Mathematical Sciences MPhil/PhD

Major code: MPMR


The annual intake of postgraduate students varies, but typically around ten postgraduate students per year begin a research PhD. Part-time study where an external supervisor is available is also possible.

Current postgraduate opportunities

Research is structured around the following 9 clusters and 3 research centres: full details are from the departmental web page

  • Algebraic Geometry,
  • Applied Probability,
  • Dynamical Systems,
  • Financial and Actuarial Mathematics,
  • Mathematical Biology,
  • Quantum Field Theory and Applications,
  • Singularity Theory and its Applications,
  • String Phenomenology,
  • Waves and Solid Mechanics,
  • Research Centre in Mathematics and Modelling (RCMM)
  • Centre for Mathematical Imaging Techniques (CMIT)
  • Environmental Radioactivity Research Centre (ERRC)


The Department of Mathematical Sciences offers a wide range of opportunities for postgraduate research in four key areas: Applied Mathematics, Pure Mathematics, Theoretical Physics, and Financial and Actuarial Mathematics and Applied Probability. Our research strength has earned us the top numerical research rating in all four Research Assessment Exercises.

Key Facts

92% of our research impact judged as outstanding and very considerable, 28% improvement in overall research at 4* and 3*.

A dedicated student resource suite is available in the Department, with computer and reading rooms and a social area.

Why Mathematical Sciences?

Range and depth of study options

We offer a wide range of modules, ranging from Financial Mathematics to Fluid Mechanics, from Chaos to Combinatorics. In the final year, many of our degree programmes offer the opportunity to undertake an in-depth project on a topic of your choice, supervised by a leading expert in the field.

Exceptional employability

At Liverpool, we listen to employers’ needs. Alongside key problem-solving skills, employers require strong communication skills and the ability to work in a team. Both of these are integral to our Mathematics programmes. As a result, we have an excellent graduate employment record. About a third of graduates become business and finance professionals; other favoured areas include: management training, information technology, further education or training (including teacher training) and scientific research and development.

Teaching quality

We are proud of our record on teaching quality, with five members of the Department having received the prestigious Sir Alastair Pilkington Award for Teaching. We care about each student and you will find the staff friendly and approachable.


We take students from a wide variety of educational backgrounds and we work hard to give everyone the opportunity to shine.

Supportive atmosphere

Features such as the peer-assisted study scheme whereby Year Two and upwards students assist first years with maths problems, small tutorial sizes of six or seven in the first year, a common room and kitchen for the exclusive use of the Department’s students, and a lively maths society help to foster a friendly and supportive environment.