Applied and Computational Mathematics PhD

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:

• Maple
• Matlab
• 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.

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:

• English 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.

• Academic Technology Approval Scheme

Tuition fees

Award	Title	Duration	Study mode
PhD	Applied and Computational Mathematics	4 Years	Full-time	Tuition fees
PhD	Applied and Computational Mathematics	8 Years	Part-time	Tuition fees
PhD	Applied and Computational Mathematics with Internship	4 Years	Full-time	Tuition fees
PhD	Applied and Computational Mathematics with Internship	8 Years	Part-time	Tuition fees

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
• borrowing money
  • 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