Course Meeting Times
Lectures: Three sessions / week, 1 hour / session
Course Outline
- Extremal Graph Theory
- Traditional Graph Theory
- Set Combinatorics
- Additive Combinatorics
- Enumerative Combinatorics
- Geometric Combinatorics
Prerequisites
There are no official prerequisites for this course, though familiarity with combinatorics is assumed. Students should already be familiar with Catalan numbers, Ramsey Theorem, generating functions, Euler's theorem on Eulerian paths, 3-connectivity of convex polytopes in R^3, Chebychev's Inequality, Markov's Inequality, and finite groups.
Main Textbook
There are four main textbooks used for this class:
Stanley, R. P. Enumerative Combinatorics. Vol. I and II. Cambridge, UK: Cambridge University Press, 1999. ISBN: 0521553091 (hardback: vol. I); 0521663512 (paperback: vol. I); 0521560691 (hardback: vol. II).
Bollobás, B. Modern Graph Theory (Graduate Texts in Mathematics). New York, NY: Springer-Verlag, 1998. ISBN: 0387984917.
———. Extremal Graph Theory. New York, NY: Dover, 2004. ISBN: 0486435962.
Jukna, S. Extremal Combinatorics. New York, NY: Springer-Verlag, Berlin, 2000. ISBN: 3540663134.
Problem Sets
There are eight problem sets, each weighted equally for your grade. Collaboration is encouraged with a few simple rules. On every problem not more than four people can collaborate. Every student writes her/his own solution. For each problem, all collaborators should be listed.
Exams
There are no exams in this course.
Grading
The entire grade is based on the eight problem sets.