# Mathematics MSc

You will study 180 credits in total during your Mathematics MSc. A standard module is typically worth 15 credits and the research project is worth 60 credits. These are the modules studied in 2018. If you are starting in September 2019, these will give you a flavour of the modules you are likely to study. All Modules are subject to change.

Compulsory modules

**Dissertation in Mathematics - 60 credits**

On completion of this module, students should be able to:

a) demonstrate the ability to plan and execute a mathematics project

b) conduct a systematic literature review on some aspect of mathematics

c) critically appraise the literature in the chosen topic

d) communicate their project in a written dissertation and oral presentation.

Optional modules include

**Independent Learning and Skills Project - 15 credits**

On completion of this module, students should be able to:

a) develop a systematic search strategy to find material on a given topic,

b) use the library to find journal articles,

c) use Web of Science and other electronic bibliographical resources to find journal articles,

d) use the web to search for information,

**Advanced Models and Sets - 20 credits**

Set theory is generally accepted as a foundation for mathematics, in an informal sense. It is also a formal axiomatic system, as developed by Zermelo and Fraenkel, among others, building on work of Cantor. Model theory is the study of formal axiomatic systems in full generality, and also depends on set theory for many of its basic definitions and results. Model theory and set theory constitute two of the basic strands of mathematical logic. They present rather special ways of viewing different parts of mathematics from a common perspective. In this module we explain the basic notions of these interrelated subjects.We will discuss in addition some specialized and advanced topics, which may vary.

**Graph Theory - 15 credits**

This module provides an introduction to the basic ideas such as connectedness, trees, planar graphs, Eulerian and Hamiltoniangraphs, directed graphs and the connection between graph theory and the four colour problem.Graph theory is an important mathematical tool in such different areas as linguistics, chemistry and, especially, operational research. This module will include some abstract proofs.

**Advanced Linear and Nonlinear waves - 20 credits**

Waves are present all around us, the most obvious examples being sound, light and water waves. There are many other types of waves, all of which can be described by the same mathematical theory. This module covers the fundamental theory of both linear and non-linear waves. The important distinction between these is that in non-linear systems, not only are there interactions between waves of different frequencies, but there is also a tendency to form sharp fronts, such as shock waves in gases and tidal bores in shallow water. The general theory is illustrated by examples from physical theories, such as fluid mechanics, gas dynamics and biological systems.

**Philosophy of Logic and Mathematics - 20 credits**

Understanding and discussing critically in detail the philosophical issues concerning the nature and application of logic or mathematics and reading, interpreting and criticising historical and contemporary research work on the subject.

**Topology -** **15 credits**

Topology is the study of those properties of a mathematical space which are unchanged by continuous deformations. Indeed, a topology is the minimal extra structure with which we must equip a set so that the idea of "continuity" makes sense in the first place. In this module we introduce topology in an abstract setting and show how it generalizes the familiar notion of continuity from calculus.

**Advanced Mathematical Biology -** **20 credits**

This module teaches students to model certain biological phenomena described by ordinary differential equations; difference equations; discrete time Markov chains; continuous time Markov chains; discrete-time and continuous-time branching processes; Brownian motion and partial differential equations. Students will also learn to model phenomena in infectious diseases.

The full list of optional modules can be read in the course catalogue.