Class meets: Tuesday and Thursday, 1-2:30 pm,
Office hour: Tuesday 3-4 pm
Grader: Fu Liu
Combinatorial problems and methods for their solution. Prior
experience with abstraction and proofs helpful. Enumeration, generating
functions, recurrence relations, construction of bijections. Introduction to
graph theory. Network algorithms, extremal combinatorics.
Course Level: Undergraduate
through Combinatorics, Miklos Bona,
World Scientific, 2002.
errata by R. Ehrenborg,
errata by R. Stanley.
Enumerative Combinatorics, Vol 1 and Vol 2, by R. P. Stanley,
Cambridge University Press, 1996 and 1999.
Introductory Combinatorics, R. Brualdi,
3rd or 4th edition, Prentice Hall.
Grading: 3 inclass exams 50% total, problem sets
(due every second Tuesday) 50%, + bonuses.
Due every second Tuesday
Bonuses: You can get a grading bonus if you
write an article in combinatorics,
invent a new interesting integer sequence and
publish it in
Sloan's Encyclopedia of Integer Sequences,
find a new interpretation of the Catalan numbers
that is not listed in
Stanley's EC2 and
or solve some of the bonus problems in problem sets.
- R 09/08/2005. Introduction. Pigeonhole principle. Chapter 1.
- T 09/13/2005. Mathematical induction. Chapter 2.
- R 09/15/2005. Permutations. Chapter 3.
- T 09/20/2005. Binomial theorem. Chapter 4. Problem Set 1 is due.
- R 09/22/2005. Compositions. Integer Partitions. Chapter 5.
- T 09/27/2005. Set partitions.
- R 09/29/2005. Cycles in permutations. Stirling numbers. Chapter 6.
- T 10/04/2005. Exam 1. Problem Set 2 is due.
- R 10/06/2005. Inclusion-exclusion principle. Chapter 7.
T 10/11/2005. no classes (Columbus day)
- R 10/13/2005. Inclusion-exclusion (cont'd). Mobius inversion.
- T 10/18/2005. Recurrence relations.
- R 10/20/2005. Generating functions. Chapter 8.
- T 10/25/2005. Generating functions (cont'd). Problem Set 3 is due.
- R 10/27/2005. Catalan numbers.
- T 11/01/2005. Generating functions (cont'd). Problem Set 4 is due.
- R 11/03/2005. Exam 2.
- T 11/08/2005. Graphs. Eulerian walks. Hamiltionian cycles.
- R 11/10/2005. Trees. Counting trees. Chapter 10.
- T 11/15/2005. Matrix-tree theorem.
- R 11/17/2005. Matrix-tree theorem (cont'd). Problem Set 5 is due.
- T 11/22/2005. Guest lecture by Igor Pak
R 11/24/2005. no classes (Thanksgiving)
- T 11/29/2005. Matrix-tree theorem and Electrical networks.
- R 12/01/2005. Electrical networks (cont'd).
Eulerian digraphs and BEST theorem.
- T 12/06/2005. Graph colorings. Bipartite graphs and matchings.
- R 12/08/2005. Exam 3.
Problem Set 6 is due.
- T 12/13/2005. ... Polya counting. Ramsey theory. Probabilistic method.