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离散数学暨组合数学：英文版
作者：（美）James A.Anderson著
出版社：清华大学出版社
出版时间：2004-01-01
ISBN：9787302077893
定价：¥79.00
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内容简介
“大学计算机教育国外著名教材系列（影印版）”专题本书结构严谨、简洁易懂、逻辑性强，其内容涵盖了离散数学各种基础主题，每个主题的概念都与计算机工程和数学的实际应用相结合。本书不仅介绍了很多的基本概念，而且还讨论了—些扩展主题，如逻辑、集合、图、树、迭代、代数、计算理论和组合数学，并有大量实例，以帮助学生巩固所学知识。全书讨沦严谨，实例、习题多，是一本有关计算机基础数学理论的很好教材。
作者简介
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目录
Prefacexi
1TruthTables,Logic,andProofs
1.1.StatementsandConnectives1
1.2.ConditionalStatements9
1.3.EquivalentStatements13
1.4.AxiomaticSystems:ArgumentsandProofs20
1.5.CompletenessinPropositionalLogic30
1.6.KarnaughMaps3s
1.7.CircuitDiagrams41
2SetTheory51
2.1.IntroductiontoSets51
2.2.SetOperationss4
2.3.VennDiagrams60
2.4.BooleanAlgebras67
2.5.Relations72
2.6.PartiallyOrderedSets84
2.7.EquivalenceRelationsss
3Logic,Integers,andProofs94
3.1.PredicateCalculus94
3.2.BasicConceptsofProofsandtheStructureofIntegers104
3.3.MathematicalInduction109
3.4.Divisibility119
3.5.PrimeIntegers124
3.6.CongruenceRelations129
4Functionsand.Matrices136
4.1.Functions136
4.2.SpecialFunctions141
4.3.Matrices147
4.4.Cardinality158
4.5.CardinalsContinued160
5AlgorithmsantiRecursion16s
5.1.The"for"ProcedureandAlgorithmsforMatrices165
5.2.RecursiveFunctionsandAlgorithms169
5.3.ComplexityofAlgorithmsis2
5.4.SortingAlgorithmslSV
5.5.PrefixandSuffixNotation195
5.6.BinaryandHexadecimalNumbers200
5.7.SignedNumbers212
5.8.MatricesContinued217
6Graphs,DirectedGraphs,andTrecs224
6.1.Graphs22,1
6.2.DirectedGraphs231
6.3.Trees238
6.4.InstantInsanity245
6.5.EulerPathsandCycles247
6.6.IncidenceandAdjacencyMatrices254
6.7.HypercubesandGrayCode265
7NumberTheory272
7.1.SieveofEratosthenes272
7.2.Fermat'sFactorizationMethod273
7.3.TheDivisionandEuclideanAlgorithms2us
7.4.ContinuedFractions279
7.5.Convergents284
8CountingantiProbability290
8.1.BasicCountingPrinciples290
8.2.Inclusion-ExclusionIntroduced297
8.3.PermutationsandCombinations304
8.4.GeneratingPermutationsandCombinations316
8.5.ProbabilityIntroduced32o
8.6.GeneralizedPermutationsandCombinations327
8.7.PermutationsandCombinationswithRepetition332
8.8.PigeonholePrinciple337
8.9.ProbabilityRevisitedM2
8.10.Bayes'Theorem357
8.11.MarkovChains359
9AlgebraicStructuressss
9.1.PartiallyOrderedSetsRevisited365
9.2.SemigroupsandSemilattices369
9.3.Lattices374
9.4.Groups38o
9.5.GroupsandHomomorphisms386
10NumberTheoryRevisited393
10.1.IntegralSolutionsofLinearEquations393
10.2.SolutionsofCongruenceEquations395
10.3.ChineseRemainderTheorem399
10.4.PropertiesoftheFunction405
10.5.OrderofanInteger410
11RecursionRevisited418
11.1.HomogeneousLinearRecurrenceRelations418
11.2.NonhomogeneousLinearRecurrenceRelations430
11.3.FiniteDifferences44o
11.4.FactorialPolynomials444
11.5.SumsofDifferences45s
12CountingContinued462
12.1.OccupancyProblems462
12.2.CatalanNumbers468
12.3.GeneralInclusion-ExclusionandDerangements474
12.4.RookPolynomialsandForbiddenPositions480
13GeneratingFunctions494
13.t.DefininingtheGeneratingFunction(optional)494
13.2.GeneratingFunctionsandRecurrenceRelations496
13.3.GeneratingFunctionsandCounting508
13.4.Partitionssis
13.5.ExponentialGeneratingFunctions521
14GraphsRevisiteds2s
14.1.AlgebraicPropertiesofGraphs528
14.2.PlanarGraphs551
14.3.ColoringGraphs557
14.4.HamiltonianPathsandCycles569
14.5.WeightedGraphsandShortestPathAlgorithms578
15Trees590
15.1.PropertiesofTrees590
15.2.BinarySearchTrees597
15.3.WeightedTrees6o2
15.4.TraversingBinaryTrees613
15.5.SpanningTrees62O
15.6.MinimalSpanningTrees642
16Networks650
16.1.NetworksandFlows650
16.2.Matching664
16.3.PetriNets672
17TheoryofComputation681
17.1.RegularLanguages681
17.2.Automata
17.3.Grammars696
18TheoryofCodes70s
18.1.Introduction708
18.2.GeneratorMatrices712
18.3.HammingCodes721
19EnumerationofColors72s
19.1.Burnside'sTheorem728
19.2.Polya'sTheorem733
20Rings,IntegralDomains,andFields740
20.1.RingsandIntegralDomains740
20.2.IntegralDomains749
20.3.Polynomials752
20.4.AlgebraandPolynomials759
21GroupandSemigroupCharacters769
21.1.ComplexNumbers769
21.2.GroupCharacters770
21.3.SemigroupCharacters775
22ApplicationsofNumberTheory780
22.1.Application:PatternMatching780
22.2.Application:HashingFunctions787
22.3.Application'Cryptography794
Bibliography801
HintsandSolutionstoSelectedExercisesA-1
IndexI-1
1TruthTables,Logic,andProofs
1.1.StatementsandConnectives1
1.2.ConditionalStatements9
1.3.EquivalentStatements13
1.4.AxiomaticSystems:ArgumentsandProofs20
1.5.CompletenessinPropositionalLogic30
1.6.KarnaughMaps3s
1.7.CircuitDiagrams41
2SetTheory51
2.1.IntroductiontoSets51
2.2.SetOperationss4
2.3.VennDiagrams60
2.4.BooleanAlgebras67
2.5.Relations72
2.6.PartiallyOrderedSets84
2.7.EquivalenceRelationsss
3Logic,Integers,andProofs94
3.1.PredicateCalculus94
3.2.BasicConceptsofProofsandtheStructureofIntegers104
3.3.MathematicalInduction109
3.4.Divisibility119
3.5.PrimeIntegers124
3.6.CongruenceRelations129
4Functionsand.Matrices136
4.1.Functions136
4.2.SpecialFunctions141
4.3.Matrices147
4.4.Cardinality158
4.5.CardinalsContinued160
5AlgorithmsantiRecursion16s
5.1.The"for"ProcedureandAlgorithmsforMatrices165
5.2.RecursiveFunctionsandAlgorithms169
5.3.ComplexityofAlgorithmsis2
5.4.SortingAlgorithmslSV
5.5.PrefixandSuffixNotation195
5.6.BinaryandHexadecimalNumbers200
5.7.SignedNumbers212
5.8.MatricesContinued217
6Graphs,DirectedGraphs,andTrecs224
6.1.Graphs22,1
6.2.DirectedGraphs231
6.3.Trees238
6.4.InstantInsanity245
6.5.EulerPathsandCycles247
6.6.IncidenceandAdjacencyMatrices254
6.7.HypercubesandGrayCode265
7NumberTheory272
7.1.SieveofEratosthenes272
7.2.Fermat'sFactorizationMethod273
7.3.TheDivisionandEuclideanAlgorithms2us
7.4.ContinuedFractions279
7.5.Convergents284
8CountingantiProbability290
8.1.BasicCountingPrinciples290
8.2.Inclusion-ExclusionIntroduced297
8.3.PermutationsandCombinations304
8.4.GeneratingPermutationsandCombinations316
8.5.ProbabilityIntroduced32o
8.6.GeneralizedPermutationsandCombinations327
8.7.PermutationsandCombinationswithRepetition332
8.8.PigeonholePrinciple337
8.9.ProbabilityRevisitedM2
8.10.Bayes'Theorem357
8.11.MarkovChains359
9AlgebraicStructuressss
9.1.PartiallyOrderedSetsRevisited365
9.2.SemigroupsandSemilattices369
9.3.Lattices374
9.4.Groups38o
9.5.GroupsandHomomorphisms386
10NumberTheoryRevisited393
10.1.IntegralSolutionsofLinearEquations393
10.2.SolutionsofCongruenceEquations395
10.3.ChineseRemainderTheorem399
10.4.PropertiesoftheFunction405
10.5.OrderofanInteger410
11RecursionRevisited418
11.1.HomogeneousLinearRecurrenceRelations418
11.2.NonhomogeneousLinearRecurrenceRelations430
11.3.FiniteDifferences44o
11.4.FactorialPolynomials444
11.5.SumsofDifferences45s
12CountingContinued462
12.1.OccupancyProblems462
12.2.CatalanNumbers468
12.3.GeneralInclusion-ExclusionandDerangements474
12.4.RookPolynomialsandForbiddenPositions480
13GeneratingFunctions494
13.t.DefininingtheGeneratingFunction(optional)494
13.2.GeneratingFunctionsandRecurrenceRelations496
13.3.GeneratingFunctionsandCounting508
13.4.Partitionssis
13.5.ExponentialGeneratingFunctions521
14GraphsRevisiteds2s
14.1.AlgebraicPropertiesofGraphs528
14.2.PlanarGraphs551
14.3.ColoringGraphs557
14.4.HamiltonianPathsandCycles569
14.5.WeightedGraphsandShortestPathAlgorithms578
15Trees590
15.1.PropertiesofTrees590
15.2.BinarySearchTrees597
15.3.WeightedTrees6o2
15.4.TraversingBinaryTrees613
15.5.SpanningTrees62O
15.6.MinimalSpanningTrees642
16Networks650
16.1.NetworksandFlows650
16.2.Matching664
16.3.PetriNets672
17TheoryofComputation681
17.1.RegularLanguages681
17.2.Automata
17.3.Grammars696
18TheoryofCodes70s
18.1.Introduction708
18.2.GeneratorMatrices712
18.3.HammingCodes721
19EnumerationofColors72s
19.1.Burnside'sTheorem728
19.2.Polya'sTheorem733
20Rings,IntegralDomains,andFields740
20.1.RingsandIntegralDomains740
20.2.IntegralDomains749
20.3.Polynomials752
20.4.AlgebraandPolynomials759
21GroupandSemigroupCharacters769
21.1.ComplexNumbers769
21.2.GroupCharacters770
21.3.SemigroupCharacters775
22ApplicationsofNumberTheory780
22.1.Application:PatternMatching780
22.2.Application:HashingFunctions787
22.3.Application'Cryptography794
Bibliography801
HintsandSolutionstoSelectedExercisesA-1
IndexI-1
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