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.

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

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 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 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 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.

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.