Combinatorics

This final year mathematics course aims to equip you to apply concepts in symbolic methods and analysis to solve a variety of problems in combinatorics. The tools developed in the course are useful for future graduate courses in mathematics, applied mathematics and engineering.

Course Content

• Combinatorial Structures and Ordinary Generating Functions: symbolic enumeration methods, integer compositions and partitions, words and regular languages, tree structures
• Labelled Structures and Exponential Generating Functions: labelled classes, surjections, set partitions, words, alignments, permutations, labelled trees, mapping and graphs
• Complex Analysis, Rational and Meromorphic Asymptotics: generating functions as analytic objects, analytic functions and meromorphic functions, singularities and exponential growth of coefficients
• Singularity Analysis of Generating Functions: coefficient asymptotics, process of singularity analysis