Mathematical Sciences Integrated PhD

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. 

You will benefit from this integrated PhD programme immensely if you want to:  

• receive a more much guided and hands-on supervision of your learning and research process, especially if you come from more traditional teaching cultures
• increase your chances for timely completion of your PhD programme in comparison to students taking traditional route PhD, cutting down the expenses associated with prolonged study
• access to tailored, highly specialist research training not available as part of the support provided to traditional route PhD students
• maximise your chances for a successful research analysis by applying practical assignments and training which are part of the integrated PhD directly to the research you do for your thesis     
• receive an official Postgraduate Diploma in Research in addition to your PhD award to certify the completion of skills training which may be required by employers in some countries if you wish to pursue an academic career 

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. Mikhailov, M. 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. Langdon, M. Maischak, S. Shaw, M. Warby, J. 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. Langdon, M. Maischak, S. 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. Date, J.W. Lim)
• Applications of machine learning in financial models. (P. Date, E. Boguslavskaya)
• Optimisation problems in power system transmission networks (P. Date, C. Lucas)
• Modelling paradigms and stochastic optimisation applied to (financial) decision making under uncertainty and risk (P. Date, D. Roman, C. Lucas)
• Meta heuristics for solving large combinatorial problems. (C. Lucas)
• Preventative maintenance modelling in the face of uncertainty (P. Date, C. Lucas)
• Stochastic optimal control, with applications in finance (D. Roman, C. Lucas)
• Efficient simulation of Levy processes (E. Boguslavskaya, J.W. Lim)

Mathematical Physics and Applied Mathematics:

• Random matrix theory and its applications (D. Savin, I. Smolyarenko)
• Resonances and transport in open wave chaotic systems (D. Savin)
• Quantum information and quantum computing (S. Virmani)
• Algebraic geometry, birational geometry (A.-S. Kaloghiros)
• Complex networks (G. Rodgers, I. Smolyarenko)
• Statistical mechanics of complex systems and econophysics (G. Rodgers)
• Waves in solids and fluids (M. Greenhow, J. Lawrie, E. Nolde)
• Structural acoustics and diffraction theory (M. Greenhow, J. Lawrie)
• Asymptotic theory of thin elastic structures (E. Nolde , A. Pichugin)
• Layout optimization of structures (A. Pichugin)

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. Chakrabarty, K. Yu)
• Random Geometric Graphs & Networks (D. Chakrabarty, B. 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. Yu, B. Parker)
• Nonparametric smoothing (K. Yu)
• Advanced regression analysis of carbon emissions (K. Yu)
• Applications of Statistics in Health Science, Biology and Genomics (K. Yu)

The Brunel Integrated PhD combines PhD research with a programme of structured research, professional and subject training. The programme typically takes 4 years (compared to 3 years for a non-integrated PhD programme). On successful completion, you will be awarded a PhD with an Integrated Postgraduate Diploma in Research in your chosen subject specialisation.

The programme involves demonstrating through original research or other advanced scholarship the creation and interpretation of new knowledge, a systematic acquisition and understanding of a substantial body of knowledge at the forefront of an academic discipline or professional practice, the ability to conceptualise, design and implement a project for the general of new knowledge, applications or understanding at the forefront of the discipline.

The programme of taught modules runs in parallel to your research work during the first three years of study, with the fourth year providing time for you to focus on writing up your PhD thesis. The taught modules cover research and professional skills as well as providing discipline-specific content. The Brunel Integrated PhD aims to support an individual’s development as a research professional. It aims to produce researchers who are well prepared to embark on careers as academics or professional researchers. As well as the skills to conduct and disseminate high-quality academic research, researchers will develop a range of broader (‘transferable’) skills to help ensure that their work has an impact in the wider world.

Find out more here. 

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

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

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