●Preface iv About theAuthor xiii The Companion Website xiv To the Studentxvi List of Symbols xix 1 The Foundations：Logic and Proofs 1．1 Propositional Logic 1．2 Applications of Propositional Logic 1．3 Propositional Equivalences 1．4 Predicates andQuantifiers 1．5 Nested Quantifiers 1．6 Rules of Inference 1．7 Introduction to Proofs 1．8 ProofMethods and Strategy End-of-ChapterMaterial- 2 Basic Structures：Sets，Functions，Sequences，Sums，and Matrices 2．1 Sets 2．2 Set Operations 2．3 Functions 2．4 Sequences and Summations 2．5 Cardinality of Sets 2．6 Matrices End-of-ChapterMaterial 3 Algorithms 3．1 Algorithms 3．2 The Growth of Functions 3．3 Complexity of Algofithms End-of-Chapter Material 4 Number Theory and Cryptography 4．1 Divisibilitv andModular Arithmetic 4．2 Integer Representations AndAlgorithms 4．3 Primesand Greatest Common Divisors 4．4 Solving Congruences 4．5 Applications of Congruences 4．6 Cryptography End-of-Chapter Material 5 Induction and Recursion 5．1 Mathematical Induction 5．2 Strong Induction and Well-Ordering 5．3 Recursive Definitions and Structural Induction 5．4 Recursive Algorithms 5．5 Program Correctness End-of-Chapter Material 6 Counting 6．1 Tlle Basics of Counting 6．2 The Pigeonhole Principle 6．3 Permutations and Combinations 6．4 Binomial Coefficients and Identities 6．5 Generalized Permutations and Combinations 6．6 Generating Permutations and Combinations End-of-Chapter Material 7 Discrete Probability 7．1 An Introduction to Discrete Probability 7．2 Probability Theory 7．3 Bayes’Theorem 7．4 Expected Value and Variance End-of-Chapter Material 8 Advanced Counring Technigues 8．1 Applications of Recurrence Relations 8．2 Solving Linear Recurrence Relations 8．3 Divide-and-Conquer Algorithms and Recurrence Relations 8．4 Generating Functions 8．5 Inclusion-Exclusion 8．6 Applications of Inclusion-Exclusion End―of-Chapter Material 9 Relations 9．1 Relations and Their Properties 9．2 n-ary Relations and TheirApplications 9．3 Representing Relations 9．4 Closures of Relations 9．5 Equivalence Relations 9．6 Partial Orderings End-of-Chapter Material 10 Graphs 10．1 Graphs andGraphModels 10．2 Graph Terminology and Spe Types of Graphs 10．3 Representing Graphs and Graph Isomorphism 10．4 Connectivity 10．5 EulerandHamiltonPaths 10．6 Shortest．PathProblems 10．7 PlanarGraphs 10．8 GraphColoring End-of-Chapter Material 11 Trees 11．1 Introduction to Trees 11．2 Applications of Trees 11．3 Tree Travcrsal 11．4 Spanning Trees 11．5 Minimum Spanning Trees End-of-Chapter Material 12 Boolean Algebra 12．1 Boolean Functions 12．2 Representing Boolean Functions 12．3 Logic Gates 12．4 Minimization of Circuits End-of-Chapter Material 13 Modeling Cornputation 13．1 Languagesand Grammars 13．2 Finite-State Machines with Output 13．3 Finite-State Machines with No Output 13．4 LanguageRecognition 13．5 Turing Machines End-of-Chapter Material Appendixes 1 Axioms for the Real Numbers and the Positive Integers 2 Exponential and Logarithmic Functions 3 Pseudocode SuggestedReadings B-1 Answers to Odd-Numbered Exercises S-1 Photo Credits C-1 Index ofBiographies I-1 Index I-2
