1. Sets, Sequences, and Functions. Some Warmup Questions. Factors and Multiples. Office Hours 1.2. Some Special Sets. Set Operations. Functions. Sequences. Properties of Functions. Office Hours 1.7. Supplementary Exercises.
Informal Introduction. Propositional Calculus. Getting Started with Proofs. Methods of Proof. Office Hours 2.4. Logic in Proofs. Analysis of Arguments. Supplementary Exercises.
Relations. Digraphs and Graphs. Matrices. Equivalence Relations and Partitions. The Division Algorithm and Integers Mod p. Supplementary Exercises.
Loop Invariants. Mathematical Induction. Office Hours 4.2. BigOh Notation. Recursive Definitions. Recurrence Relations. More Induction. The Euclidean Algorithm. Supplementary Exercises.
Basic Counting Techniques. Elementary Probability. InclusionExclusion and Binomial Methods. Counting and Partitions. Office Hours 5.4. PigeonHole Principle. Supplementary Exercises.
Graphs. Edge Traversal Problems. Trees. Rooted Trees. Vertex Traversal Problems. Minimum Spanning Trees. Supplementary Exercises.
General Recursion. Recursive Algorithms. DepthFirst Search Algorithms. Polish Notation. Weighted Trees. Supplementary Exercises.
Digraphs Revisited. Weighted Digraphs and Scheduling Networks. Office Hours 8.2. Digraph Algorithms. Supplementary Exercises.
Independence in Probability. Random Variables. Expectation and Standard Deviation. Probability Distributions. Supplementary Exercises.
Boolean Algebras. Boolean Expressions. Logic Networks. Karnaugh Maps. Isomorphisms of Boolean Algebras. Supplementary Exercises.
Partially Ordered Sets. Special Orderings. Multiplication of Matrices. Properties of General Relations. Closures of Relations. Supplementary Exercises.
Groups Acting on Sets. Fixed Points and Subgroups. Counting Orbits. Group Homomorphisms. Semigroups. Other Algebraic Systems. Supplementary Exercises.
Quantifiers and Predicates. Elementary Predicate Calculus. Infinite Sets. Supplementary Exercises.
