## Table of Contents

**1. Sets, Sequences, and Functions.**

Some Warm-up Questions. Factors and Multiples. Office Hours 1.2. Some Special Sets. Set Operations. Functions. Sequences. Properties of Functions. Office Hours 1.7. Supplementary Exercises.

**2. Elementary Logic.**

Informal Introduction. Propositional Calculus. Getting Started with Proofs. Methods of Proof. Office Hours 2.4. Logic in Proofs. Analysis of Arguments. Supplementary Exercises.

**3. Relations.**

Relations. Digraphs and Graphs. Matrices. Equivalence Relations and Partitions. The Division Algorithm and Integers Mod p. Supplementary Exercises.

**4. Induction and Recursion.**

Loop Invariants. Mathematical Induction. Office Hours 4.2. Big-Oh Notation. Recursive Definitions. Recurrence Relations. More Induction. The Euclidean Algorithm. Supplementary Exercises.

**5. Counting.**

Basic Counting Techniques. Elementary Probability. Inclusion-Exclusion and Binomial Methods. Counting and Partitions. Office Hours 5.4. Pigeon-Hole Principle. Supplementary Exercises.

**6. Introduction to Graphs and Trees.**

Graphs. Edge Traversal Problems. Trees. Rooted Trees. Vertex Traversal Problems. Minimum Spanning Trees. Supplementary Exercises.

**7. Recursion, Trees and Algorithms.**

General Recursion. Recursive Algorithms. Depth-First Search Algorithms. Polish Notation. Weighted Trees. Supplementary Exercises.

**8. Digraphs.**

Digraphs Revisited. Weighted Digraphs and Scheduling Networks. Office Hours 8.2. Digraph Algorithms. Supplementary Exercises.

**9. Discrete Probability.**

Independence in Probability. Random Variables. Expectation and Standard Deviation. Probability Distributions. Supplementary Exercises.

**10. Boolean Algebra.**

Boolean Algebras. Boolean Expressions. Logic Networks. Karnaugh Maps. Isomorphisms of Boolean Algebras. Supplementary Exercises.

**11. More on Relations.**

Partially Ordered Sets. Special Orderings. Multiplication of Matrices. Properties of General Relations. Closures of Relations. Supplementary Exercises.

**12. Algebraic Structures.**

Groups Acting on Sets. Fixed Points and Subgroups. Counting Orbits. Group Homomorphisms. Semigroups. Other Algebraic Systems. Supplementary Exercises.

**13. Predicate Calculus and Infinite Sets.**

Quantifiers and Predicates. Elementary Predicate Calculus. Infinite Sets. Supplementary Exercises.

**Dictionary.**

Discrete Mathematics, 5th Edition

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