| 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
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| 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
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| 3 |
Counting Sets
- Set theory and Boolean logic
- Inclusion/exclusion - Easy as PIE
- How many handshakes?
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| 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
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| 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
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| 6 |
Discrete Probability
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| 7 |
More Probability
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| 8 |
Graph Theory
A whirlwind tour Vertices, edges, degree, paths, cycles Connectivity and components Acyclic graphs - Trees and forests Directed graphs
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| 9 |
More Graph Theory
Eulerian tours Graph coloring Ramsey Theory Turan's Theorem
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| 10 |
Contest Problems
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