# 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 2019. If you are starting in September 2020, 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 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.

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.

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.