Courses:

Combinatorial Theory: Introduction to Graph Theory, Extremal and Enumerative Combinatorics >> Content Detail



Syllabus



Syllabus

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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:

Amazon logo Stanley, R. P. Enumerative Combinatorics. Vol. I and II. Cambridge, UK: Cambridge University Press, 1999. ISBN: 0521553091 (hardback: vol. I); Amazon logo 0521663512 (paperback: vol. I); Amazon logo 0521560691 (hardback: vol. II).

Amazon logo Bollobás, B. Modern Graph Theory (Graduate Texts in Mathematics). New York, NY: Springer-Verlag, 1998. ISBN: 0387984917.

Amazon logo ———. Extremal Graph Theory. New York, NY: Dover, 2004. ISBN: 0486435962.

Amazon logo 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.


 








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