Mathematical Sciences MPhil, PhD

Mathematical Sciences
Entry requirements:
2:1 +
3 years (PhD), 2 years (MPhil)
6 years (PhD), 4 years (MPhil)
Start date:
January, April, July, October 2018
UK/EU fees:
International fees:



of research classed as 'internationally recognised'

REF 2014


in the UK for Mathematics

The Complete University Guide 2018


Our Mathematical Sciences department is committed to driving forward innovation across the teaching and research of both pure and applied mathematics.

The Department of Mathematical Sciences attracts staff and students from all over the world, making it a diverse and stimulating environment in which to study. Active in high quality research across the broad spectrum of mathematics, the Department has an international reputation, with four fifths of research rated internationally-leading (or better) in REF 2014.

Our Department undertakes research in both pure and applied mathematics and is located in the newly-refurbished Schofield Building. The department consists of around 35 members of staff and 50 PhD students from all over the world.

The Department’s work is complemented and underpinned by senior visiting academics, research associates and a large support team.

Our programmes reflect our strengths, and in some cases represent established collaborative training ventures with industrial partners. Our graduates go on to work with companies such as BAE Systems, Citigroup, Experian, GE Aviation, Mercedes Benz, Nuclear Labs USA and PwC.

The Department of Mathematical Sciences is the proud holder of the Athena SWAN silver award in recognition of its commitment to gender equality and its work to advance the representation of women in science, technology, engineering, mathematics and medicine (STEMM) subjects.

It is also part of the London Mathematical Society’s Good Practice Scheme, which supports mathematics departments interested in embedding equal opportunities for women within their working practices.

Applicants should have a 1st class or good 2:1 degree in mathematics or a related discipline.

IELTS: overall 6.5 with minimum 6.0 in each component.

Our facilities

Our Department undertakes research in both pure and applied mathematics and is located in the newly-refurbished Schofield Building. You will have access to spacious study areas, with the latest audio-visual equipment to support teaching and research.

Research areas

This group studies a wide range of aspects of dynamical systems theory, such as Hamiltonian and dissipative dynamics, dynamical chaos in classical and quantum systems, dynamics of multi-scale systems, ergodic theory, random matrix theory, and bifurcation theory.

Applications include problems of celestial mechanics, plasma physics, semi-classical methods, atomic physics, and the dynamics of chemical reactions.

The theory of integrable systems studies differential equations which are, in a sense, exactly solvable and possess regular behaviour. Such systems play a fundamental role in mathematical physics providing an approximation to various models of applied interest.

Dating back to Newton, Euler and Jacobi, the theory of integrable systems now plays a unifying role in mathematics bringing together algebra, geometry and analysis. The research of the group includes both classical and quantum integrable systems in relation to representation theory and special functions, as well as algebraic, differential and symplectic geometry.

Global analysis and the theory of partial differential equations (PDEs) are classical fields of mathematics that have a wide range of applications, for instance in number theory, group theory, geometry and topology. They also have important applications outside of mathematics in physics, engineering and chemistry.

The Global Analysis and PDEs Research Group is rooted in pure mathematics and focuses on geometric and topological aspects of analysis. The interests of the group include spectral and scattering theory on manifolds, regularity and existence of global solutions to pseudo-differential equations and boundary value problems, topological questions related to generalisations of the Atiyah-Singer index theorem, applications of theory of PDE to approximation theory, as well as other topics.

The group’s interests are in wave motion in a variety of physical situations including geophysical fluid dynamics, water waves, solid mechanics, Bose-Einstein condensates, electromagnetism and acoustics. The group develop and apply exact, numerical, asymptotic and perturbation techniques to pursue research on linear and nonlinear waves with a focus on solitary waves and soliton theory, stochastic wave systems, wave generation, and diffraction and scattering by obstacles.

Members of the group apply a variety of techniques from applied mathematics to diverse problems in medicine, biology, fluid dynamics, materials and soft matter science. The biological systems studied range from intracellular processes to those at the scale of organisms and populations. The fluid flows studied range from environmental buoyancy-driven flows to technologically important micro- and nano-fluidic flows.

The modelling of materials involves the use of mathematical and computational techniques to solve a wide and varied class of problems. This includes nanoscale devices where the fate of individual atoms is important. It spans length scales and time scale that vary over many orders of magnitude and involves the solution of equations that range from continuum to quantum mechanical descriptions.

Stochastic analysis is currently a very active and important basic research area in mathematics. Rooted in probability and measure theory and beginning with the fundamental work of Wiener, Kolmogorov, Levy and Ito, stochastic analysis has intrinsic and deep connections and many applications in analysis and partial differential equations, geometry, dynamical systems, physics, geophysics, engineering, biology etc. in which many problems are modelled by stochastic differential equations or stochastic partial differential equations.

Stochastic analysis has become the basic mathematics for mathematical finance thanks to the pioneering idea of Black, Scholes and Merton. It has been a main research area in probability theory in recent years and the trend is still increasing. In our group, the research topics include: stochastic analysis, in particular interactions with analysis; stochastic methods in (nonlinear) partial differential equations and mathematical physics; stochastic dynamical systems; stochastic differential equations; stochastic partial differential equations; infinite-dimensional analysis; stochastic analysis on geometric spaces; Markov processes and Dirichlet forms; quantum stochastic analysis; rough path; Schramm Loewner evolution; and mathematics of finance.

Your personal and professional development

Support from your supervisor

You will have at least two academic supervisors who will guide you in your research. You’ll also be provided with a desk, computer, photocopying facilities and can apply for funds for conference attendance.

Skills and experience

A PhD programme will give you the opportunity to develop new and highly sought after skills which can set you up for a range of careers. It’s a chance to make a novel contribution to knowledge, to become a world expert in a particular field, and it can open a range of doors with different employers. You'll also enhance your interpersonal skills, such as networking and relationship building, which will be invaluable in your future career.

In addition to the University’s extensive training provision, you’ll also enjoy a dynamic research atmosphere with regular workshops, international visitors and a wide range of research seminars to which you’ll be invited to make presentations.

Fees and funding


Tuition fees cover the cost of your teaching, assessment and operating University facilities such as the library, IT equipment and other support services. University fees and charges can be paid in advance and there are several methods of payment, including online payments and payment by instalment. Special arrangements are made for payments by part-time students.

Who you'll be working with

How to apply

If you can't find a suitable PhD opportunity that fits your interests and experience from our funded (studentships) and unfunded opportunities, you can submit a research proposal to the Department of Mathematical Sciences in the hope of finding a supervisor who will work with you on your dream project.

If you wish to apply for a PhD through this method, you do not need to submit a detailed research proposal with your application, but you should indicate which area of research you wish to pursue and/or names of staff members you are interested in working with.