Discrete mathematics

著者

書誌事項

Discrete mathematics

John A. Dossey ... [et al.]

Pearson/Addison Wesley, c2006

5th ed

  • : Pearson international ed

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注記

Includes bibliographical references (p. 613-617) and index

内容説明・目次

内容説明

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.

目次

(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 Project Section 1.2 A Matching Problem Section 1.3 A Knapsack Problem Section 1.4 Algorithms and Their Efficiency Historical Notes Supplementary Exercises Computer Projects Suggested Readings 2: Sets, Relations, and Functions Section 2.1 Set Operations Section 2.2 Equivalence Relations Section 2.3_ Partial Ordering Relations Section 2.4 Functions Section 2.5 Mathematical Induction Section 2.6 Applications Historical Notes Supplementary Exercises Computer Projects Suggested Readings 3: Coding Theory Section 3.1 Congruence Section 3.2 The Euclidean Algorithm and Diophantine Equations Section 3.3 The RSA Method Section 3.4 Error-Detecting and Error-Correcting Codes Section 3.5 Matrix Codes Section 3.6 Matrix Codes That Correct All Single-Digit Errors Historical Notes Supplementary Exercises Computer Projects Suggested Readings 4: Graphs Section 4.1 Graphs and Their Representations Section 4.2 Paths and Circuits Section 4.3 Shortest Paths and Distance Section 4.4 Coloring a Graph Section 4.5 Directed Graphs and Multigraphs Historical Notes Supplementary Exercises Computer Projects Suggested Readings 5: Trees Section 5.1 Properties of Trees Section 5.2 Spanning Trees Section 5.3 Depth-First Search Section 5.4 Rooted Trees Section 5.5 Binary Trees and Traversals Section 5.6 Optimal Binary Trees and Binary Search Trees Historical Notes Supplementary Exercises Computer Projects Suggested Readings 6: Matching Section 6.1 Systems of Distinct Representatives Section 6.2 Matchings in Graphs Section 6.3 A Matching Algorithm Section 6.4 Applications of the Algorithm Section 6.5 The Hungarian Method Historical Notes Supplementary Exercises Computer Projects Suggested Readings 7: Network Flows Section 7.1 Flows and Cuts Section 7.2 A Flow Augmentation Algorithm Section 7.3 The Max-Flow Min-Cut Theorem Section 7.4 Flows and Matchings Historical Notes Supplementary Exercises Computer Projects Suggested Readings 8: Counting Techniques Section 8.1 Pascal's Triangle and the Binomial Theorem Section 8.3 Permutations and Combinations Section 8.4 Arrangements and Selections with Repetitions Section 8.5 Probability Section 8.6* The Principle of Inclusion-Exclusion Section 8.7* Generating Permutations and r -Combinations Historical Notes Supplementary Exercises Computer Projects Suggested Readings 9: Recurrence Relations and Generating Functions Section 9.1 Recurrence Relations Section 9.2 The Method of Iteration Section 9.3 Linear Difference Equations with Constant Coefficients Section 9.4* Analyzing the Efficiency of Algorithms with Recurrence Relations Section 9.5 Counting with Generating Functions Section 9.6 The Algebra of Generating Functions Historical Notes Supplementary Exercises Computer Projects Suggested Readings 10: Combinatorial Circuits and Finite State Machines Section 10.1 Logical Gates Section 10.2 Creating Combinatorial Circuits Section 10.3 Karnaugh Maps Section 10.4 Finite State Machines Historical Notes Supplementary Exercises Computer Projects Suggested Readings Appendix A: An Introduction to Logic and Proof Section A.1 Statements and Connectives Section A.2 Logical Equivalence Section A.3 Methods of Proof Historical Notes Supplementary Exercises Suggested Readings Appendix B Matrices Historical Notes Appendix C The Algorithms in This Book Bibliography Answers to odd-numbered exercises Index

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