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| Sets and Logic | |
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| Sets | |
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| Propositions | |
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| Conditional Propositions and Logical Equivalence | |
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| Arguments and Rules of Inference | |
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| Quantifiers | |
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| Nested QuantifiersProblem-Solving Corner: Quantifiers | |
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| Proofs | |
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| Mathematical Systems, Direct Proofs, and Counterexamples | |
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| More Methods of ProofProblem-Solving Corner: Proving Some Properties of Real Numbers | |
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| Resolution Proofs | |
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| Mathematical InductionProblem-Solving Corner: Mathematical Induction | |
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| Strong Form of Induction and the Well-Ordering Property Notes Chapter Review Chapter Self-Test Computer Exercises | |
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| Functions, Sequences, and Relations | |
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| FunctionsProblem-Solving Corner: Functions | |
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| Sequences and Strings | |
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| Relations | |
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| Equivalence RelationsProblem-Solving Corner: Equivalence Relations | |
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| Matrices of Relations | |
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| Relational Databases | |
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| Algorithms | |
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| Introduction | |
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| Examples of Algorithms | |
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| Analysis of AlgorithmsProblem-Solving Corner: Design and Analysis of an Algorithm | |
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| Recursive Algorithms | |
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| Introduction to Number Theory | |
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| Divisors | |
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| Representations of Integers and Integer Algorithms | |
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| The Euclidean AlgorithmProblem-Solving Corner: Making Postage | |
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| The RSA Public-Key Cryptosystem | |
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| Counting Methods and the Pigeonhole Principle | |
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| Basic PrinciplesProblem-Solving Corner: Counting | |
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| Permutations and CombinationsProblem-Solving Corner: Combinations | |
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| Generalized Permutations and Combinations | |
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| Algorithms for Generating Permutations and Combinations | |
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| Introduction to Discrete Probability | |
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| Discrete Probability Theory | |
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| Binomial Coefficients and Combinatorial Identities | |
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| The Pigeonhole Principle | |
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| Recurrence Relations | |
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| Introduction | |
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| Solving Recurrence RelationsProblem-Solving Corner: Recurrence Relations | |
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| Applications to the Analysis of Algorithms | |
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| Graph Theory | |
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| Introduction | |
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| Paths and CyclesProblem-Solving Corner: Graphs | |
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| Hamiltonian Cycles and the Traveling Salesperson Problem | |
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| A Shortest-Path Algorithm | |
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| Representations of Graphs | |
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| Isomorphisms of Graphs | |
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| Planar Graphs | |
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| Instant Insanity | |
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| Trees | |
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| Introduction | |
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| Terminology and Characterizations of TreesProblem-Solving Corner: Trees | |
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| Spanning Trees | |
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| Minimal Spanning Trees | |
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| Binary Trees | |
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| Tree Traversals | |
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| Decision Trees and the Minimum Time for Sorting | |
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| Isomorphisms of Trees | |
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| Game Trees | |
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| Network Models | |
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| Introduction | |
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| A Maximal Flow Algorithm | |
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| The Max Flow, Min Cut Theorem | |
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| MatchingProblem-Solving Corner: Matching | |
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| Boolean Algebras and Combinatorial Circuits | |
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| Combinatorial Circuits | |
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| Properties of Combinatorial Circuits | |
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| Boolean AlgebrasProblem-Solving Corner: Boolean Algebras | |
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| Boolean Functions and Synthesis of Circuits | |
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| Applications | |
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| Automata, Grammars, and Languages | |
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| Sequential Circuits and Finite-State Machines | |
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| Finite-State Automata | |
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| Languages and Grammars | |
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| Nondeterministic Finite-State Automata | |
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| Relationships Between Languages and Automata | |
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| Computational Geometry | |
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| The Closest-Pair Problem | |
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| An Algorithm to Compute the Convex Hull | |
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| Appendix | |
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| Matrices | |
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| Algebra Review | |
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| Pseudocode | |
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| References | |
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| Hints and Solutions to Selected Exercises | |
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| Index | |