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[美]约翰逊鲍夫 著 / 电子工业出版社 / 2009-04 / 平装
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国外计算机科学教材系列:离散数学(第7版)(英文版)
本书从算法分析和问题求解的角度,全面系统地介绍了离散数学的基础概念及相关知识,并在其前一版的基础上进行了修改与扩展。书中通过大量实例,深入浅出地讲解了数理逻辑、组合算法、图论、布尔代数、网络模型、形式语言与自动机理论等与计算机科学密切相关的前沿课题,既着重于各部分内容之间的紧密联系,又深入探讨了相关的概念、理论、算法和实际应用。本书内容叙述严谨、推演详尽,各章配有相当数量的习题与书后的提示和答案,为读者迅速掌握相关知识提供了有效的帮助。
本书既可作为计算机科学及计算数学等专业的本科生和研究生教材,也可作为工程技术人员和相关人员的参考书。
PrefaceXI1SetsandLogic1.1Sets1.2Propositions1.3ConditionalPropositionsandLogicalEquivalence1.4ArgumentsandRulesofInference1.5Quantifiers1.6NestedQuantifiersProblem-SolvingCorner:QuantifiersNotesChapterReviewChapterSelf-TestComputerExercises2Proofs2.1MathematicalSystems,DirectProofs,andCounterexamples2.2MoreMethodsofProofProblem-SolvingCorner:ProvingSomePropertiesofRealNumbers2.3ResolutionProofst2.4MathematicalInductionProblem-SolvingCorner:MathematicalInduction2.5StrongFormofInductionandtheWell-OrderingPropertyNotesChapterReviewChapterSelf-TestComputerExercises3Functions,Sequences,andRelations3.1FunctionsProblem-SolvingCorner:Functions3.2SequencesandStrings3.3Relations3.4EquivalenceRelationsProblem-SolvingCorner:EquivalenceRelations3.5MatricesofRelations3.6RelationalDatabasesNotesChapterReviewChapterSelf-TestComputerExercises4Algorithms4.1Introduction4.2ExamplesofAlgorithms4.3AnalysisofAlgorithmsProblem-SolvingCorner:DesignandAnalysisofanAlgorithm4.4RecursiveAlgorithmsNotesChapterReviewChapterSelf-TestComputerExercises5IntroductiontoNumberTheory5.1Divisors5.2RepresentationsofIntegersandIntegerAlgorithms5.3TheEuclideanAlgorithmProblem-SolvingCorner:MakingPostage5.4TheRSAPublic-KeyCryptosystemNotesChapterReviewChapterSelf-TestComputerExercises6CountingMethodsandthePigeonholePrinciple6.1BasicPrinciplesProblem-SolvingCorner:Counting6.2PermutationsandCombinationsProblem-SolvingComer:.Combinations6.3GeneralizedPermutationsandCombinations6.4AlgorithmsforGeneratingPermutationsandCombinations6.5IntroductiontoDiscreteProbabilityt6.6DiscreteProbabilityTheoryt6.7BinomialCoefficientsandCombinatorialIdentities6.8ThePigeonholePrincipleNotesChapterReviewChapterSelf-TestComputerExercises7RecurrenceRelations7.1Introduction7.2SolvingRecurrenceRelationsProblem-SolvingCorner:RecurrenceRelations7.3ApplicationstotheAnalysisofAlgorithms..NotesChapterReviewChapterSelf-TestComputerExercises8GraphTheory8.1Introduction8.2PathsandCyclesProblem-SolvingCorner:Graphs8.3HamiltonianCyclesandtheTravelingSalespersonProblem8.4AShortest-PathAlgorithm8.5RepresentationsofGraphs8.6IsomorphismsofGraphs8.7PlanarGraphs8.8InstantInsanitytNotesChapterReviewChapterSelf-TestComputerExercises9Trees9.1Introduction9.2TerminologyandCharacterizationsofTreesProblem-SolvingCorner:Trees9.3SpanningTrees9.4MinimalSpanningTrees9.5BinaryTrees9.6TreeTraversals9.7DecisionTreesandtheMinimumTimeforSorting9.8IsomorphismsofTrees9.9GameTreestNotesChapterReviewChapterSelf-TestComputerExercises10NetworkModels10.1Introduction10.2AMaximalFlowAlgorithm10.3TheMaxFlow,MinCutTheorem10.4MatchingProblem-SolvingCorner:MatchingNotesChapterReviewChapterSelf-TestComputerExercises11BooleanAlgebrasandCombinatorialCircuits11.1CombinatorialCircuits11.2PropertiesofCombinatorialCircuits11.3BooleanAlgebrasProblem-SolvingCorner:BooleanAlgebras11.4BooleanFunctionsandSynthesisofCircuits11.5ApplicationsNotesChapterReviewChapterSelf-TestComputerExercises12Automata,Grammars,andLanguages12.1SequentialCircuitsandFinite-StateMachines12.2Finite-StateAutomata12.3LanguagesandGrammars12.4NondeterministicFinite-StateAutomata12.5RelationshipsBetweenLanguagesandAutomataNotesChapterReviewChapterSelf-TestComputerExercises13ComputationalGeometry13.1TheClosest-PairProblem13.2AnAlgorithmtoComputetheConvexHullNotesChapterReviewChapterSelf-TestComputerExercisesAppendixAMatricesBAlgebraReviewCPseudocodeReferencesHintsandSolutionstoSelectedExercisesIndex
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