Postgraduate research in mathematics
Ready to start your research career? Explore our postgraduate research degrees in mathematics
The University of Portsmouth is the number 1 modern university for research quality in Mathematics
Research Excellence Framework (REF) 2021
If you're ready to take your existing knowledge and qualifications in Mathematics into a postgraduate research degree, Portsmouth is the perfect place to achieve your goals.
Our existing research in Mathematics challenges the way we think about and use numbers, and using our expertise to find solutions to some of the planet's most-pressing technological, environmental and societal problems. When you join us to study for a postgraduate research degree, you'll have the opportunity to make your own contribution to the work we're doing – and play an important role transforming our research into impact.
Across our areas of expertise in industrial mathematics, and applied mathematics, nonlinear and complex systems, we're delivering exceptional collaborative research – in the most recent Research Excellence Framework (REF 2021), 92% of our research outputs were judged to be internationally excellent or world-leading.
Types of research degrees
Find out about our PhD, MPhil, and PhD by Publication opportunities in Maths below, including how to apply, entry requirements and funding your degree. For more detailed information about the application process, visit our How to Apply pages.
Mathematics PhDs and MPhils
Explore our pre-approved funded and self-funded PhD projects in Mathematics, or submit your own research idea.
PhD and MPhil projects
- Complex differential equations with algebraic singularities
- Design and analysis of inventory policies for a remanufacturing system that models returns from past sales
- Freight micro-consolidation for last mile delivery in the Solent region
- Gaining insight into the dynamics of drug-cancer cell interactions with the aid of continuous and hybrid multiscale models
- Geometric aspects of complex differential equations
- Incorporating remanufacturing in a periodic review inventory system: Optimal and heuristic inventory control policies
- Integrability in nonlinear systems
- Mathematical Foundations of Topological Data Analysis; Theory & Applications
- Mathematical models for improved lithium-ion batteries
- Measuring and modelling speech sounds and their evolution
- Optimising the Vehicle Ferry Loading
- Quantum optical networking and communication
- Real-time Drone Routing and Scheduling for Medical Logistics in the Solent Region
- Renormalisation for coupled systems
- Renormalisation in dynamical systems
- Resilient pharmaceutical supply chain design – Case studies in drug discovery
- Spaces of initial values for Hamiltonian systems
- Using deep learning to optimise the large-scale vehicle routing problems
Submit your own idea
If you already have a research idea, find a supervisor whose research interests match yours by searching our Find a PhD Supervisor page. Once you've identified someone suitable, contact them to discuss your idea.
PhD by Publication
A PhD by publication is a postgraduate research degree based on research you've already undertaken and had published (excluding self-publishing) before registering with us.
Eligible research outputs include peer-reviewed academic papers, complete books or chapters in anthologies, and other materials accepted for publication, exhibited or performed. You'll have to submit these materials for examination between 6–12 months after registering with us.
For more information, please visit our PhD by Publication page.
Duration, fees and funding
What do my tuition fees cover?
If you're self-funding your PhD, you'll pay tuition fees to the University to cover course and university costs.
Your tuition fees cover:
- The cost of your postgraduate research programme* at the University as well as charges for registration, tuition, supervision, and examinations
- Bespoke training, professional development courses, networking, and research support through The Graduate School
- Research seminars and workshops (university-wide and faculty-specific)
- A contribution to funding to attend a conference or development activity in your research field
- Tailor-made weekly and monthly events, including weekly, themed experienced researcher-led talks and workshops
- Helping you become part of our thriving research community, including Research and Innovation services where 77% of our research is world leading and internationally excellent in REF 2021
- Your graduation ceremony
- Viva examination and administration costs
- The facilities and equipment you need to complete your studies, such as computer rooms, access to laptops, the Library, and laboratories
- Access to resources including electronic journals, alternative guide to funding, and thousands of hours of educational videos on LinkedIn Learning
- University support services including academic, financial, careers and wellbeing support and personal tutors
- Membership of the Students' Union (giving you the right to vote in elections, join clubs and societies, and get free independent advice)
- Access to software such as Microsoft Office, SPSS and Adobe Creative Suite (this includes Photoshop, InDesign, and Adobe Premiere Pro)
*Please note that some research programmes may come with additional bench fees.
How long will my research degree take?
- MPhil: 2 years full-time, 4 years part-time
- PhD: 3 years full-time, 6 years part-time
- PhD by Publication: 1 year part-time
How much will my degree cost?
PhD and MPhil
UK, Channel Islands and Isle of Man students
- Full-time: £4,786 per year
- Part-time and part-time distance learning: £2,393 per year
EU students
(including Transition Scholarship)
- Full-time: £4,786 per year
- Part-time and part-time distance learning: £2,393 per year
International students
- Full-time students: £19,200 (may be subject to annual increase)
- Part-time and part-time distance learning: £9,600 (may be subject to annual increase)
PhD by Publication
External candidates: £4,786
Members of staff: £1,950
All fees are subject to annual increase. If you are an EU student starting a programme in 2024/25 please visit this page
Bench fees
Some PhD projects may include additional fees – known as bench fees – for equipment and other consumables, and these will be added to your standard tuition fee. Speak to the supervisory team during your interview about any additional fees you may have to pay. Please note, bench fees are not eligible for discounts and are non-refundable.
Funding support
MPhil full-time and part-time courses are eligible for the Government Postgraduate Loan (UK/EU students only).
PhD full-time and part-time courses are eligible for the Government Doctoral Loan (UK/EU students only).
For information on other sources of funding, visit our funding your postgraduate research degree page.
Entry requirements
The entry requirements for a PhD, or MPhil include an upper second class honours degree or equivalent in a relevant subject, or a master’s degree in an appropriate subject. Equivalent professional experience and/or qualifications may be considered. All applicants are subject to interview.
If English is not your first language, you'll need English language proficiency at a minimum of IELTS band 6.5 with no component score below 6.0.
If you don't meet the English language requirements yet, you can achieve the level you need by successfully completing a pre-sessional English programme before you start your course.
Support and facilities
When you join us, you'll be supported by our Graduate School, alongside your assigned supervisory team, who'll help you get the most from our facilities. The Graduate School will help you become part of our thriving, collaborative research community, and help grow your skills as a researcher through the Graduate School Development Programme, which offers training, workshops and events.
What can a postgraduate research degree do for my career?
Once you complete your postgraduate research degree, you'll be a highly-skilled researcher with the knowledge and skills to make an impact in many different industries.
Your postgraduate research qualification demonstrates to potential employers that you're an intelligent, capable and motivated person, with provable abilities and experience in critical thinking, problem-solving, project management, communication, leadership and creativity.
Apply
Apply for a research degree in Mathematics by completing our online form.
February (2025 start)
April (2025 start)
October (2025 start)
Current research
Explore the work we're doing in our areas of research expertise in Mathematics.
Applied Mathematics, Nonlinear and Complex Systems
We're studying how complexity and order arise from the simple underlying rules of physics. Explore our applied mathematics nonlinear and complex systems research.
Industrial Mathematics
We're delivering insight into roles of different physical mechanisms within a process to develop practical solutions and guidance in science and industry. Explore our industrial mathematics research.