Study modes: Full-time, Part-time
Programme website: Algebra
Our algebra and number theory research group is made up of international leaders in the field who have won between them the European Mathematical Society Prize, the Whitehead Prize of the London Mathematical Society, the Waclaw Sierpinski Prize of the Polish Academy of Sciences and the Berwick Prize of the London Mathematical Society.
Our members have given invited lectures at both the International Congress of Mathematicians and the European Congress of Mathematicians.
The School of Mathematics is a vibrant community of more than 60 academic and related staff supervising 60 students.
Our research centres on the following areas:
- non-commutative ring theory
- non-commutative algebraic geometry
- the geometry of algebraic numbers
- Lie-theoretic representation theory
- quantum algebra
- category theory
Much of our research is related to the areas of geometry and topology, and mathematical physics, which has lead to the formation of the Hodge Institute:
Through the School’s membership of the Maxwell Institute, we present regular seminars, and run our own informal seminars and colloquia. We also serve on editorial boards of various international journals.
All of our PhD students take part in international conferences and symposia, and in part thanks to this global exposure, many have gone on to postdoctoral positions throughout the world.
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.
You will enjoy excellent facilities, ranging from one of the world’s major supercomputing hubs to generous library provision 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 the University’s sites, many of which are open 24 hours a day. In addition, if you are a research student, you will have your own desk with desktop computer.
We provide all our mathematics postgraduates with access to software packages such as Maple, Matlab and Mathematica. Research students are allocated parallel computing time on ‘Eddie’ – the Edinburgh Compute and Data Facility. It is also possible to arrange use of the BlueGene/Q supercomputer facility if your research requires it.
These entry requirements are for the 2023/24 academic year and requirements for future academic years may differ. Entry requirements for the 2024/25 academic year will be published on 2 October 2023.
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.
Check whether your international qualifications meet our general entry requirements:
English language requirements
You must demonstrate a level of English language competency at a level that will enable you to succeed in your studies, regardless of your nationality or country of residence.
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.
- 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 62 with at least 59 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:
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).
If you are not a national of a majority English speaking country, then your degree must be no more than three and a half 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.
- School of Mathematics funding opportunities
- Research scholarships for international students
- Principal's Career Development PhD Scholarships
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 residency status.
Programmes studied on a part-time intermittent basis are not eligible.
Other funding opportunities
Search for scholarships and funding opportunities:
Select your programme and preferred start date to begin your application.
PhD Algebra and Number Theory - 3 Years (Full-time)
PhD Algebra and Number Theory - 6 Years (Part-time)
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.