离散数学及其应用 英文精编版PDF电子书下载

Chapter 1 The Foundations:Logic and Proofs 1

1.1 Propositional Logic 1

1.2 Propositional Equivalences 16

1.3 Predicates and Quantifiers 24

1.4 Nested Quantifiers 40

1.5 Rules of Inference 49

1.6 Introduction to Proofs 59

1.7 Proof Methods and Strategy 69

End-of-Chapter Material 84

Chapter 2 Basic Structures:Sets,Functions,Sequences,and Sums 91

2.1 Sets 91

2.2 Set Operations 98

2.3 Functions 107

2.4 Sequences and Summations 120

End-of-Chapter Material 131

Chapter 3 Counting 137

3.1 The Basics of Counting 137

3.2 The Pigeonhole Principle 147

3.3 Permutations and Combinations 153

3.4 Binomial Coefficients 159

3.5 Generalized Permutations and Combinations 166

3.6 Generating Permutations and Combinations 175

End-of-Chapter Material 179

Chapter 4 Advanced Counting Techniques 187

4.1 Recurrence Relations 187

4.2 Solving Linear Recurrence Relations 196

4.3 Divide-and-Conquer Algorithms and Recurrence Relations 207

4.4 Generating Functions 215

4.5 Inclusion-Exclusion 227

4.6 Applications of Inclusion-Exclusion 233

End-of-Chapter Material 239

Chapter 5 Relations 246

5.1 Relations and Their Properties 246

5.2 n-ary Relations and Their Applications 254

5.3 Representing Relations 260

5.4 Closures of Relations 266

5.5 Equivalence Relations 275

5.6 Partial Orderings 283

End-of-Chapter Material 296

Chapter 6 Graphs 304

6.1 Graphs and Graph Models 304

6.2 Graph Terminology and Special Types of Graphs 312

6.3 Representing Graphs and Graph Isomorphism 323

6.4 Connectivity 332

6.5 Euler and Hamilton Paths 340

6.6 Shortest-Path Problems 351

6.7 Planar Graphs 360

6.8 Graph Coloring 367

End-of-Chapter Material 374

Chapter 7 Trees 384

7.1 Introduction to Trees 384

7.2 Applications of Trees 394

7.3 Tree Traversal 407

7.4 Spanning Trees 418

7.5 Minimum Spanning Trees 430

End-of-Chapter Material 435