| week | topics |
| 1 | logic (ch 1): |
| propositional and quantifier logic | |
| 2 | mathematical proof (ch 4): |
| proof methods; mathematical induction | |
| 3 | fundamental mathematics (ch 2): |
| sets, relations, and functions | |
| 4 | growth of functions (ch 3): |
| asymptotic notation | |
| 5 | arithmetic and geometric sums (ch 2): |
| recursion (ch 4) | 6 | recurrences (ch 7): |
| methods of solving recurrences | |
| 7 | counting (ch 5): |
| counting methods | |
| 8 | discrete probability (ch 6): |
| independence and conditional probability | |
| 9 | Bayes's theorem (ch 6): |
| Bernoulli trials and binomial distribution | |
| 10 | random variables and expected value (ch 6): |
| linearity of expectation and variance | |
| 11 | graph theory (ch 9): |
| Euler and Hamilton cycles; connectedness | |
| 12 | trees, bipartite graphs, matching (ch 10) |
| graph isomorphism; planar graphs | |
| 13 | modular arithmetic (ch 3); |
| Euclid's algorithm; multiplicative inverses | |
| 14 | final exam |