Tuesdays and Thursdays 11:30-1:00, 4151 USB

Another useful guide, though more geared toward contest problems: How to Write a Solution - by Richard Rusczyk & Mathew Crawford

Take home midterm to be handed out Oct. 6, due Oct. 13 in class.

Take home final handed out in class on December 13, due at 3:30 pm December 20 (return exams to me in my office).

September 6, 8: Graph theory basics: paths, trees, and cycles, Eulerian trails (following parts of Chapters 1 and 2 of West)

Problem Set 1, Due: Tuesday, September 13

September 13, 15: Kruskal's algorithm, Hall's matching theorem, Konig-Egervary theorem (following parts of Ch. 2 and 3 of West)

Problem Set 2, Due: Tuesday, September 20

Note: for problem 5, a matching that covers A is the same as a matching that saturates A.

September 20, 22: Tutte's 1-factor theorem, connectivity, Menger's theorems (Ch. 3 and 4 of West)

Problem Set 3, Due: Tuesday, September 27

September 27, 29: Max-flow min-cut theorem, graph coloring (Ch. 4 and 5 of West)

Problem Set 4, Due: Tuesday, October 4

October 4, 6: Mycielski's construction, graph minors, planar graphs, Euler's formula (Ch. 5 and 6 of West)

Midterm, Due: Thursday, October 13

October 11, 13: Haewood's formula, outerplanar graphs, Kuratowski's theorem (Ch. 6 of West)

Problem Set 5, Due: Tuesday, October 25

No class October 18: Fall break

October 20: The perfect graph theorem (following notes by Andras Gyarfas, pages 64-67)

October 25, 27: Binomial coefficients, inclusion-exclusion, derangements, Euler's phi function (Ch. 10 and 13 of Van Lint and Wilson)

Notes on inclusion-exclusion and generalizations. Pages 789-795 are all we need for now. Also see section 3.6 of Stanley.

Problem Set 6, Due: Tuesday, November 1

November 1, 3: Generating functions, Catalan numbers (Ch. 14 of Van Lint and Wilson)

Problem Set 7 (Problem 1 has been corrected), Due: Tuesday, November 8

November 8, 10: More generating functions, eigenvalues of graphs (Section 8.6 of West and Ch. 36 of Van Lint and Wilson)

Spectra of Graphs by Andries Brouwer and Willem Haemers. See page 26 for a table of spectra of small graphs.

Problem Set 8, Due: Tuesday, November 15

November 15, 17: Eigenvalues of graphs, ADE Dynkin diagrams, the matrix tree theorem (Theorem 3.1.3 of Spectra of Graphs, Section 2.2 of West and Ch. 36 of Van Lint and Wilson)

Problem Set 9, Due: Tuesday, November 22

November 22: Fisher's inequality and other linear algebra applications (pages 46-56 of notes by Andras Gyarfas)

No class November 24: Thanksgiving break

November 29, December 1: linear algebra applications continued, the chromatic polynomial (Section 5.3 of West)

Problem Set 10, Due: Tuesday, December 6

For problem 5, nonnegative eigenvalues must be counted with multiplicities

December 6, 8: The Tutte polynomial, Knot invariants

Problem Set 11, Do not turn in (but it may be helpful for the final). Problem 5 was wrong; I think it is now correct.

December 13: Review

Final, Due: Tuesday, December 20

Office hours this week: Wednesday 4-5:30, Friday 12-1, Monday 12-1