18.314 | Fall 2014 | Undergraduate
Combinatorial Analysis

Most of the readings are assigned from the required textbook Bona, Miklos. A Walk Through Combinatorics: An Introduction to Enumeration and Graph Theory. World Scientific Publishing Company, 2011. ISBN: 9789814335232. [Preview with Google Books]

1 Pigeonhole Principle Chapter 1
2 Induction, Elementary Counting Chapter 2 and start Chapter 3.
3 Elementary Counting (concluded) Chapter 3 (continued)
4 Binomial Theorem, Compositions Chapter 4
5 Compositions (concluded), Integer Partitions Chapter 5

6 Integer Partitions (concluded)
7 Set Partitions
8 Permutations, Cycle Type Chapter 6

9 Permutations (cont.), Stirling Numbers of the First Kind
10 Permutations (concluded)
11 The Sieve Chapter 7

12 The Sieve (cont.), Generating Functions
13 Generating Functions (continued) Chapter 8

14 Generating Functions (concluded)
15 Catalan Numbers
16 Midterm One-Hour Exam 1 (Chapters 1–7, omitting pp. 123–24)
17 Partitions Chapter 8 (continued)

18 Exponential Generating Functions
19 Exponential Generating Functions (concluded)
20 Vertex Degree, Eulerian Walks Chapter 9

21 Isomorphism, Hamiltonian Cycles
22 Tournaments, Trees Chapter 10

23 Counting Trees
24 Minimum Weight Spanning Trees

Matrix-Tree Theorem (PDF)
paralleling Section 10.4. There are
also two exercises.

More on Matrix-Tree Theorem (PDF)
for information only to see some
more algebraic combinatorics.

25 Matrix-Tree Theorem Chapter 10 (continued)
26 Matrix-Tree Theorem (concluded), Bipartite Graphs Finish Chapter 10 and start Chapter 11.
27 Bipartite Graphs (concluded) Chapter 11
28 Matchings in Bipartite Graphs Chapter 11 (continued)
29 Midterm One-Hour Exam 2 (Chapters 8–10.2)
30 Latin Rectangles, Konig-Egervary Theorem Chapter 11 (continued)

31 Matchings in Bipartite Graphs (concluded)
32 Chromatic Polynomials
33 Planar Graphs Chapter 12

34 Polyhedra
35 Polyhedra (concluded)
36 Coloring Maps
37 Ramsey Theory Chapter 13

38 A Probabilistic Proof
39 Discussion of Final Exam, Answering Questions
40 Final Exam (Chapters 1–12)