Mathematical Sciences

Qualification(s) available: PhD

Entry requirements
3 years
6 years
Start date
1 January, 1 April, 1 July or 1 October
UK fee
To be confirmed
International fee


Our Mathematical Sciences department is committed to driving forward innovation in both pure and applied mathematics.

We attract staff and students from all over the world, making our department a diverse and stimulating environment in which to study. Active in high-quality research across the broad spectrum of mathematics, we have an excellent international reputation.

Our key research themes include analysis, dynamical systems, geometry and mathematical physics, linear and nonlinear waves, mathematical modelling, statistics, and stochastic analysis. We also host regular seminar series and colloquia, as well as international conferences and workshops.

As part of the School of Science, our Mathematical Sciences staff and PhD students contribute to our interdisciplinary research centres:

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Why you should choose us

Where you'll study

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

Our research

Research undertaken in the Department of Mathematical Sciences spans a wide range of key themes within science and technology. Our cutting-edge research uncovers both impactful and exciting outcomes that apply to many aspects of the modern world.

The mathematical sciences often form an 'unseen' part of our everyday lives, yet they underpin many aspects of the modern world. Mathematics is a key driver in advancing many areas within science and technology, making continued research in mathematics both impactful and exciting.

The researchers in our department collaborate with mathematicians, scientists and industry partners from around the globe to deliver top quality research. Our strengths were reflected in the latest Research Excellence Framework (REF) results (2014) where 87% of research was assessed as 'internationally recognised' or 'internationally excellent' and a further 10% was rated 'world leading'.

Analysis and PDEs

The research interests of the group include analysis of partial differential equations (PDEs), including hyperbolic equations and systems with multiplicities, microlocal, spectral and harmonic analysis, eigenvalue estimates for Dirac and Schrödinger type operators, inverse spectral transform method for integrable PDEs, applications to approximation theory, as well as other topics.

Dynamical Systems

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.

Geometry and Mathematical Physics

The research of the group covers a broad range of topics in geometry and related areas of mathematical physics, including the theory of both classical and quantum integrable systems. Another research focus is algebraic geometry, in particular, birational geometry and mirror symmetry.

Linear and Nonlinear Waves

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.

Mathematical Modelling

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 scales that vary over many orders of magnitude and involves the solution of equations that range from continuum to quantum mechanical descriptions.

You can find further details here.

Stochastic Analysis

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. Furthermore, it has 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
  • mathematics of finance.


The Statistics group is involved in methodological research in contemporary issues in mathematical and computational statistics, as well as in making diverse applications to the natural, biological and social sciences, including engineering, medical imaging, astrophysics, materials science, ecology, testing theory, etc.

Your development

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.

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.

Our extensive training provision, supported by the Doctoral College, will also enhance your skills and experience as a researcher. You will 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.

Your future career

Graduates from the Department of Mathematical Sciences have gone on to pursue further research opportunities or academic careers. Others have taken up rewarding positions in diverse fields such as finance, software engineering, and data analysis.

Entry requirements

Our entry requirements are listed using standard UK undergraduate degree classifications i.e. first-class honours, upper second-class honours and lower second-class honours. To learn the equivalent for your country, please choose it from the dropdown below.

Entry requirements for United Kingdom

A minimum of a high 2:1 honours degree (or equivalent international qualification) in mathematics.

English language requirements

Applicants must meet the minimum English language requirements. Further details are available on the International website.

Fees and funding

UK fee

Full-time degree per annum
To be confirmed

International fee

Full-time degree per annum

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. Fees are reviewed annually and are likely to increase to take into account inflationary pressures.

Find out more about research degree funding

How to apply

If you can't find an advertised project that fits your interests and experience, you can submit a research proposal to the Department of Mathematical Sciences to find a supervisor who will work with you on your project. You can view our list of academic staff on our website or you can email us for guidance.

Your research proposal should include the aims of your study, a brief literature review, an outline of the proposed research methods, and your preferred member of staff to supervise the project. Further information on preparing your proposal can be found here.

You are strongly recommended to contact us before applying to discuss your topic, availability and funding.

Apply now