Courses

I will be teaching three courses in the first semester of the 2015-16 academic year.

Course Notes

These are both very work in progress - they get updated each time I teach the course. The topology notes are in an more mature state than the rigidity notes

Undergraduate Supervision

Proposals for final year projects

Polyhedra

I am interested in anything to do with the geometry or combinatorics of polyhedra. Possible topics include: Cauchy's Rigidity Theorem, flexible polyhedra, classification theorems for highly symmetric polyhedra.

Frameworks and Tensegrities

A bar and joint framework is a structure consisting of rigid bars that are joined together by universal joints. There is a very interesting mathematical theory of such structures which studies the rigidity or flexibility of such structures. This project could consist of a survey of some of that theory. A tensegrity is a similar structure, but now, some of the rigid bars may be replaced with cables or struts.

Fair division problems and topology

This project will look at applications of classical theorems such as the Brouwer fixed point theorem and the Borsuk-Ulam theorem to problems of fair disvision of an asset. It may be of interest to a Financial Maths student who would like to learn how abstract mathematical topics like topology can be useful in more applied disciplines like econometrics.

Coordinates in planar geometry

This topic is particularly suited to a student with an interest in post primary maths education. The project will begin with a survey of some of the standard coordinate systems that are used in the Euclidean plane - rectangular, polar, areal, trilinear. Subsequently we will investigate the use of these coordinate systems in proving many results that are commonly proved using synthetic arguments. In many (if not most) second level textbooks coordinate geometry and synthetic geometry are preseneted as if they are completely independent topics. One of the goals of this project is to create a library of examples that might be used by a second level teacher to illustrate the fact that coordinate geometry and synthetic methods in fact complement each other.