Discrete Mathematics (5TH)

Discrete Mathematics (5TH)

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  • 製本 Hardcover:ハードカバー版/ページ数 664 p.
  • 言語 ENG
  • 商品コード 9780321305152
  • DDC分類 511.1

Full Description


An ever-increasing percentage of mathematic applications involve discrete rather than continuous models. Driving this trend is the integration of the computer into virtually every aspect of modern society. Intended for a one-semester introductory course, the strong algorithmic emphasis of Discrete Mathematics is independent of a specific programming language, allowing students to concentrate on foundational problem-solving and analytical skills. Instructors get the topical breadth and organizational flexibility to tailor the course to the level and interests of their students.

Contents

(Each Chapter concludes with "Historical Notes," "Supplementary Exercises," "Computer Projects," and "Suggested Readings.").1: An Introduction to Combinatorial Problems and Techniques Section 1.1 The Time to Complete a ProjectSection 1.2 A Matching ProblemSection 1.3 A Knapsack ProblemSection 1.4 Algorithms and Their EfficiencyHistorical NotesSupplementary ExercisesComputer ProjectsSuggested Readings 2: Sets, Relations, and Functions Section 2.1 Set OperationsSection 2.2 Equivalence RelationsSection 2.3_ Partial Ordering RelationsSection 2.4 FunctionsSection 2.5 Mathematical InductionSection 2.6 ApplicationsHistorical NotesSupplementary ExercisesComputer ProjectsSuggested Readings 3: Coding Theory Section 3.1 CongruenceSection 3.2 The Euclidean Algorithm and Diophantine EquationsSection 3.3 The RSA MethodSection 3.4 Error-Detecting and Error-Correcting CodesSection 3.5 Matrix CodesSection 3.6 Matrix Codes That Correct All Single-Digit ErrorsHistorical NotesSupplementary ExercisesComputer ProjectsSuggested Readings 4: Graphs Section 4.1 Graphs and Their RepresentationsSection 4.2 Paths and CircuitsSection 4.3 Shortest Paths and DistanceSection 4.4 Coloring a GraphSection 4.5 Directed Graphs and MultigraphsHistorical NotesSupplementary ExercisesComputer ProjectsSuggested Readings 5: Trees Section 5.1 Properties of TreesSection 5.2 Spanning TreesSection 5.3 Depth-First SearchSection 5.4 Rooted TreesSection 5.5 Binary Trees and TraversalsSection 5.6 Optimal Binary Trees and Binary Search TreesHistorical NotesSupplementary ExercisesComputer ProjectsSuggested Readings 6: Matching Section 6.1 Systems of Distinct RepresentativesSection 6.2 Matchings in GraphsSection 6.3 A Matching AlgorithmSection 6.4 Applications of the AlgorithmSection 6.5 The Hungarian MethodHistorical NotesSupplementary ExercisesComputer ProjectsSuggested Readings 7: Network Flows Section 7.1 Flows and CutsSection 7.2 A Flow Augmentation AlgorithmSection 7.3 The Max-Flow Min-Cut TheoremSection 7.4 Flows and MatchingsHistorical NotesSupplementary ExercisesComputer ProjectsSuggested Readings 8: Counting Techniques Section 8.1 Pascal's Triangle and the Binomial TheoremSection 8.3 Permutations and CombinationsSection 8.4 Arrangements and Selections with RepetitionsSection 8.5 ProbabilitySection 8.6* The Principle of Inclusion-ExclusionSection 8.7* Generating Permutations and r -CombinationsHistorical NotesSupplementary ExercisesComputer ProjectsSuggested Readings 9: Recurrence Relations and Generating Functions Section 9.1 Recurrence RelationsSection 9.2 The Method of IterationSection 9.3 Linear Difference Equations with Constant CoefficientsSection 9.4* Analyzing the Efficiency of Algorithms with Recurrence RelationsSection 9.5 Counting with Generating FunctionsSection 9.6 The Algebra of Generating FunctionsHistorical NotesSupplementary ExercisesComputer ProjectsSuggested Readings 10: Combinatorial Circuits and Finite State Machines Section 10.1 Logical GatesSection 10.2 Creating Combinatorial CircuitsSection 10.3 Karnaugh MapsSection 10.4 Finite State MachinesHistorical NotesSupplementary ExercisesComputer ProjectsSuggested Readings Appendix A: An Introduction to Logic and Proof Section A.1 Statements and ConnectivesSection A.2 Logical EquivalenceSection A.3 Methods of ProofHistorical NotesSupplementary ExercisesSuggested Readings Appendix B Matrices Historical Notes Appendix C The Algorithms in This Book Bibliography Answers to odd-numbered exercises Index

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