I am involved in teaching the following modules.
MT4514: Graph Theory
(Semester 1).
Graph theory investigates the properties of graphs - not graphs which are "data-plots", but graphs consisting of a collection of nodes joined by edges. These graphs are a natural way of modelling situations involving connections between objects - transport networks, the internet, assigning students to placements, and many more - and are very interesting mathematical objects in their own right. Topics which we investigate include: whether is is possible to travel around a graph visiting every edge or vertex once, whether graphs which have two distinct sets of vertices have a matching between them, colouring problems (related to the well-known map-colouring problem) and how sufficiently large graphs must possess certain structure. Graph theory is a topic which has a natural interplay between theory and application.
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MT4516: Finite Mathematics
(Semester 1).
The module MT4516 Finite Mathematics explores a range of mathematical structures which, while rooted in algebra and combinatorics, have a wide variety of real-life applications. This area of mathematics has been called "the applied mathematics of the digital age" due to its applications to information security and theoretical computer science. We explore topics including include error-correcting codes, finite geometry, Latin squares and combinatorial designs, and highlight the sometimes-unexpected mathematical connections which link all these topics.
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MT3505: Rings and Fields
(Semester 2).
MT3505 Rings and Fields builds on the study of Abstract Algebra which was begun in MT2505. It shows how various familiar mathematical structures such as the integers, the real numbers, sets of matrices and sets of polynomials can all be viewed as examples of a structure called a "ring" which captures the property of having two operations (addition and multiplication). We develop theory to understand rings in general, which then enables us to better understand various properties of these examples - some familiar and some new to us. We also take useful or interesting properties of the motivating examples (eg number theory as performed in the integers) and see how this can be meaningfully extended to other rings. In the process, we also briefly investigate a few other topics (for example the order theory of partially ordered sets) and see how this can be used to prove ring theory results.
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sh70 - at - st-andrews.ac.uk
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