Computational Mathematics with Modelling MSc

About the Course

This course provides a thorough grounding in modern numerical analysis, keeping in mind a balance between the theoretical and the practical.

Aims

The practical aspects of the subject are emphasised by providing intensive instruction in those areas of numerical analysis useful in industry and of which the academic staff, through their applied research and consultative activities, have specialist knowledge.

The course differs from those at other universities in that it covers a wider spectrum of numerical methods. The computational aspects of these methods are emphasised by the introduction of more laboratory work into the course. The modelling addresses diverse topics from science, engineering and finance.

Enquiries

Further Information

If you have any questions, or require further information, please contact:

The Postgraduate Admissions Secretary
Department of Mathematical Sciences 
Brunel University

Email mscmaths@brunel.ac.uk
Tel +44 (0)1895 265392
Web www.brunel.ac.uk/siscm/mathematical-sciences

Course Director: Dr Matthias Winter

Course Content

Modules (all core)

Computational Methods
Main topics of study include: LaTeX2e: the notion of a mark-up language, document style and structure, mathematical typesetting, cross-referencing; MATLAB programming: data types and structures, arithmetic operations, functions, input and output, interface programming, graphics; implementation of numerical methods such as: Galerkin method, 2d-diffusion, 2d-heat equation, 2d-obstacle, American and European options, penalty methods, boundary element Galerkin method for integral equations of the first kind; uniform meshes, structured meshes, error estimators, adaptive versions, preconditioners.

Numerical and Variational Methods for PDEs
Main topics of study include: calculus of variations; finite element methods for elliptic problems; an abstract overview of the finite element procedure including Galerkin orthogonality and best approximation in the energy norm; error analysis for the finite element method; numerical methods for time-dependent problems; advanced techniques of the finite element method.

Stochastic Models and Mathematical Finance
Main topics of study include: stochastic processes; random walk; Markov chains; Poisson process and its relatives; economic and probability background; mathematical finance in discrete time; Brownian motion; mathematical finance in continuous time.

Methods of Mathematical Modelling
Main topics of study include: principles of modelling; methods of analysing models; examples of models; boundary integral methods; integral equations.

Dissertation
The dissertation has a long-established tradition in Numerical Analysis research and the specialist interests of staff are often reflected in the dissertation topics undertaken. However our students are also permitted to suggest their own dissertation topics. Examples from recent years include:

• Fluid sloshing in an axisymmetric container
• Heat loss from buildings
• Contrived chaos in the numerical solution of dynamical systems

Assessment

Assessment is by a combination of coursework and examination. Examinations are held in May. The dissertation is of a practical nature and related to the focus of the course. Each student working on their dissertation will have a university supervisor and, in some cases, an industrial supervisor as well.

A Master's degree is awarded if you reach the necessary standard on the taught part of the course and submit a dissertation of the required standard. If you do not achieve the standard required, you may be awarded a Postgraduate Diploma.

Careers

This programme can lead to a wide range of careers. Previous graduates of this programme have obtained employment as:

• researchers in mathematical, physical and engineering sciences at universities and in companies;
• quantitative financial analysts;
• IT specialists.

Fees for 2012/13 entry

Home/EU students: £6,440 full-time

International students: £12,650 full-time

Read about funding opportunities available to postgraduate students

Fees quoted are per annum and are subject to an annual increase.

Entry Requirements for 2012 Entry

English Language Requirements

Brunel also offers our own BrunELT English Test and accept a range of other language courses. We also have a range of Pre-sessional English language courses, for students who do not meet these requirements, or who wish to improve their English.