| Sep 2 | Sections 1.1, 1.2: Pigeonhole principle; 2.1, 2.2: Induction |
| Sep 4 | Review of functions, Section 3.1: Permutations |
| Sep 7 | Holiday |
| Sep 9 | Section 3.2: Strings / words |
| Sep 11 | Section 3.3: Choice problems; Poker probability HW1 due |
| Sep 14 | Polynomial interpolation, Section 5.1: Compositions |
| Sep 16 | Section 5.2: Set partitions |
| Sep 18 | Sections 4.1, 4.2: Binomial theorem, multinomial theorem HW2 due |
| Sep 21 | Section 5.3: Integer partitions |
| Sep 23 | Sections 7.1, 7.2: Inclusion-exclusion |
| Sep 25 |
Formal power series; Section 4.3: General binomial theorem HW3 due |
| Sep 28 | Section 8.1: Solving recurrence relations |
| Sep 30 | Section 8.1: Ordinary generating functions, partitions |
| Oct 2 | Section 8.1: Catalan numbers HW4 due |
| Oct 5 | Section 8.1: Compositions of ordinary generating functions |
| Oct 7 | Review / catchup |
| Oct 9 | Midterm 1 |
| Oct 12 | Midterm review |
| Oct 14 | Section 8.2: Exponential generating functions and products |
| Oct 16 | Section 8.2: Exponential generating functions and compositions
HW5 due |
| Oct 19 | Section 9.1: Graph theory terminology; Eulerian trails |
| Oct 21 | Finish 9.1; Section 9.3: directed graphs (definitions and Theorem 9.6 only);
Section 9.2: Hamiltonian cycles |
| Oct 23 | Finish 9.2; Section 9.4: Graph isomorphisms
HW6 due |
| Oct 26 | Section 10.1: Trees |
| Oct 28 | Section 10.1: Cayley's formula for number of trees (via Prüfer encoding) |
| Oct 30 | Section 10.2: Minimum-weight spanning trees, Kruskal's greedy algorithm
HW7 due |
| Nov 2 | Section 10.3: Adjacency matrices; Section 10.4: Kirchhoff's Matrix-tree theorem |
| Nov 4 | Finish 10.4 |
| Nov 6 | Section 11.1: Graph colorings, chromatic polynomials
HW8 due |
| Nov 9 | Section 11.2: Bipartite graphs (just Theorem 11.5); Section 11.3: Hall's theorem |
| Nov 11 | Review / catchup |
| Nov 13 | Midterm 2: Study guide |
| Nov 16 | Finish 11.3; Stable matchings; Section 11.5: Tutte's theorem (just statement of Theorem 11.17) |
| Nov 18 | Section 12.1: Planar graphs, see supplementary notes |
| Nov 20 | Section 12.3: Coloring planar graphs
HW9 due |
| Nov 23 | Sperner's lemma and fair division (Sections 1,3,6,7 of handout) |
| Nov 25 | Fun applications of linear algebra to combinatorics |
| Nov 27 | Holiday |
| Nov 30 | Section 11.4: Turán's theorem Section 13.1: Ramsey theory (graphs) |
| Dec 2 | Finish 13.1 |
| Dec 4 | Section 13.2: Generalizations of Ramsey's theorem, Erdős-Szekeres theorem
HW10 due |
| Dec 7 | Finish 13.2 |
| Dec 9 |
Section 15.2: Lower bounds for Ramsey numbers Section 15.4.2: Non-constructive (probabilistic) existence proofs |
| Dec 11 | Summary of course |
| Dec 14 | Review HW11 due |
| Dec 21 | Final exam 2:45PM - 4:45PM, Study guide |