This module extends analytical and algebraic techniques to functions of complex variables, and their applications. You will develop powerful tools for studying functions via their zeroes and poles, including the powerful Residue Theorem for calculating real integrals.

How do you apply an algorithm or numerical method to a problem? What are the advantages? And the limitations? Understand the theory and application of nonlinear programming. Learn the principles of good modelling and know how to design algorithms and numerical methods. Critically assess issues regarding computational algorithms.

In this module you will learn techniques underpinning algorithms for studying integer-valued systems, and apply these algorithms to solve integer and mixed integer problems with cutting-plane algorithms.

The subject of Ordinary Differential Equations (ODEs) is a very important and fascinating branch of mathematics. These equations describe many phenomena, for instance in physics, biology, engineering, chemistry, finance and neuroscience and elsewhere. This module will introduce you to advanced topics in ODEs and dynamical systems.

Can you calculate confidence intervals for parameters and prediction intervals for future observations? Represent a linear model in matrix form? Or adapt a model to fit growth curves? Learn to apply linear models to analyse data. Discuss underlying assumptions and standard approaches. Understand methods to design and analyse experiments.

This module will enable you to expand your knowledge on multiple statistical methods. You will learn the concepts of decision theory and how to apply them, have the chance to explore Monte Carlo simulation, and develop an understanding of Bayesian inference, and the basic concepts of a generalised linear model.

Why are arbitrage arguments important in modern finance? How can a binomial model evaluate derivatives? What are the main models for interest rates? Understand the mathematical techniques underlying the modelling of derivative pricing. Acquire skills in the development of pricing and risk management. Explore stochastic methods and credit risk.

In this module, you will study three application areas of statistics - multivariate methods, demography and epidemiology, and sampling, and how to apply and assess these methods in a variety of situations.

This module will cover partial differential equations (PDEs), which can describe a wide array of physical processes and phenomena. You will learn the properties of first and second order PDEs, the concepts behind them and the methods for solving such equations.