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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 | |