Mathematical Sciences PhD / MPhil

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.

Why study with us?

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.

Overview

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.

Our research interests closely match our research themes.

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).

Study options and fees


MPhil / PhD Duration UK students International Students
Full time 2-4 years £4,500* (2021) £24,250* ^ (lab based programmes)
£18,450* (non Lab based programmes) (2021)
Part time 4-6 years £2,250* (2021) £12,125* (lab based programmes)
£9,225* (non Lab based programmes) (2021)

* This excludes potential research support fees also known as ‘bench fees. You will be notified of any fee which may apply in your offer letter.

^ Self funded full time international students studying a lab based programme will receive a £2,000 reduction in their fees for the first year only.

If an EU student starts their studies in 2020-21, before 1 August 2021, they will have a fee classification of EU and pay UK fee rates for the duration of this registration. The exception being ROI students, who will continue to be charged fees at the UK fee rate, post 1 August 2021.


Entry requirements

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

IELTS Academic requirement - SELT and non-SELT Overall 6.5 no band below 5.5
TOEFL iBT requirement Minimum 88 overall with L 17 W 17 R 17 and S 19
C1 Advanced CAE requirement Overall 176 with no less than 162 in any paper
PTE Academic requirement61 with minimum scores of 46 in each component
Trinity College London, Intergrated Skills in English (ISE II)ISE II with an overall pass with merit in components
Cambridge IGCSE as a First LanguageGrade C
Cambridge IGCSE as a Second LanguageGrade B
Cambridge English Level 3 Certificate in ESOL International (Proficiency)Overall 176 with 162 in components
Cambridge English Level 3 Certificate in ESOL International (Advanced)Overall 176 with 162 in components
Cambridge English Level 2 Certificate in ESOL International (Advanced)Overall 176 with 162 in components

How to apply

Research degree applications can be made online.  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

Before you apply, we recommend that you identify a supervisor and develop a research proposal


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Need help finding a supervisor? Contact us


Related studentships: self-funded and funded PhD projects


Related Doctoral Training Partnerships

Doctoral Training Partnerships support future researchers with funding and a rewarding learning environment where you can collaborate with leading researchers.

Find a scholarship

We offer a range of scholarships to help you meet the costs of studying a research degree.

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