The PhD in Mathematical Sciences at Liverpool provides a vibrant environment where postgraduate researchers engage in cutting-edge research across applied mathematics, pure mathematics, theoretical physics, and financial mathematics. With access to advanced resources and a collaborative community, you’ll contribute to pioneering work in areas like quantum theory, mathematical biology, and financial mathematics, while developing expertise that leads to impactful discoveries.
The Mathematical Sciences PhD at Liverpool provides a comprehensive research experience, allowing you to work within one of the nine research groups across the department. The programme is designed to support you in developing both advanced mathematical techniques and critical research skills, with opportunities to contribute to pioneering research in areas like algebraic geometry, dynamical systems and mathematical biology.
Liverpool offers a structured environment, combining independent research with professional development, including access to dedicated resources such as high-performance computing facilities and specialised workshops. You’ll benefit from the expertise of academic supervisors and collaborative research groups, enabling you to make significant contributions to international research efforts. Graduates leave with strong analytical skills and a deep understanding of mathematical theory, well-prepared for roles in academia or industry, as well as research-based positions in finance and technology.
This PhD offers a wide range of research topics across several broad themes, with the flexibility for you to suggest your own topic within these areas. Research themes include:
The Department of Mathematical Sciences fosters an active and collaborative research culture, with a diverse range of research groups focusing on both pure and applied mathematics.
The department supports a dynamic learning environment where you can engage in cutting-edge research. Postgraduate researchers benefit from a strong network of experts and are encouraged to contribute to global research initiatives while developing academic and professional skills.
The department emphasises interdisciplinary collaboration and offers a supportive atmosphere for emerging scholars.
View the staff list for the Department of Mathematical Sciences, for details of potential supervisors in this area.
If you’d like any help finding a supervisor, please email spspgr@liverpool.ac.uk.
You may need the following documents to complete your online application:
Finally, register and apply online. You'll receive an email acknowledgment once you've submitted your application. We'll be in touch with further details about what happens next.
Your tuition fees, funding your studies, and other costs to consider.
Tuition fees for a full-time place on this programme in academic year 2025-26 are:
Tuition fees for a part-time place on this programme in academic year 2025-26 are:
Please note, the tuition fee you pay will reflect the nature of your research project. Some research projects incur a higher fee than others, for example if you’re required to undertake laboratory work. You’ll be informed of the fee for your intended PhD in your offer letter.
We understand that budgeting for your time at university is important, and we want to make sure you understand any costs that are not covered by your tuition fee. This could include buying a laptop, books, or stationery.
Find out more about the additional study costs that may apply to this degree.
If you're a UK national, or have settled status in the UK, you may be eligible to apply for a Postgraduate Doctoral Loan worth up to £30,301 to help with course fees and living costs.
There’s also a variety of alternative sources of funding. These include funded research opportunities and financial support from UK research councils, charities and trusts. Your supervisor may be able to help you secure funding.
We offer a range of scholarships and bursaries that could help pay your tuition fees and living expenses.
If you’re awarded this prestigious scholarship, you’ll receive significant funding to support your postgraduate research. This includes full payment of your PhD fees and a cash bursary of £17,000 per year while you study. One award is available in each academic year.
If you’re a UK student, either born in or with strong family connections to Merseyside, you could be eligible to apply for financial support worth up to £12,000 per year for up to three years of full-time postgraduate research (or up to five years part-time pro-rata).
Apply to receive tailored training support to enhance your sporting performance. Our athlete support package includes a range of benefits, from bespoke strength and conditioning training to physiotherapy sessions and one-to-one nutritional advice.
PhD researchers have access to high-performance computing clusters, advanced software for mathematical modelling and simulations, and specialist labs for research in applied mathematics, theoretical physics, and financial mathematics.
These are the trailblazers, the leaders, the true originals. Our postgraduate researchers are shaping their future, and the future of the world we live in, advancing knowledge with each discovery.
Want to find out more about studying a PhD with us? Chat with our postgraduate research student ambassadors and ask any questions you have.
Discover the qualifications you'll need to apply for this course.
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 this higher qualification may be required to follow some or all of the taught part of the Mathematical Sciences MSc.
You'll need to demonstrate competence in the use of English language, unless you’re from a majority English speaking country.
We accept a variety of international language tests and country-specific qualifications.
International applicants who do not meet the minimum required standard of English language can complete one of our Pre-Sessional English courses to achieve the required level.
| Qualification | Details |
|---|---|
| IELTS | 6.5 overall, with no component below 5.5 |
| TOEFL iBT | 88 overall, with minimum scores of listening 17, writing 17, reading 17 and speaking 19. TOEFL Home Edition not accepted. |
| Pearson PTE Academic | 61 overall, with no component below 59 |
Do you need to complete a Pre-sessional English course to meet the English language requirements for this course?
The length of Pre-sessional English course you’ll need to take depends on your current level of English language ability.
If you don’t meet our English language requirements, we can use your most recent IELTS score, or the equivalent score in selected other English language tests, to determine the length of Pre-sessional English course you require.
Use the table below to check the course length you're likely to require for your current English language ability and see whether the course is available on campus or online.
| Your most recent IELTS score | Pre-sessional English course length | On campus or online |
|---|---|---|
| 6.0 overall, with no component below 5.5 | 6 weeks | On campus |
| 5.5 overall, with no component below 5.5 | 10 weeks | On campus and online options available |
| 5.5 overall, with no more than one component below 5.5, and no component below 5.0 | 12 weeks | On campus and online options available |
| 5.5 overall, with no component below 4.5 | 20 weeks | On campus |
| 5.0 overall, with no component below 4.5 | 30 weeks | On campus |
| 4.5 overall, with no more than one component below 4.5, and no component below 4.0 | 40 weeks | On campus |
If you’ve completed an alternative English language test to IELTS, we may be able to use this to assess your English language ability and determine the Pre-sessional English course length you require.
Please see our guide to Pre-sessional English entry requirements for IELTS 6.5 overall, with no component below 5.5, for further details.
Have a question about this research opportunity or studying a PhD with us? Please get in touch with us, using the contact details below, and we’ll be happy to assist you.