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 aims of this module are:

• to introduce Bayesian statistics;
• to study posterior distributions and their properties;
• to discuss applications of Bayesian statistics to a range of data sets.

The aim of this module is to introduce students to the notions and methods of the theory of dynamical systems with an emphasis on its applications.

This module provides an introduction to the mathematical theory of formal languages - i.e. sets of sequences of symbols. It is the primary goal of the module to develop a student's knowledge of various concepts of defining formal languages, and to raise awareness of their relation to a range of fields of application, such as data mining, programming languages and natural language processing. In addition, the module shall explain the intrinsic connection of formal language theory to the mathematical foundations of computer science, thus deepening a student's understanding of the nature of computation.

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 the basics of algebraic geometry
• compare the structure of affine and projective varieties
• analyse examples and their properties including dimension and singularities

The aim of this module is to provide students with fundamental methods of classical number theory and some of its diverse applications.

The aims of this module are:

• To introduce students to the nature of operational research and its techniques.
• To study linear programming, its applications and associated algorithms.

The aims of this module are:

• 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 is a 10 credit module from the University-wide language programme.

The aims of this module are to develop oral and written communication skills through writing and presenting an individual report, and for students to have the opportunity to learn unfamiliar topics in mathematics largely independently.

The aims of this module are to introduce students to more advanced complex variable methods and demonstrate how these can be applied to sum series, evaluate integrals and define special functions.

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:

• introduce students to the geometry of elliptic curves
• illustrate the difference between complex geometry and Diophantine geometry over the rational numbers

The aim of this module is to explore fundamental algebraic structures and their connection to solving equations.

The aims of this module are:

• To introduce rigorous mathematical tools which are useful in economics analysis.
• To give students a solid mathematical background in game theoretic models.

The aims of this module are:

• that students gain familiarity with linear ODEs with non-constant coefficients
• to introduce linear PDEs with constant and non-constant coefficients

The aims of this module are:

• To introduce some mathematical models of biological systems and various techniques for analysing them.
• To enable students to appreciate how mathematics can be used to model biological systems.

The aims of this module are to reinforce students' skills in interpreting statistical tests and using statistical software, and to introduce the methods and theory for the design and analysis of medical trials.

The aims of this module are to:

• introduce the group representations as symmetries of vector spaces
• examine the special characteristics of the category of representations
• help students appreciate and use the connections between different areas of mathematics

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 aims of the module are:

• To develop a range of skills within students and provide an early introduction to teaching for those interested in pursuing it, or a related field, as a career.
• To develop confidence and competence in communicating their subject.
• To provide opportunities to devise and develop science and mathematics projects and teaching methods appropriate to the age and ability of those the student is working with.

The aim of this module is to investigate physical phenomena that involve vibrations and waves using appropriate mathematical tools.

This is a 10 credit module from the University-wide language programme.