Mathematics Research (MPhil/PhD)
Advance mathematical research that underpins modelling, data and real-world solutions.
Key information
PhD
Duration: 3 years full-time, 6 years part-time
Fees (UK / Overseas): Annual tuition fees apply and vary by student status and study mode.
See fees and funding
Start date: April 2026 / October 2026 / February 2027
Other research degree routes
MPhil:
A shorter research degree, often a pathway to PhD
PhD by Publication:
For researchers with an existing body of published work
Course summary
- Turn your knowledge and qualifications in Mathematics into a postgraduate research degree that challenges how we think about and use numbers.
- Apply maths to urgent real-world problems and contribute to research developing solutions to some of the planet's most pressing technological, environmental and societal challenges.
- Work within areas including industrial mathematics, applied mathematics, and nonlinear and complex systems.
- Join a culture of collaborative research and make your own contribution to work recognised for international excellence (REF 2021), and help transform our research into impact.
Find a supervisor
Why choose Mathematics at Portsmouth for research?
From discovery to impact
Take on research in mathematics that can shift understanding and solve problems in the real world; you’ll be supported to test ideas, challenge assumptions and turn results into meaningful outcomes.
Expert support, every step
You’ll be backed by the Doctoral College alongside your supervisory team, helping you make the most of training, workshops and the wider research community
A connected research-active community
Work with researchers across industrial and applied mathematics in a setting that values shared problem-solving and partnership.
1st
among modern UK universities for overall performance and research environment.
Research Excellence Framework (REF) 2021
PGR Research Excellence Framework — Maths 192%
of our outputs were judged to be internationally excellent or world-leading.
Research Excellence Framework (REF) 2021
PGR Research Excellence Framework — Maths 2100%
of our impact was rated as having very considerable or outstanding reach and significance.
Research Excellence Framework (REF) 2021
PGR Research Excellence Framework — Maths 3
Research areas in Mathematics
Explore the work we're doing across the three areas of expertise in our Mathematical research. Including funded and self-proposed research opportunities.
View available PhD projects and see funded opportunities.
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.
Operational Research and Decision Analysis
We're researching how we can apply quantitative methodologies, management tools and digital technologies to improve decision-making across multiple sectors.
Research degree options in Mathematics
We offer several postgraduate research routes in Mathematics, including PhD, MPhil and PhD by Publication. Find out about our research degree opportunities below, including how to apply, entry requirements and funding your degree. You can apply for an existing project or propose your own research idea. For more detailed information about the application process, visit our How to Apply pages.
Available PhD and MPhil projects
You can apply for a pre-approved PhD or MPhil project, or develop your own research proposal.
There are currently no funded PhD projects available in this area — for more information on funding your own research project, visit our pages on funding your research degree.
- 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
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.
From October 2026, all PhD by Publications will be completed by distance learning. However, there is no expectation that any student applying for a start date before this should be on campus.
Entry requirements
The entry requirements for a PhD, MPhil or Professional Doctorate 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.
Fees and funding
April 2026
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Full-time and full-time distance learning: £5,006 per year (may be subject to annual increase)
- Part-time and part-time distance learning: £2,503 per year (may be subject to annual increase)
(Including EU Scholarship)
- Full-time and full-time distance learning: £5,006 per year (may be subject to annual increase)
- Part-time and part-time distance learning: £2,503 per year (may be subject to annual increase)
- Full-time and full-time distance learning: £19,200 per year (may be subject to annual increase)
- Part-time and part-time distance learning: £9,600 per year (may be subject to annual increase)
- External candidates: £5,006
- Members of staff: £2,000
- All fees are subject to annual increase. If you are an EU student starting a programme in 2025/26 please visit this page.
October 2026 and February 2027
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Full-time and full-time distance learning: £5,238 per year (may be subject to annual increase)
- Part-time and part-time distance learning: £2,619 per year (may be subject to annual increase)
- Full-time and full-time distance learning: £19,950 per year (may be subject to annual increase)
- Part-time and part-time distance learning: £9,975 per year (may be subject to annual increase)
EU students may be eligible to receive our EU Scholarship.
- Full-time and full-time distance learning: £19,950 per year (may be subject to annual increase)
- Part-time and part-time distance learning: £9,975 per year (may be subject to annual increase)
- External candidates: £5,238
- Members of staff: £2,100
- Tuition fees terms and conditions
Additional fees
Some PhD projects may include additional bench fees for equipment and other consumables. 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
Government Postgraduate Loan
Eligible for MPhil full-time and part-time courses (UK/EU students).
Other funding options
For information on other sources of funding, visit our funding your postgraduate research degree page.
What do my tuition fees cover?
If you are self-funding your PhD, your tuition fees cover the full cost of your postgraduate research programme and access to a wide range of academic, professional and support services, including:
Research training and development
Bespoke training, professional development courses, seminars, workshops and researcher-led events delivered through The Doctoral College.
Research community and support
Access to our research environment, Research and Innovation services, and researcher networking (77% of our research is world-leading or internationally excellent, REF 2021).
Facilities, equipment and resources
Libraries, laboratories, computer rooms, laptops, electronic journals, specialist software (Microsoft Office, SPSS and Adobe Creative Suite), funding guidance and LinkedIn Learning. Explore our facilities.
Student support services
Including academic, financial, careers and wellbeing support, including access to personal tutors. Read more on our guidance support.
Your PhD programme
Registration, tuition, supervision, examinations and viva administration.
Conference and development support
A contribution towards attending conferences or research-related development activities.
Students' Union membership
Giving you the right to vote in elections, join clubs and societies, and get free independent advice.
Graduation
Your graduation ceremony will recognise the significant contribution your research has made to your discipline.
Support and facilities
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Support from our Doctoral College, helping you become part of a thriving, collaborative research community
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Guidance from a dedicated supervisory team throughout your research degree
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Access to the Doctoral Development Programme, offering specialist training, workshops and research events to develop your skills as a researcher
What can a postgraduate research degree do for my career?
A postgraduate research degree develops advanced expertise and transferable skills valued across academia, industry and the public sector.
You’ll graduate with:
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Advanced research and analytical expertise
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Critical thinking and problem-solving skills
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Experience managing complex, independent projects
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Strong communication and presentation skills
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Leadership and research management capability
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Deep subject knowledge in your chosen field
How to apply
You apply for a research degree in Mathematics by completing our online application form. For more detailed information about the application process, visit our How to Apply pages.
Not ready to apply just yet?
Get in touch
We're here to help. Feel free to ask us a question.
Come to an Open Evening
Why not come to our next open evening? Open evenings are the perfect place to talk to staff and students, visit our campus and get all the information you need.
- 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
We recommend you get in touch with the relevant subject area supervisor using our “Find a Supervisor” tool ahead of applying. You can discuss your research ideas with them and ensure we have supervisory expertise to support you.
Yes. You can apply with your own research proposal, or apply for one of our advertised funded projects.
Where next?
Find out more about Portsmouth's postgraduate opportunities and community.
Postgrad Research Degrees Webinar series
From applications to flexible study — get the insights you need to plan your research degree.
Find a PhD Supervisor
If you've already got your own research idea, start looking for a supervisor whose research interests match yours.
How to apply for postgraduate research
Read our guide on how to complete and submit your postgraduate research application. Take the next step in your academic career today.
