Applied Mathematics PhD

Start date
Contact us for start date.
PhD: 3 years full-time; 6 years part-time
Course Type
Postgraduate, Doctoral research

We charge an annual tuition fee. Fees for 2020/21 are as follows:
£4,407 (UK/EU students)
£17,580 (International Students)
Further fee information is available.

The Applied Mathematics group contributes to research on a wide range of topics in Continuum Mechanics, Mathematical Biology, Nonlinear Systems, Numerical Analysis and Scientific Computing.


Please rest assured that we will make all reasonable efforts to provide you with the courses, services and facilities described. However, it may be necessary to make changes due to significant disruption, for example in response to COVID-19.

Information for future students and applicants

The Applied Mathematics Group is recognised for world leading and internationally excellent research and has active collaborations with researchers from industry, healthcare, and other areas of science and engineering. The group provides opportunities for postgraduate research across many areas of Applied Mathematics. Many PhD projects arise from engineering applications and involve collaborations with academic and industrial partners.

Continuum Mechanics is a traditionally strong research field within the School. Active research is pursued in the areas of bubble dynamics, biological and physiological fluid mechanics, dynamic wetting, flow in porous media, dynamics of liquid jets and drops, flows with phase transitions, fuel cells and many more. This research involves mathematical modelling, mathematical analysis of models and the underlying physical phenomena, as well as development of novel computational tools.

Research activities in Mathematical Biology range from applications in healthcare (antimicrobial resistance, cancer, epilepsy, microsurgical robots and infertility for example) and climate change (response of plants to increasing carbon dioxide levels), through fundamental biology (left-right symmetry-breaking in early embryo development; the role of anisotropy in tissue growth) and ecology (complexity of ecosystems and food webs), to novel mathematical and computational methods (meshfree computations for viscous flow, spitting schemes for stochastic differential equations). This research has close links to a range of stakeholders, in particular, the Centre for Systems Modelling and Quantitative Biomedicine, Institute for Microbiology and Infection, Healthcare Technology Institute, and Birmingham Institute for Forestry Research.

Research in the broad area of Nonlinear Systems combines the development of fundamental mathematical theory and methodology for solving reaction-diffusion systems, inverse problems and dynamical systems with contribution to a wide range of engineering and industrial applications. The application areas include nonlinear waves in river flows, oil pipeline flows, free surface flows and jets, chemical reactions and hydrogen fuel cell models.

Research in Numerical Analysis and Scientific Computing covers a wide range of areas related to the design, analysis and implementation of robust and accurate numerical algorithms for solving mathematical problems coming from real-life applications. The areas of particular focus and expertise include numerical methods for partial differential and boundary integral equations, adaptive algorithms, numerical linear algebra, approximation theory, numerical methods for uncertainty quantification, algorithms for large-scale problems, and research software development.

Researchers and PhD students have access to powerful computing resources and facilities, including the University High Performance Computing cluster BlueBEAR and large-data storage facility (BEAR Research Data Store).

Training of PhD students is provided through individual supervision of research as well as by taking relevant taught modules and attending advanced research seminars and conferences.

Why study Applied Mathematics PhD at Birmingham?

  • The School of Mathematics has a strong research culture, with researchers of international stature in each of its main specialisms.
  • The University of Birmingham is one of the prestigious Russell group research-intensive Universities in the UK. The School of Mathematics attracts gifted graduate students from across the world.
  • The School collaborates widely with multiple disciplines, including Biological and Medical Sciences, Chemical Engineering and within industry.  In particular, Birmingham is an emerging centre for multidisciplinary Biological Systems Science research, and is in a unique position, being adjacent to one of the largest super-hospitals in Europe, catering for a highly diverse population. 
  • Learn from world leaders in their fields.

Coronavirus (COVID-19) latest updates and FAQs for future students and offer-holders

Visit our FAQs


We charge an annual tuition fee. Tuition Fees 2020/21 academic year:

  • £4,407 UK/EU students, full-time
  • £2,190 UK/EU students, part-time
  • £17,580 International students, full-time

Learn more about fees and funding.

Postgraduate Doctoral Loan

A Postgraduate Doctoral Loan can help with course fees and living costs while you study a postgraduate doctoral course, such as a PhD. You will be able to apply for funding for the 2018 to 2019 academic year in summer 2018.

Follow the video link below to find out more
Postgraduate Doctoral Loan

Further information is available at the student finance zone.

Scholarships and studentships

We offer a range of postgraduate scholarships for taught programmes and research opportunities to ensure the very best talent is nurtured and supported at postgraduate level.

Additional scholarships can be found in the funding database.

Contact the department for further information.

We award up to ten home/EU EPSRC doctoral training grants each year to eligible students. In exceptional circumstances fully-funded School doctoral training grants may be awarded. Additional income can often be generated by tutorial and marking work.

For students applying for the 2020/21 academic year

The UK Government has confirmed that EU students will continue to be eligible for 'home fee status' for entry in September 2020, and will continue to have access to financial support available via student loans for the duration of their course. For more information take a look at the website.

How To Apply

When clicking on the Apply Now button you will be directed to an application specifically designed for the programme you wish to apply for where you will create an account with the University application system and submit your application and supporting documents online. Further information regarding how to apply online can be found on the How to apply pages

Apply now

Our Standard Requirements

A 2:1 Honours degree in a Mathematics-related subject, or a lower degree plus an MSc or substantial relevant experience. Learn more about entry requirements


International Requirements

International Students

English language

For students whose first language is not English, one of the following English language qualifications are required:


IELTS 6.0 with no less than 5.5 in any band is equivalent to:

  • TOEFL: 80 overall with no less than 19 in Reading, 19 in Listening, 21 in Speaking and 19 in Writing
  • Pearson Test of English (PTE): Academic 51 in all four skills
  • Cambridge English (exams taken from 2015): Advanced – minimum overall score of 169, with no less than 162 in any component

We are internationally renowned for our world-leading research, which involves international and multidisciplinary collaboration. We have strong research groups in algebra, analysis, combinatorics, continuum mechanics, initiatives and infrastructures, mathematical biology, nonlinear systems, numerical analysis, statistics, and theoretical and computational optimization.

The Applied Mathematics Group is recognised for world leading and internationally excellent research and has collaborations with researchers from industry, healthcare, and other areas of science and engineering.

Visit our Applied Mathematics research group website for further information.

Find a PhD

University Careers Network

Preparation for your career should be one of the first things you think about as you start university. Whether you have a clear idea of where your future aspirations lie or want to consider the broad range of opportunities available once you have a Birmingham degree, our Careers Network can help you achieve your goal.

Our unique careers guidance service is tailored to your academic subject area, offering a specialised team (in each of the five academic colleges) who can give you expert advice. Our team source exclusive work experience opportunities to help you stand out amongst the competition, with mentoring, global internships and placements available to you. Once you have a career in your sights, one-to-one support with CVs and job applications will help give you the edge.

If you make the most of the wide range of services you will be able to develop your career from the moment you arrive.

Culture and collections

Schools, institutes and departments

Services and facilities