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| Preface | |
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| The MathZone Companion Website To the Student | |
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| The Foundations: Logic and Proofs | |
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| Propositional Logic | |
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| Propositional Equivalences | |
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| Predicates and Quantifiers | |
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| Nested Quantifiers | |
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| Rules of Inference | |
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| Introduction to Proofs | |
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| Proof Methods and Strategy End-of-Chapter Material | |
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| Basic Structures: Sets, Functions, Sequences and Sums | |
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| Sets | |
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| Set Operations | |
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| Functions | |
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| Sequences and Summations End-of-Chapter Material | |
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| The Fundamentals: Algorithms, the Integers, and Matrices | |
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| Algorithms | |
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| The Growth of Functions | |
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| Complexity of Algorithms | |
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| The Integers and Division | |
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| Primes and Greatest Common Divisors | |
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| Integers and Algorithms | |
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| Applications of Number Theory | |
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| Matrices End-of-Chapter Material | |
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| Induction and Recursion | |
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| Mathematical Induction | |
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| Strong Induction and Well-Ordering | |
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| Recursive Definitions and Structural Induction | |
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| Recursive Algorithms | |
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| Program Correctness End-of-Chapter Material | |
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| Counting | |
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| The Basics of Counting | |
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| The Pigeonhole Principle | |
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| Permutations and Combinations | |
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| Binomial Coefficients | |
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| Generalized Permutations and Combinations | |
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| Generating Permutations and Combinations End-of-Chapter Material | |
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| Discrete Probability | |
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| An Introduction to Discrete Probability | |
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| Probability Theory | |
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| Bayes’ Theorem | |
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| Expected Value and Variance End-of-Chapter Material | |
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| Advanced Counting Techniques | |
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| Recurrence Relations | |
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| Solving Linear Recurrence Relations | |
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| Divide-and-Conquer Algorithms and Recurrence elations | |
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| Generating Functions | |
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| Inclusion-Exclusion | |
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| Applications of Inclusion-Exclusion End-of-Chapter Material | |
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| Relations | |
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| Relations and Their Properties | |
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| n-ary Relations and Their Applications | |
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| Representing Relations | |
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| Closures of Relations | |
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| Equivalence Relations | |
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| Partial Orderings End-of-Chapter Material | |
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| Graphs | |
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| Graphs and Graph Models | |
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| Graph Terminology and Special Types of Graphs | |
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| Representing Graphs and Graph Isomorphism | |
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| Connectivity | |
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| Euler and Hamilton Paths | |
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| Shortest-Path Problems | |
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| Planar Graphs | |
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| Graph Coloring End-of-Chapter Material | |
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| Trees | |
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| Introduction to Trees | |
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| Applications of Trees | |
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| Tree Traversal | |
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| Spanning Trees | |
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| Minimum Spanning Trees End-of-Chapter Material | |
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| Boolean Algebra | |
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| Boolean Functions | |
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| Representing Boolean Functions | |
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| Logic Gates | |
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| Minimization of Circuits End-of-Chapter Material | |
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| Modeling Computation | |
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| Languages and Grammars | |
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| Finite-State Machines with Output | |
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| Finite-State Machines with No Output | |
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| Language Recognition | |
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| Turing Machines End-of-Chapter Material | |
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| Appendixes | |
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| Axioms for the Real Numbers and the Positive Integers | |
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| Exponential and Logarithmic Functions | |
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| Pseudocode Suggested Readings | |
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| Answers to Odd-Numbered Exercises | |
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| Photo Credits | |
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| Index of Biographies | |
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| Index | |