Introduction to Combinatorics and Graph Theory - 0366.1123.01

Noga Alon ( nogaa@tau.ac.il )
2nd (=Spring) Semester, 2014-2015, Monday 14-16, Holzblatt.
Instructor: Gal Kronenberg, Monday 16-17, Orenstein 111.
School of Mathematics
Tel-Aviv University

Procedural Matters:

Desirable background: Introduction to Set Theory, Linear Algebra 1, Calculus 1.
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 and Catalan numbers, the pigeonhole principle, inclusion-exclusion, asymptotic estimates, recurrence relations, generating functions, the basics of Graph theory: connectivity, bipartite graphs, matchings.

(Much) more relevant information, including exercises, will appear in the course page in Moodle: Introduction to Combinatorics and Graph Theory

Course Outline (to be updated during the term):

  1. March 9:
    Introduction, Basic enumeration methods, Basic enumeration problems
  2. March 16:
    The Binomial coefficients
  3. March 23:
    Catalan numbers
  4. April 13:
    The pigeonhole principle, The Erdos Szekeres Theorem
  5. April 20:
    Inclusion Exclusion
  6. April 27:
    Asymptotic estimates
  7. May 4:
    Recurrence relations
  8. May 11:
    More recurrence relations
  9. May 18:
    End of recurrence relations, Generating functions
  10. May 25:
    More generating functions
  11. June 1:
    End of generating functions, Basic Graph Theory
  12. June 8:
    More Graph Theory
  13. June 15:
    End of Graph Theory, conclusion

Exams from previous years:

Spring 2010, Moed A

Spring 2010, Moed B

Spring 2011, Moed A

Spring 2011, Moed B

Spring 2013, Moed A

Spring 2013, Moed B

Spring 2014, Moed A

Spring 2014, Moed B