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Class notes

1. Introduction; Basic counting rules
2. Permutations, combinations, balls in boxes
3. Partitions, Pascal's formula, binomial thm., multinomial thm.
4. Newton's binomial thm., inclusion/exclusion
5. Pigeonhole principle, Erdos-Szekeres thm
6. Probability spaces, conditional probability
7. Independence, Binomial distribution
8. Linearity of expectation, indicator variables, Markov's inequality
9. Recurrences: examples, annihilators
10. Recurrences: more annihilators
11. Recurrences: divide and conquer
12. Recurrences: divide and conquer, other techniques
13. Graph theory: Platonic Solids
14. Problem Session
15. Approximations of various coefficients and Ramsey Theory
16. Theory of Computation: cardinality of sets

TAs