The Adapter's Words
Preface
Online Resources
To the Student
About the Author
List of Symbols
1 The Foundations: Logic and Proofs 1
1.1 Propositional Logic 1
1.2 Applications of Propositional Logic 15
1.3 Propositional Equivalences 22
1.4 Predicates and Quantifiers 34
1.5 Nested Quantifiers 51
1.6 Rules of Inference 62
1.7 Introduction to Proofs 72
1.8 Proof Methods and Strategy 84
End-of-ChapterMaterial (Online)
2 Basic Structures: Sets, Functions, Sequences, Sums, and Matrices 101
2.1 Sets 101
2.2 Set Operations 111
2.3 Functions 124
2.4 Sequences and Summations 140
2.5 Cardinality of Sets 153
2.6 Matrices 161
End-of-ChapterMaterial (Online)
3 Counting 169
3.1 The Basics of Counting 169
3.2 The Pigeonhole Principle 182
3.3 Permutations and Combinations 189
3.4 Binomial Coefficients and Identities 197
3.5 Generalized Permutations and Combinations 204
3.6 Generating Permutations and Combinations 215
End-of-ChapterMaterial (Online)
4 Advanced Counting Techniques 221
4.1 Applications of Recurrence Relations 221
4.2 Solving Linear Recurrence Relations 232
4.3 Divide-and-Conquer Algorithms and Recurrence Relations 244
4.4 Generating Functions 253
4.5 Inclusion朎xclusion 268
4.6 Applications of Inclusion朎xclusion 273
End-of-ChapterMaterial (Online)
5 Relations 281
5.1 Relations and Their Properties 281
5.2 n-ary Relations and Their Applications 292
5.3 Representing Relations 302
5.4 Closures of Relations 308
5.5 Equivalence Relations 317
5.6 Partial Orderings 327
End-of-ChapterMaterial (Online)
6 Graphs 343
6.1 Graphs and Graph Models 343
6.2 Graph Terminology and Special Types of Graphs 354
6.3 Representing Graphs and Graph Isomorphism 371
6.4 Connectivity 380
6.5 Euler and Hamilton Paths 393
6.6 Shortest-Path Problems 405
6.7 Planar Graphs 415
6.8 Graph Coloring 423
End-of-ChapterMaterial (Online)
7 Trees 431
7.1 Introduction to Trees 431
7.2 Applications of Trees 442
7.3 Tree Traversal 456
7.4 Spanning Trees 468
7.5 Minimum Spanning Trees 481
End-of-ChapterMaterial (Online)
8 Boolean Algebra 487
8.1 Boolean Functions 487
8.2 Representing Boolean Functions 494
8.3 Logic Gates 497
8.4 Minimization of Circuits 503
End-of-ChapterMaterial (Online)
Suggested Readings (Online)
Answers to Odd-Numbered Exercises (Online)
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