Preface | |

The MathZone Companion Website To the Student | |

The Foundations: Logic and Proofs | |

Propositional Logic | |

Propositional Equivalences | |

Predicates and Quantifiers | |

Nested Quantifiers | |

Rules of Inference | |

Introduction to Proofs | |

Proof Methods and Strategy End-of-Chapter Material | |

Basic Structures: Sets, Functions, Sequences and Sums | |

Sets | |

Set Operations | |

Functions | |

Sequences and Summations End-of-Chapter Material | |

The Fundamentals: Algorithms, the Integers, and Matrices | |

Algorithms | |

The Growth of Functions | |

Complexity of Algorithms | |

The Integers and Division | |

Primes and Greatest Common Divisors | |

Integers and Algorithms | |

Applications of Number Theory | |

Matrices End-of-Chapter Material | |

Induction and Recursion | |

Mathematical Induction | |

Strong Induction and Well-Ordering | |

Recursive Definitions and Structural Induction | |

Recursive Algorithms | |

Program Correctness End-of-Chapter Material | |

Counting | |

The Basics of Counting | |

The Pigeonhole Principle | |

Permutations and Combinations | |

Binomial Coefficients | |

Generalized Permutations and Combinations | |

Generating Permutations and Combinations End-of-Chapter Material | |

Discrete Probability | |

An Introduction to Discrete Probability | |

Probability Theory | |

Bayes’ Theorem | |

Expected Value and Variance End-of-Chapter Material | |

Advanced Counting Techniques | |

Recurrence Relations | |

Solving Linear Recurrence Relations | |

Divide-and-Conquer Algorithms and Recurrence elations | |

Generating Functions | |

Inclusion-Exclusion | |

Applications of Inclusion-Exclusion End-of-Chapter Material | |

Relations | |

Relations and Their Properties | |

n-ary Relations and Their Applications | |

Representing Relations | |

Closures of Relations | |

Equivalence Relations | |

Partial Orderings End-of-Chapter Material | |

Graphs | |

Graphs and Graph Models | |

Graph Terminology and Special Types of Graphs | |

Representing Graphs and Graph Isomorphism | |

Connectivity | |

Euler and Hamilton Paths | |

Shortest-Path Problems | |

Planar Graphs | |

Graph Coloring End-of-Chapter Material | |

Trees | |

Introduction to Trees | |

Applications of Trees | |

Tree Traversal | |

Spanning Trees | |

Minimum Spanning Trees End-of-Chapter Material | |

Boolean Algebra | |

Boolean Functions | |

Representing Boolean Functions | |

Logic Gates | |

Minimization of Circuits End-of-Chapter Material | |

Modeling Computation | |

Languages and Grammars | |

Finite-State Machines with Output | |

Finite-State Machines with No Output | |

Language Recognition | |

Turing Machines End-of-Chapter Material | |

Appendixes | |

Axioms for the Real Numbers and the Positive Integers | |

Exponential and Logarithmic Functions | |

Pseudocode Suggested Readings | |

Answers to Odd-Numbered Exercises | |

Photo Credits | |

Index of Biographies | |

Index | |

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