Applied Mathematics (1 year) [MSc]

Manchester has been at the forefront of applied mathematics for over a century, and has acted as home to leading mathematicians including Lamb, Lighthill, Richardson, Goldstein and Turing.

Today, our Applied Mathematics research group 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 units and the writing of a research dissertation. The latter can be carried out with an industrial sponsor.

Within this course, students can take either the general MSc in Applied Mathematics or choose the specific Industrial Modelling pathway or the Numerical Analysis pathway.


Funding Opportunities and Prizes

Information about fees for this programme can be found here. There are a variety of funding opportunities including a number of industrially sponsored dissertations (worth up to £3000) and loyalty bursaries for University of Manchester students (worth £2000) together with an additional 10% reduction for University of Manchester students with a first class degree, and the UK government's postgraduate loan scheme. Contact the admissions team for further details of these opportunities.

In addition, annually we award the Thales prize in applied mathematics (worth £750) to the student achieving the best performance in the physical applied mathematics modules.


Industrial Modelling pathway

This pathway forms an important part of our industrial engagement and significant interaction with industrial partners takes place during the course, including industrial sponsorship and invited lectures from industrial partners.

Industrial Mathematics (any aspect of mathematics that can influence the way industry approaches or solves problems) is having an increasing importance within a variety of industrial sectors. This is reflected by the enhanced funding from industry for this course. Typical examples of industrial modelling problems are modifications to the way that fluid is pumped through a pipe, the design of algorithms for data encryption, modelling new types of materials used for sound reduction, understanding the instability between fluids of different viscosities, and determining how soft tissue deforms under applied forces.

Full list of course units (current academic year)

Numerical Analysis pathway

Numerical Analysis — the study of algorithms for the problems of continuous mathematics — has been an area of strength since the first stored-program electronic digital computer, the Baby, was born at the University of Manchester in 1948, and we have run an MSc course in numerical analysis continuously since 1959.

The MSc in Applied Mathematics with Numerical Analysis develops essential skills for analysing, designing and implementing mathematical algorithms for leading edge scientific computing.

It covers the whole spectrum from fundamental theory through to software development. It is ideal preparation for PhD studies in Manchester's postgraduate community and opens up a wide range of career opportunities.

Full list of course units (current academic year)

Course structure

The below constitutes eight taught modules, which is worth a total of 120 credits over semesters one and two. From June until September, students work on a dissertation worth 60 credits, usually choosing a topic from the plethora of possible titles available with our research staff, including all the industrial projects offered by our partners in industry.

Full list of current course units (current academic year).

Expected Background

Formal entry requirements are listed here 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 below, 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 us.

A good background in basic vector calculus and ordinary differential equations is essential; see for example the two courses Calculus and Vectors A and Calculus and Applications A. 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 highly desirable; see for instance the content of Partial differential equations and vector calculus. Knowledge of solving partial differential equations numerically is desirable but not essential as this is taught on the course.

Knowledge of basic linear algebra is essential. For example we would expect incoming students to have taken a basic linear algebra course such as Linear Algebra A. Higher level training in numerical linear algebra such as Numerical Analysis 1 is useful but is not essential. 

The modules in Uncertainty Quantification require no previous experience in probability or statistics, though Jochen Voss’s textbook “An Introduction to Statistical Computing” (Wiley) would be useful background reading.

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.

Although there is no formal requirement for previous programming experience, a familiarity with writing computer programs (for example, in Python, MATLAB, C/C++ or Java) is highly desirable. Working through self-study websites such as or is useful practice.

A basic 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.

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, Viscous Flow, Waves and Modelling reactive flow would be good as background but are not essential prerequisites.


Contact us:

Tel: +44(0)161 275 5826



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