The aims of this module are:

• to develop oral and written communication skills
• to give students the experience of working independently on an advanced topic in mathematics or its applications

The aims of this module are:

• To introduce the concept of small and large parameters in equations and how they can be exploited to simplify difficult mathematical problems.
• To introduce a wide range of approximation techniques to analyse differential equations and integrals.

The aim of this module is:

• to derive the fundamental equations of fluid mechanics
• to develop students' expertise in solving simplified forms of these equations applicable to a variety of fluid flows
• to learn about some industrial and environmental applications of fluid mechanics

The aim of this module is to create awareness of the power and range of abstract mathematical concepts through a basic introduction to the methods of functional analysis.

The aims of this module are:

• to introduce manifolds, tensors and integration theory on manifolds
• to study basic geometric operations and their properties
• to discuss applications of geometric methods to submanifold geometry, differential equations and general relativity

The aims of this module are to introduce the notions of a Lie group and Lie algebra and to study their properties and methods.

The aims of this module are:

• To develop skills in the mathematical modelling of real life situations.
• To develop the ability to work effectively in a group.

The aims of this module are to:

• provide a mathematical understanding of the Lebesgue measure and integration
• generalise concepts to abstract measure spaces
• build a solid rigorous mathematical background for students to proceed to stochastic analysis and financial mathematics

The aim of this module is to:

• to provide students with a rigorous mathematical introduction to the modern financial theory of security markets in discrete and continuous time models
• to give students a solid theoretical background in the derivatives industry in discrete and continuous time models.

This module aims to:

• introduce numerical methods and associated theory for modelling of financial options
• teach students how to implement such numerical methods on computers
• gain experience in interpreting numerical results

The aims of this module are:

• To develop skills in the mathematical modelling of real life situations.
• To develop the ability to work effectively in a group.

The aims of this module are to:

• introduce students to the main ideas and techniques of the modern theory of nonlinear waves
• demonstrate how these ideas and techniques can be used in a wide range of applications

The aim of this module is to create awareness of the power and range of abstract mathematical concepts through a basic introduction to the methods of spectral theory.

The aim of this module is to gain familiarity with theory and techniques of static optimisation and dynamic optimisation.

The aim of this module is:

• to introduce both supervised and unsupervised methods for learning from data
• to introduce methods of dimensionality reduction
• to introduce the R statistical programming language for implementing methods using real data

The aim of this module is to introduce students to:

• the basics of stochastic calculus by using Brownian motion as an integrator
• mathematical modelling of pricing via the Black-Scholes model

The aims of this module are to gain familiarity with modern qualitative theory of linear PDE's with particular emphasis on second-order equations, as well as to study selected aspects of modern methods for simple nonlinear PDEs.