# Mathematics MSc

The following modules are available in 2022/23 for the Mathematics MSc and are examples of the modules you are likely to study. All Modules are subject to change. You will study 180 credits in total.

### Compulsory modules

**Dissertation in Mathematics - 60 credits**

On completion of this module, students should be able to demonstrate the ability to plan and execute a mathematics project, conduct a systematic literature review on some aspect of mathematics, critically appraise the literature in the chosen topic and 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 develop a systematic search strategy to find material on a given topic, use the library to find journal articles, use Web of Science and other electronic bibliographical resources to find journal articles and use the web to search for information.

**Calculus in the Complex Plane - 15 credits**

This module will develop the theory of differentiable functions of a single complexvariable, an outstanding highlight of 19th century mathematics, in a coherent and mathematically rigorous way. Towards the end, complex analytic techniques will be used to solve seemingly intractable problems in real analysis.

**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.

**Statistical Computing - 15 credits**

This module gives an overview of the foundations and basic methods in statistical computing.One of the most important ideas in statistical computing is, that often properties of a stochastic model can be found experimentally, by using a computer to generate many random instances of the model, and then statistically analysing the resulting sample. The resulting methods are called Monte Carlo methods, and discussion of such methods forms the main focus of this module.

**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.