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Find out about the research we do in Mathematics

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Mathematics PhD

Start date




Mode of study

3 years full-time

6 years part-time



International £18,410

UK £4,596

MPhil option available
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Research profile

Our research-active academics are involved in cutting-edge research covering a range of topics including applied analysis, computational mathematics, continuum mechanics and mathematical physics, financial mathematics, operational research and applied statistics. We address problems of real biological or engineering importance and investigate the underlying mathematical and phenomenological processes. There is a strong emphasis on the development of innovative analytic, asymptotic, computational and hybrid methods. Our research also focuses on random matrix theory, quantum information theory, mathematical foundations of quantum mechanics, mesoscopic disordered systems, statistical mechanics, graph theory, matroid theory, and infinite-dimensional Riemannian geometry, algebraic geometry and orthogonal polynomials. 

Find out about the exciting research we do in this area. Browse profiles of our experts, discover the research groups and their inspirational research activities you too could be part of. We’ve also made available extensive reading materials published by our academics and PhD students.  

Learn more about research in this area.

You can explore our campus and facilities for yourself by taking our virtual tour.

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Find a supervisor

Our researchers create knowledge and advance understanding, and equip versatile doctoral researchers with the confidence to apply what they have learnt for the benefit of society. Find out more about working with the Supervisory Team.

You are welcome to approach your potential supervisor directly to discuss your research interests. Search for expert supervisors for your chosen field of research.

View supervisors by research area

Applied and Numerical Analysis:

  • Analysis of partial differential equations, including nonlinear PDEs of fluid mechanics and mathematical biology (S. MikhailovM. Winter)
  • Analysis and numerical implementation of boundary-domain integral and integro-differential equations (S. Mikhailov)
  • Computational modelling of problems in solid mechanics, as well as acoustic, elastic and electromagnetic wave propagation, by Finite Element and Boundary Element methods (S. LangdonM. MaischakS. ShawM. WarbyJ. Whiteman)
  • Approximation of orthogonal polynomials and special functions (I. Krasikov)
  • Abstract bifurcation and singularity theory (J. Furter)
  • Fast solvers and preconditioners, error estimators and adaptive algorithms, high performance and scientific computing, software development (S. LangdonM. MaischakS. Shaw)
  • Theoretical and computational modelling of fatigue, damage, durability, and fracture (S. Mikhailov)

Financial Mathematics and Operational Research:

  • Financial modelling; in particular, forecasting of spreads in commodity futures prices using latent state based models/ MCMC filters (P. DateJ.W. Lim)
  • Applications of machine learning in financial models. (P. DateE. Boguslavskaya)
  • Optimisation problems in power system transmission networks (P. DateC. Lucas)
  • Modelling paradigms and stochastic optimisation applied to (financial) decision making under uncertainty and risk (P. DateD. RomanC. Lucas)
  • Meta heuristics for solving large combinatorial problems. (C. Lucas)
  • Preventative maintenance modelling in the face of uncertainty (P. DateC. Lucas)
  • Stochastic optimal control, with applications in finance (D. RomanC. Lucas)
  • Efficient simulation of Levy processes (E. BoguslavskayaJ.W. Lim)

Mathematical Physics and Applied Mathematics:

Statistics and Data Science:

  • High-dimensional Bayesian Learning (D. Chakrabarty)
  • Learning in the Absence of Training Data (D. Chakrabarty)
  • Applications of Statistics in Astronomy, Materials Science, etc. using MCMC-based inference (D. ChakrabartyC. SpireK. Yu)
  • Random Geometric Graphs & Networks (D. ChakrabartyB. Parker)
  • Design of Experiments for Network Science (B. Parker)
  • Algorithms for Experimental Design (B. Parker)
  • Bayesian regression beyond the mean (K. Yu)
  • Weibull analysis for lifetime data analysis (K. Yu)
  • Quantile regression for big data (K. Yu)
  • Machine learning methods and application (K. YuB. Parker)
  • Nonparametric smoothing (K. Yu)
  • Advanced regression analysis of carbon emissions (K. Yu)
  • Applications of Statistics in Health Science, Biology and Genomics (K. Yu)

PhD topics

While we welcome applications from student with a clear direction for their research, we are providing you with some ideas for your chosen field of research:

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Research journey

This course can be studied 3 years full-time or 6 years part-time, starting in January. Or this course can be studied 3 years full-time or 6 years part-time, starting in October. Or this course can be studied 3 years full-time or 6 years part-time, starting in April.

Find out about what progress might look like at each stage of study here: Research degree progress structure.

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Research support

Research support

Excellent research support and training

The Graduate School provides a range of personal, professional and career development opportunities. This includes workshops, online training, coaching and events, to enable you to enhance your professional profile, refine your skills, and plan your next career steps as part of the Researcher Development Programme. The researcher development programme (RDP) offers workshops and seminars in a range of areas including progression, research management, research dissemination, and careers and personal development. You will also be offered a number of online, self-study courses on BBL, including Research Integrity, Research Skills Toolkit, Research Methods in Literature Review and Principles of Research Methods.

Library services

Brunel's Library is open 24 hours a day, has 400,000 books and 250,000 ebooks, and an annual budget of almost £2m. Subject information Specialists train students in the latest technology, digital literacy, and digital dissemination of scholarly outputs. As well as the physical resources available in the Library, we also provide access to a wealth of electronic resources. These include databases, journals and e-books. Access to these resources has been bought by the Library through subscription and is limited to current staff and students.

Dedicated research support staff provide guidance and training on open access, research data management, copyright and other research integrity issues.

Find out more: Brunel Library

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Careers and your future

You will receive tailored careers support during your PhD and for up to three years after you complete your research at Brunel. We encourage you to actively engage in career planning and managing your personal development right from the start of your research, even (or perhaps especially) if you don't yet have a career path in mind. Our careers provision includes online information and advice, one-to-one consultations and a range of events and workshops. The Professional Development Centre runs a varied programme of careers events throughout the academic year. These include industry insight sessions, recruitment fairs, employer pop-ups and skills workshops.

In addition, where available, you may be able to undertake some paid work as we recognise that teaching and learning support duties represent an important professional and career development opportunity.

Find out more.

Following the completion of the course students may follow several career paths:

  • Career path within academia starting as a Post-doc or Lecturer/Assistant Professor at a university
  • Career progression within research institutions commencing as a Researcher and progressing to Senior Researcher.
  • Career path within the industry as a Research Scientist, Senior Research Scientists, Financial Analyst, etc.
  • Career path in secondary education as Maths teacher, Maths Subject Leader
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UK entry requirements

The general University entrance requirement for registration for a research degree is normally a First or Upper Second Class Honours degree (1st or 2:1). 

An interview will be required as part of the admissions process and will be conducted by at least two academic staff members remotely via MS Teams, Zoom, or face to face.

Applicants will be required to submit a personal statement and a research statement.
Please contact your proposed supervisor, where possible, to receive feedback and guidance on your research statement before submitting it. Learn how to prepare a research statement here.  

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EU and International entry requirements

If you require a Tier 4 visa to study in the UK, you must prove knowledge of the English language so that we can issue you a Certificate of Acceptance for Study (CAS). To do this, you will need an IELTS for UKVI or Trinity SELT test pass gained from a test centre approved by UK Visas and Immigration (UKVI) and on the Secure English Language Testing (SELT) list. This must have been taken and passed within two years from the date the CAS is made.

English language requirements

  • IELTS: 6.5 (min 6 in all areas)
  • Pearson: 59 (59 in all subscores)
  • BrunELT: 63% (min 58% in all areas)
  • TOEFL: 90 (min 20 in all) 

You can find out more about the qualifications we accept on our English Language Requirements page.

Should you wish to take a pre-sessional English course to improve your English prior to starting your degree course, you must sit the test at an approved SELT provider for the same reason. We offer our own BrunELT English test and have pre-sessional English language courses for students who do not meet requirements or who wish to improve their English. You can find out more information on English courses and test options through our Brunel Language Centre.

Please check our Admissions pages for more information on other factors we use to assess applicants. This information is for guidance only and each application is assessed on a case-by-case basis. Entry requirements are subject to review, and may change.

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Fees and funding

2022/23 entry


£18,410 full-time

£9,205 part-time


£4,596 full-time

£2,295 part-time

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

Fees for EU applicants – For entry in 2023/24 academic year, eligible EU applicants will have the same tuition fees as UK students to continue our support during this transition period. These fees will be applied for the duration of the course.  

Some courses incur additional course related costs. You can also check our on-campus accommodation costs for more information on living expenses.

Brunel offers a number of funding options to research students that help cover the cost of their tuition fees, contribute to living expenses or both. Recently the UK Government made available the Doctoral Student Loans of up to £25,000 for UK and EU students and there is some funding available through the Research Councils. Many of our international students benefit from funding provided by their governments or employers. Brunel alumni enjoy tuition fee discounts of 15%.

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