MATH 84530: Combinatorics

Instructor: János Pach

Email: pach@cims.nyu.edu

Recommended Texts: J. Matousek and J. Nesetril: Invitation to Discrete Mathematics, Oxford University Press, Oxford, 1998.
L. Lovasz, J. Pelikan and K. Vesztergombi: Discrete Mathematics, Springer-Verlag, New York, 2003.

Course outline:We give a systematic introduction to some core areas of combinatorics with special emphasis on links between seemingly unrelated areas and on applications to problems in other parts of mathematics. Some basic knowledge of linear algebra, calculus, and familiarity with the notion of finite fields are required. We cover the following topics:

• Counting trees
• Coloring graphs and Ramsey's theorem
• Turan's theorem and extremal graph theory
• Dilworth' theorem and extremal set theory
• Sieve methods and inversion formulae
• Recursions and generating functions
• Partitions
• Hadamard matrices and codes
• Combinatorial designs