| WEEK # | TOPICS |
| 1 | Introduction Platonic solids - Counting faces, edges, and vertices Planar graphs, duality Euler's formula for planar graphs - A constructive proof Non-existence of a sixth platonic solid Proving non-planarity by counting |
| 2 | Counting 101 First Law of Counting - Multiplying the possibilities Shepard's Law - To count the sheep, count the feet Counting by cases - Break it down and add it up Counting by subtraction - Cases to exclude |
| 3 | Counting Sets - Set theory and Boolean logic
- Inclusion/exclusion - Easy as PIE
- How many handshakes?
|
| 4 | Counting Subsets Binomial coefficients The wonders of Pascal's triangle Counting by block walking Counting by committee The most useful combinatorial identity known to man - "The Hockey Stick" The n days of Christmas |
| 5 | Problem Solving Applying what we know - Examples of counting How to recognize an apparently unfamiliar problem What to do when you are lost in the forest - How to get unstuck More examples - kids and candy, flower arrangements |
| 6 | Discrete Probability |
| 7 | More Probability |
| 8 | Graph Theory A whirlwind tour Vertices, edges, degree, paths, cycles Connectivity and components Acyclic graphs - Trees and forests Directed graphs |
| 9 | More Graph Theory Eulerian tours Graph coloring Ramsey Theory Turan's Theorem |
| 10 | Contest Problems |
