Programme Director and Admissions Officer

Dr. Will Parnell          William.Parnell [at] manchester.ac.uk     +44(0)161 27 55908

Funding is Available for 2013/14

We have numerous industrial bursaries to support students, of up to £3000 . This will also allow the student to work on a project of interest to the industrial sponsor. See below for further details regarding sponsors. DEADLINE FOR INDUSTRIAL SPONSORSHIP IS 30th JUNE 2013: To apply for this funding, please indicate so by uploading a short statement with your application as to why you would like to carry out a research dissertation with an industrial partner.

Programme Overview

Manchester has been at the forefront of applied mathematics for over a century and has acted as home to the leading mathematicians Lamb, Lighthill, Richardson, Goldstein and Turing. Today the Applied Mathematics group at the University of Manchester has diverse expertise, carrying out research in the areas of Combustion theory, Experimental research Fluid dynamics Granular Materials Inverse Problems Numerical Analysis Scientific Computing, Solid mechanics, Stochastic Differential Equations and Waves.

All of these areas are of extreme importance in understanding and modelling the world around us as well as being of scientific interest in their own right.

This MSc develops the core mathematical skills required to carry out research in these areas and allows students to specialise through choice of taught modules and the writing of a research dissertation. The latter can be carried out with an industrial sponsor.

Over the last five years the School of Mathematics has engaged with industry very successfully, and has recently appointed a Lecturer in Industrial Mathematics. This MSc forms an important part of this industrial engagement and significant interaction with industrial partners takes place during the course, including industrial sponsorship and invited lectures from industrial partners.

Within the MSc, students can take either the general MSc in Applied Mathematics with a choice from several optional courses (see below) or alternatively choose to go down the specific Industrial Modelling pathway or the Numerical Analysis pathway.

Goals of the Programme

The goal of the MSc programme is to give excellent training in a range of topics in Applied Mathematics with a specific aim being to encourage a mature approach to solving applied mathematical problems that arise in the real world. Students will develop a suite of mathematical techniques as well as learning a variety of computational skills including programming in matlab and C++.

An important goal of the MSc is to give students the important skills for their future career, both technical and personal. This includes the development of important communication and presentation skills, both written and verbal. Much of this is done via sessions involving mathematical modelling of real-world problems.

Upon successful completion of the MSc, students will be well placed to go forward onto a PhD programme or move directly into employment in industry. The latter will be enhanced by the direct and continuous interaction of the programme with our industrial partners (see details below).

Course Structure

Students will study the following core modules

• Applied Dynamical Systems
• Mathematical Methods
• PDEs: Theory and practice
• Scientific Computing
• Transferable skills

Students will study three of the following optional modules

• Continuum Mechanics
• Numerical Linear Algebra
• Transport phenomena and conservation laws
• Stability theory
• Approximation theory and finite element analysis
• Numerical optimization and inverse problems

This constitutes eight taught modules, which is worth a total of 120 credits. From June until September, students work on a dissertation worth 60 credits. Students usually choose a topic from the plethora of possible titles available with our research staff. This will of course include all of the industrial projects offered by our partners in industry. Dissertations will be supervised by a member of staff in the Applied Mathematics group and if sponsored by industry, students will also have a contact from within the industrial collaborator. A list of recent dissertations is available online.

Our current industrial sponsors and collaborators include (but are not limited to)

• ARUP
• DSTL
• Mathworks
• Nikon Metrology
• Numerical Algorithms Group
• Thales Underwater Systems
• United Utilities
• Xradia

Expected Background - Informal Self Assessment

Formal entry requirements are listed below but since applicants come from many different backgrounds, it will be useful to consider yourself whether you feel as if you have the right background for the course. Some general expectations are listed here, with references to existing courses on that material in Manchester. It should hopefully give you a feel for the course and what is expected of the incoming student. We would only consider a few of these courses as absolutely essential, but some additional background is desirable and will certainly assist you greatly for course preparation. If in doubt then please contact the Programme Director.

A good background in basic vector calculus and ordinary differential equations, see e.g. the two courses Calculus and Vectors A and Calculus and Applications A is essential. Note that this second course has introductory mechanics elements within it and although not absolutely essential, students without this training may find aspects of the MSc course difficult, especially if you wish to go down the industrial modelling route.

As with most Applied Mathematics MSc programmes, a higher level in vector calculus and applied mathematical methods is very helpful, see e.g. the content of this course: Partial differential equations and vector calculus. Knowledge of solving partial differential equations numerically is not essential as this is taught on the course.

Some training in basic linear algebra will be useful. For example we would expect most incoming students to have taken a basic linear algebra course such as this one: Linear Algebra A. Higher level training in numerical linear algebra such as this course: Numerical Analysis 1 is useful but is not essential.

Some knowledge of real and complex analysis is helpful, see e.g. Real and Complex Analysis. Higher level complex analysis courses such as Applied Complex Analysis are not essential but are useful, especially as background material for the Methods and PDEs units on the MSc. Some further knowledge of mathematical methods such as courses in Asymptotic expansions and perturbation methods and PDEs would also be helpful but not absolutely essential.

No programming experience is required, although some initial training into how to structure a simple computer code in either matlab, mathematica, maple, fortran, C or C++ would be useful.

If you wish to go down the numerical analysis route, any additional courses that you have taken in this area would be useful, for example the material in Matrix analysis and Numerical analysis 2 is helpful, but not essential.

If you wish to go down the industrial modelling route, any additional courses that you have taken in continuum mechanics style courses such as Fluid Mechanics, Elasticity and Viscous Flow, Waves and Modelling reactive flow would be good as background but are not essential prerequisites.

Formal Entry Requirements

The entry requirement to the programmes is normally a good honours degree (usually 2.1 or above) in mathematics or a mathematically-related discipline such as physics or engineering or an equivalent overseas qualification in a mathematical subject. Students whose first language is not English require a minimum score of IELTS 6.5 with 6.0 in writing and 5.5 in each other component.

Funding and Fees for 2013/14

We have numerous industrial bursaries to support students, of up to £3000. This will also allow the student to work on a project of interest to the industrial sponsor. DEADLINE FOR INDUSTRIAL SPONSORSHIP IS 30th JUNE 2013: To apply for this funding, please indicate so by uploading a short statement with your application as to why you would like to carry out a research dissertation with an industrial partner.

Latest News: There will be up to 10 scholarships spread across the five MSc programmes worth £1500 each for the top students in the 2013/14 academic year.

In addition, all graduates from the University of Manchester will receive loyalty bursaries of £1,000 each. There will be a further 10% fee discount for University of Manchester graduates with a 1st Class Honours Degree. These apply to all MSc programmes.

The NAG Prize in Numerical Analysis (value £750) is awarded to the student achieving the best performance in the numerical analysis modules.

For entry in the academic year beginning September 2013, the tuition fees are as follows:

MSc (full-time)
UK/EU students (per annum): £7,200
International students (per annum): £13,000
MSc (part-time)
UK/EU students (per annum): £3,600
International students (per annum): £6,500

To Apply

If you would like to apply, please see: http://www.manchester.ac.uk/postgraduate/howtoapply/