Research course


UCL - University College London · Mathematics

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.

Months of entry


Course content

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 and applied analysis.

The department offers a unique combination of outstanding research supervision and a rich community of students. 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 as a part of interdisciplinary centres, with a unique critical mass of interdisciplinary activities at UCL.

Department specialisms

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.

Information for international students


Fees and funding

UK students
£4,635 (FT) £2,315 (PT)
International students
£16,690 (FT) £8,500 (PT)

For MPhil/PhD research two EPSRC doctoral training award are normally offered each year. Around five PhD teaching assistantships are also available each year. In addition, there are UCL Graduate Research Scholarships and Overseas Research Scholarships, and 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.

Funding opportunities available for students taking research programmes are available at:

Qualification and course duration


part time
60 months
full time
36 months


part time
60 months
full time
36 months

Course contact details

Professor Valery Smyshlyaev
+44 (0)20 7679 2839
020 7383 3001