The textbook is van Lint and Wilson, A Course in Combinatorics, 2nd edition.
+: Chapters we will almost definitely cover.
½: Chapters we will almost definitely partially cover.
0: Chapters we definitely may or may not cover.
−: Chapters we will almost definitely not cover.
| + | 1/23, 25 | 1. Graphs |
| + | 1/28 | 2. Trees (Don't worry about proving the greedy algorithm.) |
| ½ | 1/30, 2/1 | 3. Colorings of graphs and Ramsey's theorem (to before Th. 3.2) |
| + | 2/1, 4 | 4. Turán's theorem and extremal graphs |
| 2/4 | 1a–4a. Problem discussion from Ch. 4, 3, 2, 1 | |
| + | 2/6-8 | 5. Systems of distinct representatives |
| + | 2/11-13 | 6. Dilworth's theorem and extremal set theory (See the lemma for Theorem 6.4.) |
| + | 2/11 | 6a. Birkhoff polytope – see Beck-Pixton paper |
| + | 2/18 | 6b. Sperner generalization from Beck-Zaslavsky paper |
| ½ | 2/18-22 | 7. Flows in networks: to the statement of Th. 7.4; and Prob. 7F |
| − | — | 8. De Bruijn sequences |
| − | — | 9. The addressing problem for graphs |
| + | 2/22-3/1 | 10. The principle of inclusion and exclusion: inversion formulae |
| 3/1 | 10a. Problem discussion from Ch. 7, 10 | |
| − | — | 11. Permanents |
| − | — | 12. The Van der Waerden conjecture |
| + | 3/4-8 | 13. Elementary counting: Stirling numbers |
| + | 3/8-15, 25 | 14. Recursions and generating functions: to p. 141 (through Catalan) |
| + | 3/11 | App. 2. Formal power series (To see how we do power series without calculus) |
| + | 3/25 | 14. Recursions and generating functions: from p. 141 (exponential GF) |
| 3/15, 27 | 13a-14a. Problem discussion from Ch. 13, 14 (3/27: 13K, 14C, 14G, 14J, 14N) | |
| + | 3/29, 4/1 | 15. Partitions – that is, partitions of an integer |
| + | 4/3 | 16. (0,1)-matrices, to the middle of p. 175. |
| ½ | 4/5 | 17. Latin squares, to statement of Theorem 17.3, also statement of Theorem 17.4. |
| ½ | 4/8 | 18. Hadamard matrices, Reed-Muller codes: to p. 204 top, and p. 208 bottom to p. 210 top. |
| + | 4/10-22 | 19. Designs, to p. 234 (See my attempt at organizing the chapter) |
| 4/15 after class | 19a. Problem session on Ch. 18-19. Recommended problems on the notes page. | |
| − | — | 20. Codes and designs |
| − | — | 21. Strongly regular graphs and partial geometries |
| ½ | 4/24-29 | 22. Orthogonal Latin squares, to Example 22.2. |
| + | 4/26 (p.m.) | 19/22a. Problem session on Ch. 19, 22. Recommended problems on the notes page. |
| ½ | 4/29-5/3 | 23. Projective and combinatorial geometries, to Problem 23C. (See terminology. See Lemma 23LL.) |
| ½ | 5/3 | 24. Gaussian numbers and q-analogues, to p. 330 top. |
| ½ | 5/6-8 | 25. Lattices and Möbius inversion, to Problem 25C. (See extra Problem 25AA.) |
| ½ | 5/8 |
26. Combinatorial designs and projective geometries, to Example 26.1 and omit proof of Theorem 26.1. (Purpose: see designs from geometry.) |
| − | — | 27. Difference sets and automorphisms |
| − | — | 28. Difference sets and the group ring |
| − | — | 29. Codes and symmetric designs |
| ½ | 5/10 | 30. Association schemes, to Example 30.6 (don't sweat the details) |
| − | — | 31. Algebraic graph theory: eigenvalue techniques |
| − | — | 32. Graphs: planarity and duality |
| − | — | 33. Graphs: colorings and embeddings |
| − | — | 34. Electrical networks and squared squares |
| − | — | 35. Pólya theory of counting |
| − | — | 36. Baranyai's theorem |