Introductory description

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Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

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

Learning outcomes

By the end of the module, students should be able to:

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Indicative reading list

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.

Subject specific skills

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Transferable skills

Students will acquire key reasoning and problem solving skills which will empower them to address new problems with confidence.