Pure MathematicsPhD

You can explore a wide array of topics within Pure Mathematics, including Algebra, Analysis, Combinatorics, Topology and Dynamics, and Mathematical Physics.

You'll develop deep expertise in your research area and a unique problem-solving skill set, opening doors to diverse opportunities in both industry and academia.

Programme Structure

What makes a Pure Mathematics PhD at Birmingham different?

You'll tackle challenging mathematical problems and expand your mathematical knowledge and research skills 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 become a member of one of our research groups in Algebra, Analysis, Combinatorics, Topology and Dynamical Systems or Mathematical Physics.

You'll 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. 
 

• Benefit from the School of Mathematics' ambitious research programmes, featuring internationally renowned researchers in key specialisms - Algebra Analysis, Combinatorics, Probability & Algorithms, Geometry & Mathematical Physics and Topology & Dynamical Systems
• Participate in our annual national conference which welcomes speakers from other leading mathematics institutions, arranged by our students.
• Join a vibrant and diverse and inclusive mathematics academic community including approximately 60-80 PhD students.

• Learn about cutting-edge developments in your research area through seminar talks delivered by international experts in their fields
• Learn collaboratively in workshops through group work which will enhance your teamwork skills and your ability to appreciate others perspectives
• Participate in practical assignments that provide hands-on, real-world experience, allowing you to put theory into practice
• Experience the convenience and accessibility of online live classes, enabling you to participate from anywhere and accommodating diverse schedules without the need for commuting
• Benefit from 1:1 supervision that offers personalised learning which gives you the opportunity to get tailored guidance and feedback that meets your individual needs

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.

Find an Advertised PhD

Find a PhD project that suits your interests by using our FindAPhD tool.

Find a supervisor

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.

Mathematics staff

Our research themes include Algebra, Analysis, Combinatorics, Topology and Dynamical Systems and Mathematical Physics.

We have research groups in the following areas:

• Algebra
• Analysis
• Combinatorics, Probability and Algorithms
• Geometry and Mathematical Physics
• Topology and Dynamics

English language requirements

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:

• TOEFL: 80 overall with no less than 19 in Reading, 19 Listening, 21 Speaking and 19 in Writing
• Pearson Test of English (PTE): Academic 64 with no less than 59 in all four skills
• Cambridge English: C1 Advanced - minimum overall score of 169, with no less than 162 in any component
• LanguageCert ESOL SELT (UKVI): B2 'Communicator' with no less than 25 in each skill

Research proposal

If you are proposing your own research topic, you will need to submit a research proposal. It’s a key part of your application, so take your time. Your potential supervisors will use it to decide if your research is something they can support.

Your proposal should be a clear and concise summary of your research. It generally consists of an outline of your proposed research project, including your main research questions and the methods you intend to use.

You should also comment on the potential impact and importance of your intended research and on how your work would interact with current trends in your academic field. It should illustrate the relevance of your topic to the research interests and expertise of the staff within your chosen department.

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.

Paying your tuition fees

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.

Funding options

Apply for a PhD that already has funding attached

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.

Self-fund, or search for funding or a studentship once you have an offer

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.

A limited number of scholarships and studentships may be available to outstanding applicants. For further information, please explore our scholarships and funding database.

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.

ATAS - Academic Technology Approval Scheme

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.

Careers Network

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.

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.