This syllabus is tentative and subject to change (especially if we run out of time, which we will) until the classes have actually taken place. All references are to
As we have a separate introduction to graph theory, I will skip most of the graph theory in the book.
| Dates | Chapter | Topics | Remarks |
| Jan. 26-28 | 1. Graphs | Basics of graphs. | For future use. |
| Jan. 30 | 5. Systems of distinct representatives | Hall's and König's theorems. Birkhoff polytope. | An existence theory and a bit of geometric combinatorics (or is it probability?). |
| Feb. 2-9 | 6. Dilworth's theorem and extremal set theory | Posets raise their heads. | Fun theorem of my grandadvisor. Sperner theory: a corner(stone) of combinatorics. |
| Feb. 11-18 | 10. The principle of inclusion and exclusion; inversion formulae | Many important examples. Binomial identities. | Fundamental to counting. |
| Feb. 18-23 | 13. Elementary counting; Stirling numbers | Binomial identities, falling factorials, generating functions. Partitions of a set. Polynomial basis change. | Lots more like this in Stanley's book. |
| Feb. 23 - Mar. 2 | 14. Recursions and generating functions | Algebraic and analytic g.f. methods. Lagrange inversion. Catalan numbers. | Basic and effective counting method. Fun with formulas. Read Example 14.15 just to see the technique. |
| Mar. 2-6 | 15. Partitions | Partitions of an integer. Ferrers diagrams. Young tableaux. | These show up in many combinatorial problems. Read Thms. 15.7, 15.11 just to see the techniques. Omit Thms. 15.8, 15.10, and Lemma 15.9. |
| Mar. 6-11 | 16. (0,1)-Matrices | Majorization of integer partitions. Possible row and column sums. Constant line sums. | These show up in even more combinatorial problems. In Thm. 16.1, omit the network proof (pp. 170bottom - 172top). Read Thm. 16.6 lightly to see the methods, especially the estimations. |
| Mar. 13-27, Apr. 1 | 17. Latin squares | Asymptotics; partial squares; orthogonality; Latin hypercubes. | More here than meets the eye. Design of experiments (theoretically). Group and quasigroup tables. |
| Mar. 30, Apr. 15-17 | 18. Hadamard matrices, Reed-Muller codes | Geometrical origin; difficulty of construction; conference matrices; excess of +1's. Linear codes; construction from Hadamard matrices. | Important in design theory; related to signed graphs. Valuable error-correcting codes. |
| Apr. 20, May 4-8 | 19. Designs | Incidence structures; block designs; linear "spaces". Construction; numerology. Symmetric designs. Steiner triple systems. | Combinatorial design of experiments (very theoretical). Connections with finite group theory. |
| Apr. 17, May 8 | 20. Codes and designs | Error-correcting codes. | Basic concepts. (Only the first 3 pages.) |
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