Enhance your mathematical and communication skills with our Pure Mathematics PhD. You'll tackle challenging problems that are vital to the international mathematical research community and work towards becoming an expert in your field.
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.
ou 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.
At this point you will be working on delivering the project, collection and analysis of data, producing new information and potentially writing scientific papers with your supervisors and other collaborative partners.
Towards the end of your project you will be focussed on writing your thesis and delivering associated scientific papers. Extending this period of writing may be possible.
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Birmingham is ranked 68th in the QS World University Rankings 2027, maintaining our position in the top 100 universities globally and placing us in the top 10 amongst UK universities.
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.
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.
The Birmingham Doctoral Programme is a structured research experience co-ordinated by the University Doctoral School. It offers world-class supervision, a tailored development framework, and real-world engagement opportunities that prepare you to flourish, whatever your future holds.
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.
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.
Find a PhD project that suits your interests by using our FindAPhD tool.
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.
Our research themes include Algebra, Analysis, Combinatorics, Topology and Dynamical Systems and Mathematical Physics.
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 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. The broader importance of this project for society, policymakers and businesses should also be covered.
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.
If you are unsure if you meet our entry requirements, you can also contact the admissions department to discuss whether your application would be considered.
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 or a Presessional English course.
For this course we require IELTS 6.0 with no less than 5.5 in any band, which is equivalent to:
The University tuition fee covers the cost of your tuition, supervision, assessment and includes membership to the Guild of Students.
Full-time
We charge an annual tuition fee. Fees for 2027 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 and consult with a potential supervisor, explore funding opportunities, write a research proposal and apply to the relevant programme. 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.
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 strongly 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.
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.
Find out how to apply to our postgraduate research programmes. Please read this information carefully before completing your application.
If you have a question about our admissions process, including how to apply, your offer and how to track your application, please visit our admissions portal.
If you have a question about our admissions process, including how to apply, your offer and how to track your application, please speak to our team.
Your PhD will open the door to 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.
At Birmingham, we prepare our researchers to make an impact across every sector of society. Our PhD graduates are global change-makers: advancing knowledge, shaping policy, leading industries, and educating future generations.
You'll benefit from dedicated careers support tailored to your unique paths. Our expert team of Careers Advisers, including a dedicated postgraduate research adviser, offer one-to-one guidance to help researchers navigate career decisions both within and beyond academia.
Whatever you plan to do after your degree, 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.
We also offer subject specific careers consultants and a dedicated careers website for international students.
We are one of the most consistently targeted UK universities by top graduate employers (High Fliers report, The Graduate Market 2026). Read more about the achievements of our alumni and the way their university experience shaped their journey.
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.
As a postgraduate researcher, you’ll have a variety of choices of accommodation. Stay with us in our dedicated postgraduate halls or explore a wide range of private accommodation close to campus.
As one of the original pioneering cities, Birmingham is a melting pot for shopping, food and drink, nightlife, sport, culture, and industry. It’s no wonder our students fall in love with the city.
Our green and spacious campus is the place where our community comes together to learn, relax and socialise. Like a town of its own, just minutes from the hustle and bustle of the UK’s second city.
Whoever you are and wherever you come from, we are committed to providing the best possible support to all of our students so that you can get the most out of your university experience.
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.
Find new perspectives. Hear first-hand about life at Birmingham from our students, past and present.
