Mathematics MPhil/PhD

London, Bloomsbury

The department is home to many internationally renowned mathematicians. Our students go on to pursue successful careers in a variety of settings, primarily as postdoctoral researchers or in the world of finance. Excellent networking opportunities are provided by our central London location and close research links to other London universities.

UK students International students
Study mode
UK tuition fees (2024/25)
Overseas tuition fees (2024/25)
3 calendar years
5 calendar years
Programme starts
Research degrees may start at any time of the year, but typically start in September.
Applications accepted
Applications are accepted on a rolling basis.

Entry requirements

A minimum of an upper second-class UK Bachelor’s degree in a relevant discipline or an overseas qualification of an equivalent standard. Where possible, candidates are always interviewed. For overseas candidates there will be an alternative interview by telephone or Skype.

The English language level for this programme is: Level 1

UCL Pre-Master's and Pre-sessional English courses are for international students who are aiming to study for a postgraduate degree at UCL. The courses will develop your academic English and academic skills required to succeed at postgraduate level.

Further information can be found on our English language requirements page.

If you are intending to apply for a time-limited visa to complete your UCL studies (e.g., Student visa, Skilled worker visa, PBS dependant visa etc.) you may be required to obtain ATAS clearance. This will be confirmed to you if you obtain an offer of a place.

Equivalent qualifications

Country-specific information, including details of when UCL representatives are visiting your part of the world, can be obtained from the International Students website.

International applicants can find out the equivalent qualification for their country by selecting from the list below. Please note that the equivalency will correspond to the broad UK degree classification stated on this page (e.g. upper second-class). Where a specific overall percentage is required in the UK qualification, the international equivalency will be higher than that stated below. Please contact Graduate Admissions should you require further advice.

About this degree

We offer research supervision across a broad range of pure and applied mathematics. General areas of expertise in pure mathematics include analysis, geometry, number theory and topology. In applied mathematics key areas of activity include fluid dynamics, mathematical modelling, mathematical physics, mathematical biology, applied and numerical analysis and financial mathematics.

Who this course is for

Our research degree programme is aimed at graduate students in mathematics or related sciences. Applicants will have analytical skills, and have formed a strong interest in pursuing mathematical research.

What this course will give you

The department offers a unique combination of outstanding research supervision and a rich community of students. It is sufficiently large for wide-ranging research activity but remains compact enough for academic staff to be highly accessible.

UCL’s role in the London School of Geometry and Number Theory (LSGNT) and London Taught Course Centre, as well as numerous intercollegiate seminars, ensures that students are firmly integrated into the wider mathematical community.

Some PhD projects are supervised jointly with industrial partners, or with other UCL departments or by interdisciplinary centres, with a unique critical mass of interdisciplinary activities at UCL.

The foundation of your career

Many of our students have go on to careers in financial services in the City; others have proceeded to postdoctoral research and academic careers.


Recent graduates have taken up academic posts at universities such as UCL, Imperial College London, Michigan, Sheffield, Mexico, Kyoto, California State, Others have joined the financial services industry with companies such as Barclays Capital, Schroders, Deloitte, ABN Amro and J. P. Morgan; Other graduates have become mathematics teachers and computer programmers.

A further example of employer destinations in industry would be Formula One motor racing development. Some students have summer secondments, such as two recent summer secondments at the Department of Business, Innovation and Skills.


Students closely interact with their peers from other London universities via the London Taught Course Centre, which offers a programme of advanced courses in mathematics and statistics one day a week for PhD research students in the region, as well as short intensive courses open to students from elsewhere in the UK and Europe.

You will have the chance to attend the departmental postgraduate seminar run by the students for the students, as well as other seminars both within and outside the department. You'll also have the opportunity to take part in a vigorous conferences programme.

Conferences recently hosted by the department include the Numerical Methods for MFG and related PDE Workshop, a lecture course on Regularity of Area Minimising Hypersurfaces, a conference on contact geometry and the British Applied Mathematics Colloquium, and the London Mathematical Biology Conference.

Teaching and learning

The degree is predominantly research-based and is overseen by a Principal Supervisor. Additionally all students are required to undergo training aimed at developing their presentation skills and gaining a broader knowledge of mathematics through modules (e.g. those offered by the London Taught Course Centre), seminars and conference attendance.

After 12-18 months, students are upgraded from MPhil to PhD candidature subject to assessment by a panel on the basis of a written report and oral examination. Ultimately, the student submits a thesis meeting the requirements of a UCL research degree as assessed by nominated examiners at an oral examination.

In a typical week you will meet your supervisory team for up to 2 hours. Short lecture courses, attending seminars, conferences or group meetings will amount to several additional hours per week. The majority of time is self-directed study.

Research areas and structure

Departmental research specialities fall within the two main groupings of pure and applied mathematics described below, and graduate research may be pursued within either field.

  • Applied mathematics: environmental flows (including vortex dynamics, atmospheric and ocean dynamics and climate modelling); fluid mechanics (e.g. free-surface flows, polymers); industrial mathematics (e.g. inverse models, sound transmission, multi-particle interactions); mathematical biology and medicine (e.g. modelling cerebral and liver blood flow, molecular and cellular dynamics); gravitation, integrable systems; mathematical modelling; applied partial differential equations; numerical analysis and scientific computing; financial mathematics
  • Pure mathematics: functional analysis; real and complex analysis; spectral theory; combinatorics; algebraic number theory; geometric topology; discrete and convex geometry; probability theory; geometric group theory; symplectic and contact topology

Research environment

The department is home to many internationally renowned mathematicians. We are delighted to be among the strongest mathematical science departments in the UK. In the Research excellence Framework 2021, UCL Mathematical Sciences was ranked 5th in the UK in terms of the number of papers ranked 3* or 4*. The expertise of our faculty covers the range of pure and applied mathematics with particular highlights including our leadership of the London School of Geometry and Number Theory which offers outstanding opportunities to early career young researchers in these fields. Numerous subject specific college seminars as well as intercollegiate seminars ensure that all PhD students have access to cutting edge research in their field.

Your primary activity in all years of study is to pursue research on your chosen research topic. This is conducted in close consultation with your primary supervisor.

During the first year you will usually take four courses from the inter-collegiate London Taught Course Centre. 

At or near the start of the second year students you will submit an upgrade report that is examined by a viva voce. On successful completion of this upgrade you will move from "MPhil" to "PhD" status.

Your primary activity in all years of study is to pursue research on your chosen research topic. This is conducted in close consultation with your primary supervisor. During the first two years you will usually take four courses from the inter-collegiate London Taught Course Centre. At or near the end of the third year students will submit an upgrade report that is examined by a viva voce. On successful completion of this upgrade you will move from MPhil to PhD status.


Details of the accessibility of UCL buildings can be obtained from AccessAble Further information can also be obtained from the UCL Student Support and Wellbeing team.

Fees and funding

Fees for this course

UK students International students
Fee description Full-time Part-time
Tuition fees (2024/25) £6,035 £3,015
Tuition fees (2024/25) £28,100 £14,050

The tuition fees shown are for the year indicated above. Fees for subsequent years may increase or otherwise vary. Where the programme is offered on a flexible/modular basis, fees are charged pro-rata to the appropriate full-time Master's fee taken in an academic session. Further information on fee status, fee increases and the fee schedule can be viewed on the UCL Students website:

Additional costs

Funded PhD places include the provision of a laptop by the department to be purchased in the first 2 years of studies. Students own the laptop and are, therefore, expected to pay the costs of insuring and backing-up their laptop. Students who leave their studies early are expected to return their laptop if already purchased.

For more information on additional costs for prospective students please go to our estimated cost of essential expenditure at Accommodation and living costs.

Funding your studies

For MPhil/PhD research at least two EPSRC doctoral training awards are normally offered each year. Approximately seven PhD teaching assistantships are also available each year. In addition, there are UCL Graduate Research Scholarships and Overseas Research Scholarships, and small departmental scholarships for which applicants are automatically considered on accepting an offer of a place.

Further opportunities for financial support are occasionally available. The department encourages and offers financial support for conference and workshop attendance.

For a comprehensive list of the funding opportunities available at UCL, including funding relevant to your nationality, please visit the Scholarships and Funding website.

CSC-UCL Joint Research Scholarship

Value: Fees, maintenance and travel (Duration of programme)
Criteria Based on academic merit
Eligibility: EU, Overseas

Next steps

Deadlines and start dates are usually dictated by funding arrangements so check with the department or academic unit to see if you need to consider these in your application preparation. In most cases you should identify and contact potential supervisors before making your application. For more information see our How to apply page.

Please note that you may submit applications for a maximum of two graduate programmes (or one application for the Law LLM) in any application cycle.

Choose your programme

Please read the Application Guidance before proceeding with your application.

Year of entry: 2024-2025

Year of entry: 2023-2024

Got questions? Get in touch

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