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Advance your career through Applied Mathematics research. By integrating mathematics with real-world applications you'll learn to solve complex problems faced by industry.
Explore diverse topics, from Continuum Mechanics and Mathematical Biology to Nonlinear Systems, Optimisation, Numerical Analysis, and Scientific Computing.
You’ll cover a rich spectrum of research areas, paving the way for numerous opportunities inside and outside academia.
Hear more about studying at Birmingham. Chat to one of our friendly postgraduate students to get their thoughts on our courses, stunning campus and life in a vibrant and cultural city.
You will be given opportunities to attend research conferences and workshops throughout your studies. Below is an indicative idea of what you could spend your time on, but your research may be different to this and will be discussed in advance with your supervisor.
You'll begin an in-depth study of your research area. We are a proud member of the MAGIC Consortium and you will participate in MAGIC lectures.
You will work with your supervisors to define the structure of your project, start to review the scientific literature and set out the scope of work that you will undertake. Opportunities to work with colleagues at Birmingham, other universities and from industry may be involved, depending on the nature of the project that you plan.
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You'll tackle real-world challenges and expand your impact in a supportive, multidisciplinary setting. Through building on your strong mathematical background, we will train you to be an expert in your research field with our world-leading tuition and supervision.
You'll have the opporunity to get involved with leading research groups in areas such as Continuum Mechanics, Mathematical Biology, Nonlinear Systems, Optimisation, Data Science, Numerical Analysis, and Scientific Computing.
You will collaborate closely with your PhD supervisor and their research team, meeting regularly to gain advanced research skills while conducting your research. Assessments are periodically carried out by the Research Students Monitoring Group to ensure you are progressing well.
Develop soft skills in areas including coding, presenting, problem solving and more.
Take advantage of the opportunity to attend and organise student conferences throughout the programme.
Birmingham is ranked 80th in the QS World University Rankings 2025, maintaining our position in the top 100 universities globally and placing us 12th amongst UK universities.
Our School of Mathematics offers world-class research, workshops, thesis supervision, seminars, online classes, assignments and conference opportunities for students.
At Birmingham, you can apply for an advertised PhD or propose your own research. An advertised PhD is typically part of an established research project and is usually funded by the University or another funding body.
If you want to pursue your own research project, you can apply to our research programmes to propose this. This is self-funded although scholarships are available.
If you’d rather propose your own research, the first step is to find your supervisor. We encourage you to browse the biographies of faculty members to familiarise yourself with the research going on in your preferred areas. Each of these contains detailed information on research interests, current projects and recent publications.
When you apply, you can suggest one or two potential supervisors, who you think might be a good fit for you. However, this is not essential. If you know what you want to work on, but are unsure on supervisors, you can indicate this in your application and the PhD programme co-directors will study your proposal in detail, and judge who is best suited to be your supervisory team.
Find a PhD project that suits your interests by using our FindAPhD tool.
Our research themes include Continuum Mechanics, Mathematical Biology, Nonlinear Systems, Optimisation, Data Science, Numerical Analysis and Scientific Computing.
We have research groups in the following areas:
To gain a place at Birmingham you will need to meet our general entry requirements, as well as those specific to your course. Your application will be reviewed by the course’s Admissions Tutor, who will decide whether your application should receive an offer.
in a Mathematics-related subject or a lower degree plus an MSc or substantial relevant experience.
If you are an international student, you will need to demonstrate you have a suitable level of English proficiency, usually through the form of an IELTS or equivalent qualification.
For this course we require IELTS 6.0 with no less than 5.5 in any band, which is equivalent to:
Students who have not studied in English must pass a recognised English test. For more information on what proof you will need, visit our International Postgraduate requirements page
The University tuition fee covers the cost of your tuition, supervision, assessment and includes membership to the Guild of Students.
Full-time
Part-time
We charge an annual tuition fee. Fees for 2025 entry are above.
The fees quoted are for one year only. For those studying courses that are longer than one year, tuition fees will also be payable in subsequent years of your programme.
Tuition fees can either be paid in full or by instalments. You can check whether you are eligible for UK or international fees with our admissions team.
Learn more about postgraduate tuition fees and funding.
These are most common in STEM (Science, Technology, Engineering and Medicine) subjects, but they can sometimes be available for pre-defined research projects in the arts, humanities or social sciences. These may be advertised as fully funded (with fees and a stipend) or competition funded, meaning the projects compete against other projects at each institution.
You devise your own PhD topic, find a supervisor, write a research proposal and apply to the relevant programme. If you’re offered a place at Birmingham, you can then apply for studentships or funding from various sources. Our Postgraduate Scholarships and Funding database lists all available funding.
To apply for a postgraduate research programme, you will need to submit your application and supporting documents online.
If you are applying to an ‘advertised PhD’, please check the details of the specific research project for application deadlines.
If you are submitting your own research proposal, applications are accepted all year round. However, if you wish to start in September, we would encourage you to apply by 1 June. Whilst you are still welcome to apply after this date, it is important to allow time for us to review your application.
If you are seeking funding, please be aware that the majority of funding opportunities have deadlines in early spring so we would encourage you to apply as early as possible.
We have put together some helpful information on the research programme application process and supporting documents on our how to apply page. Please read this information carefully before completing your application.
There are generally two routes to a Birmingham research degree.
You can apply to an ‘advertised PhD’, which means it is part of an established research project and is usually funded by the University or other funding body. Generally, advertised PhDs are associated with the physical and life sciences subjects. Some advertised PhDs will be pre-defined but some may require you to propose your own research.
Apply to any of our PhD programmes and propose your own research that is ‘self-funded’ (by you, a sponsor, or other sources not explicitly attached to the PhD on application). Usually you submit a research proposal and identify your proposed supervisor. These are generally associated with the arts and social sciences.
International students applying for this programme will need an Academic Technology Approval Scheme (ATAS) certificate from the Foreign & Commonwealth Office before the University can issue you with a Certificate of Acceptance of Studies (CAS). We recommend that you apply for your ATAS certificate as soon as you receive an offer from us.
Your PhD will open the door to a huge variety of careers from data or computational scientist to quantitative risk analyst and statistician. Or you could choose a future in academia as a researcher, lecturer or a leader in professional services.
Whatever you plan to do after your degree, the Careers Network offers a range of events and support services including networking opportunities, career coaching, one to one guidance, careers fairs and links with leading graduate recruiters.
As a postgraduate researcher, you’ll benefit from tailored support to prepare you for a career in academia or set you up for a wide range of other professions.
We also offer subject specific careers consultants and a dedicated careers website for international students.
Find out why we are the most targeted UK university by top graduate employers (High Fliers report, The Graduate Market 2024) by meeting some of our successful alumni.
At Birmingham, your university experience isn’t just about studying. You will have the opportunity to discover new experiences, develop different skills and make friends for life.
Our bustling campus with its beautiful grounds, friendly community and excellent facilities will quickly make you feel at home. We offer you a huge variety of accommodation options in the UK’s second city, exciting activities to get involved in outside your studies, as well as all the support and advice you need.
Explore our beautiful campus from wherever you are. Get a feel for the wide range of historic and modern spaces and state of the art facilities.