Mathematical Sciences

MPhil / PhD

Mathematical Sciences at Liverpool offers wide opportunities for postgraduate study in an active research environment. Research is organised in 9 research groups, in addition to 3 research centres.

World leading research

Once you have a degree no one can take it away from you. Furthermore there always seems to be a need for more people who have studied technical disciplines such as mathematics. I know this experience and the degree I am earning will help me to be successful.

Megan Selbach-Allen - Mathematical Sciences PhD student
  • 92%

    research impact judged as 'outstanding.' REF (2014)

  • 1/3

    graduates become business and finance professionals.

  • 23/24

    of the department’s teaching was evaluated in the most recent survey by Quality Assurance Agency.

Research at Liverpool

There are 12 active research groups in many areas of Mathematics and Theoretical Physics, holding research grants from EPSRC, STFC and other sources. State of- the-art computing facilities are available. The Department’s teaching was evaluated in the most recent survey by the Quality Assurance Agency and awarded a total of 23 points out of 24 (excellent).

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.

Research themes

Our research themes include:

  • 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).

Research interests

Our research interests closely match our research themes.

Study options and fees

MPhil

The Master of Philosophy (MPhil) can be thought of as a shorter version of the PhD. It requires the same research skills, training, planning, and project management. It can be a way to assess whether you wish to undertake doctoral research - or it can be taken for its own sake.

Duration Fees: Home and EU Students Fees: International Students
Full time 2-4 years £4,260 £19,850 (Lab based programmes) £16,150 (Non Lab based programmes)
Part time 4-6 years £2,130 £9,925 (Lab based programmes) £8,075 (Non Lab based programmes)
PhD

A doctoral degree is awarded to students that have demonstrated the ability to conceptualise, design, and implement a substantial research project that results in new knowledge, applications, or understanding in their field of study. During your research, you can expect to draw on direct clinical and observational experience to produce an original thesis of 80,000-100,000 words. You'll be part of a research group which matches your research interests. Research groups offer opportunities for cross-disciplinary research collaboration, as well as support and expertise for your research.

Duration Fees: Home and EU Students Fees: International Students
Full time 2-4 years £4,260 £19,850 (Lab based programmes) £16,150 (Non Lab based programmes)
Part time 4-6 years £2,130 £9,925 (Lab based programmes) £8,075 (Non Lab based programmes)
MD

The Doctor of Medicine (MD) is a doctoral degree open to medical practitioners (technically, anyone holding a medical qualification registrable with the General Medical Council). It is equivalent in requirements and format to the PhD.

Duration Fees: Home and EU Students Fees: International Students
Full time 2-4 years £4,260 £19,850 (Lab based programmes) £16,150 (Non Lab based programmes)
Part time 2-6 years £2,130 £9,925 (Lab based programmes) £8,075 (Non Lab based programmes)

Entry requirements

Eligibility and entry qualifications

Applications are welcome from students who have (or expect to obtain) a good Honours degree (first class or 2:1) or an equivalent qualification.

Since a wide background in mathematics is required for success in research, students with a higher qualification (eg MSc, MMath, Cambridge Part III) will find they are better prepared for starting research.

Those without the higher qualification may be required to follow some or all of the taught part of the MSc.

English language requirements

To apply for this research degree, you must have reached a minimum standard of English. You need to be able to provide evidence of this.  See our English language requirements for international students for guidance on the different English language qualifications and evidence that you can provide. 

International qualifications

We welcome applications from within the EU and from around the world. You should ensure that your qualifications are equivalent to those which are required to study for this research degree.  See our guidance on international qualifications.

Additional requirements

How to apply

Research degree applications can be made online.  Before you apply, we recommend that you identify a supervisor and develop a research proposal.  You'll also need to ensure that you have funding to cover all fees.

Applications are open all year round.

More about applying for research degrees

Apply online

Find a supervisor

Your supervisor is your main source of academic support and mentoring. You'll need to find a supervisor before you start your research degree. It's helpful to identify a supervisor and discuss your research proposal before you apply.

View supervisors in this area

Need help finding a supervisor? Contact us

Related studentships

Funding

LDC module

Your training and development

Join us and you'll also join the Liverpool Doctoral College, our home for doctoral support, training and development. You'll join a vibrant and collaborative community of researchers, get tailored support for your development and have the opportunity to undertake a work placement.

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