You will choose from a range of advanced optional modules. You'll also have the option to choose modules from outside of maths if you wish.
Applied Statistical Modelling
In this module you will build on your theoretical knowledge of statistical inference by a practical implementation of the generalised linear model. You will move on to enhance your understanding of statistical methodology including the analysis of discrete and survival data. You will also be trained in the use of a high-level statistical computer program.
Coding and Cryptography
This course provides an introduction to coding theory in particular to error-correcting codes and their uses and applications. It also provides an introduction to to cryptography, including classical mono- and polyalphabetic ciphers as well as modern public key cryptography and digital signatures, their uses and applications.
Data Analysis and Modelling
This module involves the application of probability and statistics to a variety of practical, open-ended problems, typical of those that statisticians encounter in industry and commerce. Specific projects are tackled through workshops and student-led group activities.
The real-life nature of the problems requires students to develop skills in model development and refinement, report writing and teamwork. Students will have an opportunity to apply a variety of statistical methods and knowledge learned in previous modules.
In this module the concepts of discrete time Markov chains are explored and used to provide an introduction to probabilistic and stochastic modelling for investment strategies, and for the pricing of financial derivatives in risky markets. You will gain well-rounded knowledge of contemporary issues which are of importance in research and applications.
This module is concerned with the analysis of multivariate data, in which the response is a vector of random variables rather than a single random variable. A theme running through the module is that of dimension reduction. Key topics to be covered include: principal components analysis, whose purpose is to identify the main modes of variation in a multivariate dataset; modelling and inference for multivariate data, including multivariate regression data, based on the multivariate normal distribution; classification of observation vectors into sub-populations using a training sample; canonical correlation analysis, whose purpose is to identify dependencies between two or more sets of random variables. Further topics to be covered include factor analysis, methods of clustering and multidimensional scaling.
In this module a variety of techniques and areas of mathematical optimisation will be covered including Lagrangian methods for optimisation, simplex algorithm linear programming and dynamic programming. You’ll develop techniques for application which can be used outside the mathematical arena.
Scientific Computation and Numerical Analysis
You will learn how to use numerical techniques for determining the approximate solution of ordinary and partial differential equations where a solution cannot be found through analytical methods alone. You will also cover topics in numerical linear algebra, discovering how to solve very large systems of equations and find their eigenvalues and eigenvectors using a computer.
This course is concerned with the two main theories of statistical inference, namely classical (frequentist) inference and Bayesian inference.
Topics such as sufficiency, estimating equations, likelihood ratio tests and best-unbiased estimators are explored in detail. There is special emphasis on the exponential family of distributions, which includes many standard distributions such as the normal, Poisson, binomial and gamma.
In Bayesian inference, there are three basic ingredients: a prior distribution, a likelihood and a posterior distribution, which are linked by Bayes' theorem. Inference is based on the posterior distribution, and topics including conjugacy, vague prior knowledge, marginal and predictive inference, decision theory, normal inverse gamma inference, and categorical data are pursued.
Common concepts, such as likelihood and sufficiency, are used to link and contrast the two approaches to inference. You will gain experience of the theory and concepts underlying much contemporary research in statistical inference and methodology.
In this module you will develop your knowledge of discrete-time Markov chains by applying them to a range of stochastic models. You will be introduced to Poisson and birth-and-death processes and then you will move onto more extensive studies of epidemic models and queuing models with introductions to component and system reliability.
Time Series Analysis
This module will provide a general introduction to the analysis of data that arise sequentially in time. Several commonly-occurring models will be discussed and their properties derived, along with methods for model identification for real-time series data. You will develop techniques for estimating the parameters of a model, assessing its fit and forecasting future values. You will also gain experience of using a statistical package and interpreting its output.
The above is a sample of the typical modules we offer but is not intended to be construed and/or relied upon as a definitive list of the modules that will be available in any given year. Modules (including methods of assessment) may change or be updated, or modules may be cancelled, over the duration of the course due to a number of reasons such as curriculum developments or staffing changes. Please refer to the module catalogue
for information on available modules. This content was last updated on