Content:

I Enumerative Combinatorics:

• Basic counting (Lists with and without repetitions, Binomial coefficients and the Binomial Theorem)

• Applications of the Binomial Theorem (Multinomial Theorem, Multiset formula, Principle of inclusion/exclusion)

• Linear recurrence relations and the Fibonacci numbers

• Generating functions and the Catalan numbers

• Permutations, Partitions and the Stirling and Bell numbers

II Graph Theory:

• Basic concepts (isomorphism, connectivity, Euler circuits)

• Trees (basic properties of trees, spanning trees, counting trees)

• Planarity (Euler's formula, Kuratowski’s theorem, the Four Colour Problem)

• Matching Theory (Hall's Theorem and Systems of Distinct Representatives)

• Elements of Ramsey Theory

III Boolean Functions

Books:

Edward E. Bender and S. Gill Williamson, Foundations of Combinatorics with Applications, Dover Publications, 2006. Available online at the author's website: http://www.math.ucsd.edu/~ebender/CombText/

John M. Harris, Jeffry L. Hirst and Michael J. Mossinghoff, Combinatorics and Graph Theory, Springer-Verlag, 2000.