university of edinburgh math phd

• Schools & departments

Depending on the field of study you are interested in, you may be able to apply for a pre-defined PhD project, or you may need to develop your own research idea.

Research in the fields of medicine, science and engineering tend to require you to:

• apply for a project that already has specific, pre-defined aims
• compete for a place on a partially or fully funded programme (often with competitive application processes).

Research in the fields of arts, humanities and social sciences tend to require you to:

• develop your own research idea (be prepared to adapt your original idea)
• source your own funding, although some funded projects may be available.

PhD research projects

PhD projects and studentships are defined pieces of research that an organisation wishes to explore. A research council may have provided funding for the project to ensure its successful outcome, although not all defined PhD projects have funding associated with them.

Doctoral training centres and partnerships

Doctoral training centres and partnerships are four-year programmes that are sponsored by one of the UK’s research councils. They focus on your development into an independent researcher, under the guidance of an expert supervision team.

Developing your own research idea

How do you know if your own research idea is suitable for doctoral study? There are many factors you should consider, including time, topic, size and supervisor availability.

Professional doctorates

Professional doctorates are aimed at working professionals who have advanced research interests, and would like to use applied research to solve problems in their field.

This article was published on 2024-11-12

• Schools & departments

Applied and Computational Mathematics PhD

Awards: PhD

Study modes: Full-time, Part-time

Funding opportunities

Programme website: Applied and Computational Mathematics

Postgraduate Discovery Day

Join our online sessions on 19 February to learn more about postgraduate study and student life at Edinburgh, including application, fees and funding guidance.

Register now

Research profile

The Applied and Computational Mathematics research group combines expertise in dynamics, classical and statistical mechanics and advanced scientific computing techniques, to develop techniques for applications such as molecular dynamics, geophysical and astrophysical fluid dynamics and optoelectronics.

If you have a passion for applied mathematics, our facilities, people and environment will help you develop your research ideas to their full potential.

The School of Mathematics is a vibrant community of more than 60 academic and related staff supervising 60 students.

Our research interests are varied and include:

• astrophysical fluid dynamics
• multiscale modelling and analysis
• molecular dynamics
• mathematical meteorology
• Hamiltonian dynamics
• nonlinear waves in fluids and solids
• optoelectronics
• signal processing
• mathematical biology
• exponential asymptotics
• homogenisation theory

Training and support

Mathematics is a discipline of high intellect with connections stretching across all the scientific disciplines and beyond, and in Edinburgh you can be certain of thriving in a rich academic setting. Our School is one of the country’s largest mathematics research communities in its own right, but you will also benefit from Edinburgh’s high-level collaborations, both regional and international.

Research students will have a primary and secondary supervisor and the opportunity to network with a large and varied peer group. You will be carrying out your research in the company of eminent figures and be exposed to a steady stream of distinguished researchers from all over the world.

Our status as one of the most prestigious schools in the UK for mathematics attracts highly respected staff. Many of our 60 current academics are leaders in their fields and have been recognised with international awards.

Researchers are encouraged to travel and participate in conferences and seminars. You’ll also be in the right place in Edinburgh to meet distinguished researchers from all over the world who are attracted to conferences held at the School and the various collaborative centres based here. You’ll find opportunities for networking that could have far-reaching effects on your career in mathematics.

Having access to a broad community of researchers means that your work will be well distributed and recognised.

Strong links also exist with life scientists, chiefly through SynthSys (Synthetic and Systems Biology Edinburgh), a multidisciplinary Edinburgh-based centre whose mission is the analysis and design of biochemical systems using theoretical, computational, and biological techniques.

You will enjoy excellent facilities, ranging from one of the world’s major supercomputing hubs to libraries for research at the leading level, including the new Noreen and Kenneth Murray Library at King’s Buildings.

Students have access to more than 1,400 computers in suites distributed across our University’s sites, many of which are open 24 hours a day. In addition, if you are a research student, you will have access to dedicated desk space with monitors and a laptop computer.

We provide all our mathematics postgraduates with access to software packages such as:

• Mathematica

Research students are allocated parallel computing time on ‘Eddie’, the Edinburgh Compute and Data Facility. You can also request use of the BlueGene/Q supercomputer facility for your research.

You will also have access to EPCC, one of Europe’s leading supercomputing centres.

Entry requirements

These entry requirements are for the 2025/26 academic year and requirements for future academic years may differ. Entry requirements for the 2026/27 academic year will be published on 1 Oct 2025.

A UK first class honours degree, or its international equivalent, in an appropriate subject; or a UK 2:1 honours degree plus a UK masters degree, or their international equivalents; or relevant qualifications and experience.

International qualifications

Check whether your international qualifications meet our general entry requirements:

• Entry requirements by country
• English language requirements

Regardless of your nationality or country of residence, you must demonstrate a level of English language competency which will enable you to succeed in your studies.

English language tests

We accept the following English language qualifications at the grades specified:

• IELTS Academic: total 6.5 with at least 6.0 in each component. We do not accept IELTS One Skill Retake to meet our English language requirements.
• TOEFL-iBT (including Home Edition): total 92 with at least 20 in each component. We do not accept TOEFL MyBest Score to meet our English language requirements.
• C1 Advanced ( CAE ) / C2 Proficiency ( CPE ): total 176 with at least 169 in each component.
• Trinity ISE : ISE II with distinctions in all four components.
• PTE Academic: total 65 with at least 59 in each component. We do not accept PTE Academic Online.
• Oxford ELLT : 7 overall with at least 6 in each component.

Your English language qualification must be no more than three and a half years old from the start date of the programme you are applying to study, unless you are using IELTS , TOEFL, Trinity ISE or PTE , in which case it must be no more than two years old.

Degrees taught and assessed in English

We also accept an undergraduate or postgraduate degree that has been taught and assessed in English in a majority English speaking country, as defined by UK Visas and Immigration:

• UKVI list of majority English speaking countries

We also accept a degree that has been taught and assessed in English from a university on our list of approved universities in non-majority English speaking countries (non-MESC).

• Approved universities in non-MESC

If you are not a national of a majority English speaking country, then your degree must be no more than five years old at the beginning of your programme of study.

Find out more about our language requirements:

• Academic Technology Approval Scheme

If you are not an EU , EEA or Swiss national, you may need an Academic Technology Approval Scheme clearance certificate in order to study this programme.

Fees and costs

Tuition fees, scholarships and funding.

Most PhD students in Mathematics receive full scholarships to cover their tuition fees and living costs.

Others may use a combination of the following funding to pay their tuition fees and living costs:

• scholarships
• taking out a loan
• family support
• personal savings
• income from work
• employer sponsorship

Explore sources of funding for postgraduate study

Featured funding

• School of Mathematics funding opportunities
• Research scholarships for international students

UK government postgraduate loans

If you live in the UK, you may be able to apply for a postgraduate loan from one of the UK's governments.

The type and amount of financial support you are eligible for will depend on:

• your programme
• the duration of your studies
• your tuition fee status

Programmes studied on a part-time intermittent basis are not eligible.

• UK government and other external funding

Search for scholarships and funding opportunities:

• Search for funding

Further information

• Graduate School Administrator
• Phone: +44 (0)131 650 5085
• Contact: [email protected]
• School of Mathematics
• James Clerk Maxwell Building
• Peter Guthrie Tait Road
• The King's Buildings Campus
• Programme: Applied and Computational Mathematics
• School: Mathematics
• College: Science & Engineering

Select your programme and preferred start date to begin your application.

PhD in Applied and Computational Mathematics - 4 Years (Full-time)

Phd in applied and computational mathematics - 8 years (part-time), phd in applied and computational mathematics with internship - 4 years (full-time), phd in applied and computational mathematics with internship - 8 years (part-time), application deadlines.

We strongly recommend you submit your completed application as early as possible, particularly if you are also applying for funding or will require a visa. We may consider late applications if we have places available. All applications received by 20 January 2025 will receive full consideration for funding. Later applications will be considered until all positions are filled.

• How to apply

You must submit two references with your application.

Find out more about the general application process for postgraduate programmes:

• Schools & departments

School of Mathematics

Opportunities in the School of Mathematics

Edinburgh Doctoral College Scholarships

The University will offer PhD scholarships for students starting their PhD research at the University in the 2025-2026 academic session.

School of Mathematics Masters Scholarships

The School of Mathematics is offering a number of scholarships for students applying to study a Masters programme in Mathematics. These scholarships cover up to 50% of the programme fee. These awards will be based on academic merit and available to applicants domiciled in the eligible countries.

This article was published on 2024-07-29

• Schools & departments

• Computational methods

Data Science

• Fluid dynamics
• Materials: models and simulation

Mathematical Biology

Nonlinear dynamics and asymptotics.

• School of Mathematics
• Applied and Computational Mathematics

PhD Opportunities

Projects in Applied and Computational Mathematics

The Maxwell Institute Graduate School PhD programme in Modelling, (applied and numerical ) Analysis and Computation MAC-MIGS 2024+ offers great  opportunites for postgraduate research in Applied and Computational Mathematics in Edinburgh. MAC-MIGS 2024+ is a 4-year PhD programme focussed on the formulation, analysis and implementation of state-of-the-art mathematical and computational models.  Consult the MAC-MIGS 2024+ web page  for details of the programme and its application procedure, as well as a list of possible PhD topics .

When submitting your application to the Applied & Computational Mathematics PhD at Edinburgh (see also the  School's Postgraduate Research pages ), you should indicate which projects (up to two) you are interested in.

Other opportunities are available through the Edinburgh Earth, Ecology & Environment NERC DTP (for projects in Geophysical Fluid Dynamics), the Quantum Informatics EPSRC CDT (for projects in Quantum Computing) and the Sensing, Processing, and AI for Defence and Security EPSRC and MoD CDT (for projects in Information Processing). If you are interested in these opportunities, contact possible supervisors who will be able to advise on the best route to secure a PhD place.

From September 2019 to September 2023, the Applied and Computational Mathematics group recruited students for the prestigious EPSRC funded Centre for Doctoral Training  MAC-MIGS .

PhD projects are offered in all research areas represented by our staff. For selected  examples of recent PhD projects supervised, please see the links below.

Computational Methods

Fluid dynamics, materials: models and simulation.