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MA241 Content

Content:

I Enumerative combinatorics

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

  2. Applications of the Binomial Theorem (Multinomial Theorem, Multiset formula, Principle of inclusion/exclusion)
  3. Linear recurrence relations and the Fibonacci numbers

  4. Generating functions and the Catalan numbers

  5. Permutations, Partitions and the Stirling and Bell numbers

II Graph Theory

  1. Basic concepts (isomorphism, connectivity, Euler circuits)

  2. Trees (basic properties of trees, spanning trees, counting trees)

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

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

  5. Elements of Ramsey Theory

III Boolean Functions

Book:

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.