Introduction to Combinatorics and Graph Theory - 0366.1123.01

Noga Alon ( nogaa@tau.ac.il )
Instructor: Peleg Michaeli
2nd Semester, 2010-2011 - Monday 14:00-16:00 , Schreiber 6
School of Mathematics
Tel-Aviv University

Procedural Matters:

Desirable background: Introduction to Set Theory.
Exercises will be given during the course and their solutions will be graded and form about 10% of the final grade. There will also be a final exam.

Text books:

There are many books that cover the area, including the following.
A. Avron, Introduction to Discrete Mathematics (in Hebrew)
N. Linial and M. Parnas, Discrete Mathematics (in Hebrew)
J. Matousek and J. Nesetril, Invitation to Discrete Mathematics.

Course syllabus:

Basic enumeration methods, the Binomial coefficients, the pigeonhole principle, inclusion-exclusion, asymptotic estimates, recurrence relations, generating functions, the basics of Graph theory: connectivity, bipartite graphs, matchings.

More relevant information, including exercises, will appear during the term in: Introduction to Combinatorics and Graph Theory

Course Outline (to be updated during the term):

  1. Feb. 21:
    Introduction, Basic enumeration methods, Basic enumeration problems
  2. Feb. 28:
    The Binomial coefficients
  3. March 7:
    Catalan numbers
  4. March 14:
    The pigeonhole principle, The Erdos Szekeres Theorem
  5. March 21:
    No class
  6. March 28:
    Inclusion Exclusion
  7. April 4:
    Asymptotic estimates
  8. April 11:
    Recurrence relations
  9. April 18, April 25:
    Passover
  10. May 2:
    More recurrence relations, Generating functions
  11. May 9:
    Memorial Day
  12. May 16:
    More generating functions
  13. May 23:
    Even more generating functions
  14. May 30:
    Basic Graph Theory
  15. June 6:
    More Graph Theory, conclusion