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| Preface CHAPTER 1 Foundations:Sets,Logic,andAlgorithms 1.1 Sets 1.2 MathematicalLogic 1.3 ValidityofArguments 1.4 QuantifiersandFirst-OrderLogic 1.5 ProofTechniques 1.6 Algorithms ProgrammingExercises CHAPTER 2 RelationsandPosets 2.1 Relations 2.2 PartiallyOrderedSets 2.3 Application:RelationalDatabase ProgrammingExercises CHAPTER 3 ClosuresofRelations 3.1 TheMatrixofaRelationandClosures ProgrammingExercises CHAPTER 4 Functions 4.1 Functions 4.2 SpecialFunctionsandCardinalityofaSet 4.3 SequencesandStrings 4.4 BinaryOperations ProgrammingExercises CHAPTER 5 CountingPrinciples 5.1 BasicCountingPrinciples 5.2 PigeonholePrinciple 5.3 Permutations 5.4 Combinations 5.5 GeneralizedPermutationsandCombinations 5.6 DiscreteProbability ProgrammingExercises CHAPTER 6 RecurrenceRelations 6.1 SequencesandRecurrenceRelations 6.2 LinearHomogeneousRecurrenceRelations 6.3 LinearNonhomogeneousRecurrenceRelations ProgrammingExercises CHAPTER 7 GraphTheory 7.1 GraphDefinitionandNotations 7.2 Walks,Paths,andCycles 7.3 MatrixRepresentationofaGraph 7.4 SpecialCircuits 7.5 Isomorphism 7.6 GraphAlgorithms 7.7 PlanarGraphsandGraphColoring ProgrammingExercises CHAPTER 8 TreesandNetworks 8.1 Trees 8.2 RootedTree 8.3 SpanningTrees 8.4 Networks ProgrammingExercises CHAPTER 9 BooleanAlgebraandCombinatorialCircuits 9.1 Two-ElementBooleanAlgebra 9.2 BooleanAlgebra 9.3 LogicalGatesandCombinatorialCircuits ProgrammingExercises Appendix A Appendix B Appendix C Appendix D Appendix E Answers ListofSymbols References Index |
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