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
95%
of our research outputs rated as 'world leading' (4*) or 'internationally excellent' (3*) in the latest Research Excellence Framework (2021)
1/3
graduates become business and finance professionals.
90%
of our research impact is rated as 'outstanding' (4*) or 'very considerable' (3*) in the latest Research Excellence Framework (2021)
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
The fees below reflect one year of study during the 2024/25 academic year
| MPhil / PhD | Duration | UK students | International Students |
|---|---|---|---|
| Full time | 2-4 years | £4,786 |
|
| Part time | 4-6 years | £2,393 |
|
The fees stated in the table above exclude potential research support fees also known as ‘bench fees’. You will be notified of any fee which may apply in your offer letter.
* Please note that if you are undertaking a PhD within the Faculty of Science and Engineering the fee you pay, Band A or Band B, will reflect the nature of your research project. Some research projects incur a higher fee than others e.g. if you are required to undertake laboratory work. You will be informed of the fee for your programme in your offer letter.
^ Self-funded, full-time international students studying a PhD programme classified as Band A will receive a £2,000 reduction in their fees for the first year only.
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 |
| Trinity College London, Integrated Skills in English (ISE II) | ISE II with an overall pass with merit in components |
| Cambridge IGCSE as a First Language | Grade C |
| Cambridge IGCSE as a Second Language | Grade 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
Before you apply, we recommend that you identify a supervisor and develop a research proposal
Find a supervisor
View supervisors in this area
Need help finding a supervisor? Contact us
- Mrs Shirley Farrell
- Email: spspgr@liverpool.ac.uk
- Phone: +44 (0)151 794 4043
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.