- 1.1. Introduction and Overview
1.2. Basic Concepts of Logic
1.3. Sets, Set Operations, Mappings, and Functions
1.4. Algorithms and Algorithmic Complexity
1.5. Integers, Matrices, and Number Theory
- 2.1. Methods of Proof
2.2. Algebraic Derivation and Constructive Proof
2.3. Mathematical Induction
2.4. Recursion and Recursive Algorithms
2.5. Program Correctness
- 3.1. Counting and the Pigeonhole Principle
3.2. Elements of Probability Theory
3.3. Permutations and Combinations
3.4. Relations and Recurrence Relations
3.5. Divide-and-Conquer
3.6. Inclusion-Exclusion
- 4.1. Mathematics of Graphs and Trees
4.2. Graph Connectivity and Path Problems
4.3. Planar Graphs and Graph/Map Coloring
4.4. Trees, Tree Traversal, and Sorting
4.5. Spanning Trees and MSTs
- 5.1. Boolean Functions
5.2. Logic Gates and Minimization of Circuits
5.3. Languages and Grammars
5.4. Finite-State Automata and Applications
Bibliography
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or UF students officially registered for this class.