Pure Mathematics MRes

This course is a great stepping stone onto our fast-track PhD programme, making it an excellent option for you if you are looking to build strong mathematical foundations for this route.

Course Structure

What makes this course different?

The School of Mathematics at Birmingham offers a dynamic and supportive environment where you can apply your mathematical knowledge to a range of complex scenarios.

You will receive comprehensive training in research, constructing proofs, and tackling abstract problems, equipping you to critically evaluate and address intricate issues. Paired with a project supervisor for your MRes thesis, you’ll have the opportunity to work closely with internationally renowned mathematicians.

You'll work with experts in areas such as Algebra, Analysis, Combinatorics, Geometry and Mathematical Physics, Topology and other areas of Pure Mathematics. Additionally, you'll be encouraged to engage with the School's vibrant research community, participating in active seminar programs and international conferences across all areas of mathematics.

• Benefit from the School of Mathematics' ambitious research programmes and extensive inter- and intradisciplinary collaborations.
• Learn from world-leading experts in their fields
• Earn a globally respected qualification that enhances your attractiveness in a highly competitive job market

• Learn about cutting-edge developments in your chosen areas of interest through lectures and seminar talks delivered by international experts in their fields
• Receive tailored guidance and feedback in tutorials, enabling you to tackle specific challenges and enhance comprehension of the material
• Engage in projects that extend theoretical knowledge, enhancing your understanding of mathematical theories and developing your communication skills
• Benefit from 1:1 supervision that offers personalised learning and mentoring, giving you the opportunity to receive tailored guidance and feedback

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 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:

• 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

English presessional programmes

If you have a conditional offer for Birmingham where English is a requirement, you can take a Presessional English course as an alternative to retaking IELTS or a similar qualification. We offer on-campus courses all year round starting from September including additional online courses in the summer term.  Teaching takes place in small classes with no more than 18 students to maximise class participation.

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.

We charge an annual tuition fee. Fees for 2026 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.

Postgraduate Masters loan

To help with the cost of studies, this loan is available to all UK students. You can use this loan towards fees, maintenance or other costs at your own discretion. It’s available for all full-time, part-time and distance learning Masters programmes, as long as you don’t already have a Masters qualification (or equivalent).If you’re a student from Wales, Scotland or Northern Ireland, you can apply for Masters loans from your country’s government.

Scholarships

To help you afford your studies, we’ve put more than £33 million into student support and scholarships. We also offer a range of advice on searching for funding and managing your finances.

Applications are accepted all year round but 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.

Find a supervisor

To apply for an MRes, you'll need to find supervisor for your research. 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 research programme co-directors will study your proposal in detail, and judge who is best suited to be your supervisory team.

Mathematics staff

Research proposal

When you apply for an MRes, 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.

Careers Network

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, 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.

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.