, BIRTHDAY 239
Computer programs, CLTH 307
Computer programs, CONFIDE 298
Computer programs, CRAPS 302
Computer programs, DICE 245
Computer programs, EQU 253
Computer programs, EXPECT 238
Computer programs, FCTRL 236
Computer programs, FCTRL2 237
Computer programs, GAME 418
Computer programs, LINEQU 264
Computer programs, LINEQU2 266
Computer programs, LINEQU3 267
Computer programs, LINEQU4 267
Computer programs, LINEQU5 269
Computer programs, LOTTERY 297
Computer programs, LP 410
Computer programs, LP2 413
Computer programs, LP3 414
Computer programs, LP4 414
Computer programs, LP5 415
Computer programs, MATINV 253
Computer programs, MATMPY 252
Computer programs, MATSUB 251
Computer programs, OZ 256
Computer programs, RANDOM 300
Computer programs, RANDOMOZ 306
Computer programs, STRICT 417
Computer programs, TRANS 257
Computer programs, TRANS2 259
Computer programs, TRANS3 261
Computer programs, VECADD 249
Computer programs, VECADD2 250
Conclusion 31
Conditional 11
Conditional probability 96
Conditional, contrapositive of 35
Conditional, converse of 35
Conditional, variants of 35
confidence intervals 288
Conjunction 6
Connectives 6
Connectives, biconditional 12
Connectives, conditional 11
Connectives, conjunction 6
Connectives, disjunction 6 7
Connectives, negation 7
Contrapositive of conditional 35
Converse of conditional 35
Convex set 319
Cost, imputed 355
Cost-accounting model 465
Counterexample 36
Counting problems 45
Data box 329
Dceeneracy in linear programming 343 366
De Morgan.Augustus 9 28
Decision problem 171
Deer harvesting 468
Difference of two sets 50
Disjoint sets 50
Disjunction 6
Disjunction, exclusive 7
Disjunction, inclusive 7
Dominance relation 424
Dominance relation, matrices 425
Dominance relation, power in 428
Dominant gene 443
Domination 392
Dual problem 336
Dual problem, interpretations 352
Empty set 47
Equilibrium 446
Equivalence classes 432 433
Ergodic sets 437
Ergodic states 437
Expected value 132
Extreme points 322
Fair game 373
Fallacy 32
Feasible vectors 341
Fixed point 205
Gambler’s ruin 144
Game theory 370
Game theory, matrix game 379
Games, computer solution of 410
Games, fair 373
Games, matrix 379
Games, saddle value 372
Games, solution by geometric method 391
Games, solution by simplex method 402
Games, strictly determined 370 373
Games, value of 372 383
Games, zero and nonzero sum 370
Gene, dominant 443
Gene, hybrid 443
Gene, recessive 443
General principle of counting 60
Geometric method for solving games 391
Graph, directed 423
Graph, tree 22
Group 454
| Group, regular 460
Group, subgroup 454
Half-plane 317 319
Hat check problem 93
Hybrid gene 443
Hyperplane 319
Hyperplane, bounding 322
Imputed value 354
Imputed value, cost 355
Inconsistent statements 28
Independent statements 98
Independent trials process 117
Independent trials process with more than two outcomes 129
Indirect method of proof 39
Indirect method of proof, reductio ad absurdum 40
intersection of two sets 49
Inverse of a square matrix 195
Inverse of a square matrix, rule for 197
Knapsack problem 473
Labeling 64
Law of Large Numbers 121
Linear equations 184
Linear equations programs 263
Linear equations, flow diagram for 189
Linear programming problems 329
Linear programming problems, complementary slackness 343
Linear programming problems, dual problem 336
Linear programming problems, program for 410
Linear programming problems, simplex method 343
listing 59
Logical possibilities 16
Logical possibilities, analysis of 17
Logical relations 26
Logical relations, equivalence 9 27
Logical relations, implication 26
Logically false statement 18
Logically true statement 18
Markov chains 137
Markov chains, absorbing 214
Markov chains, algorithm for absorbing 462
Markov chains, applications of matrix theory to 203
Markov chains, examples from economics and finance 462
Markov chains, programs for 257 259 261
Markov chains, regular 206
Marriage rules 451
Marriage rules, choice of 458
Matrix 166
Matrix, associative law for 178
Matrix, block-triangular 437
Matrix, canonical form 215 436
Matrix, communication 423
Matrix, fixed point of 205
Matrix, fundamental 216
Matrix, game 379
Matrix, inverse of a square 195
Matrix, of a relationship 458
Matrix, payoff 371
Matrix, permutation 453
Matrix, product of two 176
Matrix, product with a vector 169
Matrix, regular 206
Matrix, sociometric 423
Matrix, square 166
Matrix, transition 204
Maximum likelihood 276
Measure 81
Measure, assignment of 82
Measure, equiprobable 88
Measure, properties of 84
Measure, tree 104
Mixed strategy 381
Mixed strategy, vector 382
Negation 7
Nondegeneracy assumption 343
Normal curve 278
Odds 86
Open Leontief example 463
Open statements 184 315
Optimal deer harvesting 468
Optimal strategy 373
Pascal triangle 69
Payoff matrix 372
Permutation 59
Permutation, complete 459
Permutation, matrix 453
Permutation, of marriage types 453
Permutation, regular group 460
Pivot 185
Pivoting 185
Polyhedral convex set 315 319
Polyhedral convex set, bounded 325
Polyhedral convex set, unbounded 325
Power 428
Premises 31
probability 81
Probability, Bayes’s 110
Probability, conditional 96
Probability, expected value 132
Probability, gambler’s ruin 144
Probability, law of large numbers 121
Probability, Markov chains 137 203
Probability, measure 82
Probability, of a statement 85
Probability, transition 137
Probability, vector 204
Product of a vector and a matrix 169
Product of two matrices 178
Product of two vectors 159
Product, associative law for 178
Programs see “Computer programs”
proof 39
Random walk 214
Reductio ad absiirdum 40
Regular Markov chain 206
Regular permutation group 460
Regular transition matrix 206
Relation, dominance 424
Relation, equivalence 433
Saddle value 372
Scalar multiplication 155
Self-contradiction 18
Sequencing problem 476
Sets 45
Sets, bounded 325
Sets, convex 319
Sets, description of 45
Sets, disjoint 50
Sets, empty 47
Sets, ergodic 437
Sets, listing of 45
Sets, proper 47
Sets, relation to compound statements 54 56
Sets, subset 47
Sets, transient 437
Sets, truth 54 315
Sets, unbounded 325
Sets, unit 47
Sets, universal 47
Simplex, flow diagram 345 364
Simplex, method 343 361
Simplex, method for matrix games 402
Simplex, tableau 339
Simulation 299
Simulation, computer programs 300 302 306 307 308
Statement 3
Statement, independent 98
Statement, open 184
Statement, relative to a set of possibilities 16
States of a Markov chain 137
States of a Markov chain, absorbing 214 434
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