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1 Fundamentals

• 1. Examples
• 2. Combinations and permutations
• 3. Binomial coefficients
• 4. Bell numbers
• 5. Choice with repetition
• 6. The Pigeonhole Principle
• 7. Sperner's Theorem
• 8. Stirling numbers

2 Inclusion-Exclusion

• 1. The Inclusion-Exclusion Formula
• 2. Forbidden Position Permutations

3 Generating Functions

• 1. Newton's Binomial Theorem
• 2. Exponential Generating Functions
• 3. Partitions of Integers
• 4. Recurrence Relations
• 5. Catalan Numbers

4 Systems of Distinct Representatives

• 1. Existence of SDRs
• 2. Partial SDRs
• 3. Latin Squares
• 4. Introduction to Graph Theory
• 5. Matchings

5 Graph Theory

• 1. The Basics
• 2. Euler Circuits and Walks
• 3. Hamilton Cycles and Paths
• 4. Bipartite Graphs
• 5. Trees
• 6. Optimal Spanning Trees
• 7. Connectivity
• 8. Graph Coloring
• 9. The Chromatic Polynomial
• 10. Coloring Planar Graphs
• 11. Directed Graphs

6 Pólya–Redfield Counting

• 1. Groups of Symmetries
• 2. Burnside's Theorem
• 3. Pólya-Redfield Counting