Mathematics MPhil/PhD

Research areas:

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.

IRIS logo

Visit the IRIS research portal to learn more about researchers' activities, research groups, research centres and interdisciplinary networks across the whole of UCL.

IRIS department: Dept of 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.

English level expected: Standard


Research degrees may start at any time of the year, but typically start in September. Deadlines and start dates are usually dictated by funding arrangements so check with the department or academic unit (contact listed in Next steps, right) 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.


  • UK/EU Full-time: £4,500
  • UK/EU Part-time: £2,250
  • Overseas Full-time: £16,200
  • Overseas Part-time: £8,250


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

Scholarships available for this department

Corte Studentship in Mathematics

For prospective and current research students of Mathematics. This studentship is based on academic merit and was founded under the will of Mrs Edith Abbott in memory of her son, Orazion Abbott Corte, a former student of UCL who was killed in action in WW1. Students must contact the Faculty of Mathematical & Physical Sciences for application information.

David Warren Scholarship

For prospective research students in Pure or Applied Mathematics. This award is based on a combination of academic merit and financial need. Students need to contact the Department of Mathematics for application information.

John Hawkes Scholarship

For current and prospective research students studying Pure Mathematics. The primary purpose of the award is to support third-year Pure Mathematics PhD students; however, where no suitable candidate(s) are found for all or part of the funds available, scholarships may be awarded to first- or second-year Pure Mathematics PhD students. Students must contact the Department of Mathematics for application information.

Sir George Jessel Studentship

For prospective and current research students in the Department of Mathematics who have also completed their undergraduate degree at UCL. There is not applicaiton procedure; all eligible students will be considered for the scholarship by the Department of Mathematics.

Edwin Power Scholarship

Archibald Richardson Scholarship

This award is based on academic merit.  

Monica Hulse Scholarship

This award is based on academic merit and is funded from a regular lifetime gift from Dr Paul Hulse, alumnus of UCL, in memory of his mother, Monica Hulse (1934-1999).

James Lighthill Scholarship

Based on a combination of academic merit and financial need.

JJ Sylvester Scholarship

To assist in advancing the education of mathematicians to realise their full potential for the benefit of us all. Awarded to an excellent student combined with an assessment of need.

Wren Bequest Scholarship

To aid mathematics research.  

CSC-UCL Joint Research Scholarship

Funding offered by UCL and the China Scholarships Council (CSC) aims to expand the educational, cultural and technological cooperation between the UK and China.

Full details of funding opportunities can be found on the UCL Scholarships website


Recent graduates have taken up academic posts at universities such as UCL, Sheffield, Kyoto and California State; others have joined the financial services industry at companies such as Barclays Capital, Schroders, Deloitte, ABN Amro and J P Morgan; and others have become mathematics teachers and computer programmers. Some students have summer secondments, with two recent ones at the Department of Business, Innovation and Skills.

Top career destinations for this programme

  • UCL, Research Associate, 2011
  • Royal Bank of Scotland, Financial Analyst, 2011
  • Mathematical Research Institute, Young Researcher, 2010
  • California State University, Post Doctoral Researcher, 2010
  • Fachhochschule Wiener Neustadt, Austria, Lecturer, 2010


Many students go onto careers in financial services in the City; many others proceed to postdoctoral research and academic careers.


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. They attend the departmental postgraduate seminar run by the students for the students, as well as other seminars both within and outside the department. The students are exposed to a vigorous conferences programme. Conferences recently hosted by the department include a Financial Mathematics conference and the British Applied Mathematics Colloquium.

Next steps


Applied Mathematics

Professor Valery Smyshlyaev

T: +44 (0)20 7679 2839

Pure Mathematics

Dr John Talbot

T: +44 (0)20 7679 4102



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Prospectus subject


Faculty overview

Mathematical and Physical Sciences


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Staff View

"Many of the world's top researchers visit London because of its strength in geometry and mathematics in general, so I have been able to network with top names in the field, leading to long-lasting connections and collaborations."

Dr Jason Lotay

Lecturer in Pure Mathematics

Student View

"It has been eye-opening and inspiring as we've learnt to pick apart assumptions about how science is done; being able to tackle scientific debates with a sociological and philosophical mind is fascinating."

Raquel Velho

Degree: Science, Technology, Medicine and Society MSc

Subject: Science and Technology Studies, Faculty: Mathematical and Physical Sciences