Combinatorial Analysis

Calendar

SES #	TOPICS	KEY DATES
1	Pigeonhole Principle
2	Induction, Elementary Counting
3	Elementary Counting (concluded)	Problem Set 1 due
4	Binomial Theorem, Compositions
5	Compositions (concluded), Integer Partitions
6	Integer Partitions (concluded)	Problem Set 2 due
7	Set Partitions
8	Permutations, Cycle Type	Problem Set 3 due
9	Permutations (continued), Stirling Numbers of the First Kind
10	Permutations (concluded)
11	The Sieve	Problem Set 4 due
12	The Sieve (continued), Generating Functions
13	Generating Functions (continued)
14	Generating Functions (concluded)	Problem Set 5 due
15	Catalan Numbers
16	Midterm One–Hour Exam 1 (Chapters 1–7, omitting pp. 123–24)
17	Partitions	Problem Set 6 due
18	Exponential Generating Functions
19	Exponential Generating Functions (concluded)	Problem Set 7 due
20	Vertex Degree, Eulerian Walks
21	Isomorphism, Hamiltonian Cycles
22	Tournaments, Trees	Problem Set 8 due
23	Counting Trees
24	Minimum Weight Spanning Trees
25	Matrix-Tree Theorem	Problem Set 9 due
26	Matrix-Tree Theorem (concluded), Bipartite Graphs
27	Bipartite Graphs (concluded)
28	Matchings in Bipartite Graphs
29	Midterm One-Hour Exam 2 (Chapters 8–10.2)
30	Latin Rectangles, Konig-Egervary Theorem	Problem Set 10 due
31	Matchings in Bipartite Graphs (concluded)
32	Chromatic Polynomials
33	Planar Graphs	Problem Set 11 due
34	Polyhedra
35	Polyhedra (concluded)
36	Coloring Maps
37	Ramsey Theory	Problem Set 12 due
38	A Probabilistic Proof
39	Discussion of Final Exam, Answering Questions
40	Final Exam (Chapters 1–12)