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Kemeny T., Snell J.L., Thompson G. — Introduction to finite mathematics
Kemeny T., Snell J.L., Thompson G. — Introduction to finite mathematics

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Название: Introduction to finite mathematics

Авторы: Kemeny T., Snell J.L., Thompson G.

Аннотация:

From game theory to the Gambler's ruin this book has classical mathematics well explained. The section on permutations and multinomials is still a valuable reference after all these years! But it is the application of permutation groups to island marriage laws that make this book a mathematical classic! How close a relative can you marry without endangering the gene pool while maximizing the number of people in your tribe that you can marry... a practical problem set to a primitive culture produced mathematical solutions!


Язык: en

Рубрика: Computer science/Дискретная математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 3rd edition

Год издания: 1974

Количество страниц: 484

Добавлена в каталог: 18.11.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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