Postgraduate study
Edinburgh: Extraordinary futures await.

Mathematical Modelling, Analysis and Computation PhD

Awards: PhD

Study modes: Full-time

Funding opportunities


On this integrated degree you will join the broader Maxwell Institute Graduate School in its Bayes Centre home.

You will benefit from:

  • dedicated academic training in subjects that include mathematical analysis, computational mathematics, multi-scale modelling, model reduction, Bayesian inference, uncertainty quantification, inverse problems and data assimilation, and machine learning

  • extensive experience of collaborative and interdisciplinary work through projects, modelling camps, industrial sandpits and internships

  • outstanding early-career training, with a strong focus on entrepreneurship

  • a dynamic and forward-looking community of mathematicians and scientists, sharing strong values of collaboration, respect, and social and scientific responsibility

You will integrate into a vibrant research environment, closely interacting with many academics, comprising mathematicians from the University of Edinburgh and Heriot-Watt University. You will also engage with computer scientists, biologists, engineers, physicists and chemists providing their own disciplinary expertise. The programme is also complemented by many industrial and government partners.

Further information about the programme and applications is available on our website:

Year 1

You will take specific core courses (30 credits), group project modules, and additional instruction either from Scottish Mathematical Sciences Training Centre (video+ on-site tutorials) or else from selected approved (level 11+) modules from the two Universities. The remainder of your studies is supervised research work.

Years 2-4

You will receive additional coursework and training (30 credits per year) with the remaining work being supervised research.

Week-long Industrial Sandpit

During each year, you will take part in a week-long Industrial Sandpit in conjunction with MAC-MIGS industrial partners to give an insight into how mathematics is used.

Work placements are negotiable and encouraged.

Visits/internships are possible at a range of some 30 companies and government agencies, with interdisciplinary partners across the sciences and engineering, and with our network of a dozen international academic partners in the US and Europe.

Advanced academic coursework, training in presentation and scientific writing, training in responsible research and innovation, advanced computing skills, training in equality, diversity and inclusion, training in entrepreneurship, project training.

Our students are housed in the Thomas Bayes Centre in Year 1.

In years 2-4 you are typically based at either the University of Edinburgh's King's Buildings campus or at the Heriot-Watt University Edinburgh campus, near Riccarton.

Access to high performance computing hardware and software will be made available, as needed for project work.

Companies in a vast range of areas, as well as government agencies, are very keen to develop modelling-based approaches and to incorporate data science into their existing models.

Prospective students are recommended to read the below government reports which make clear the tremendous scope for this area in the coming years.

Universities are also extremely keen to hire staff who can teach and conduct high quality research programmes in mathematical modelling, analysis and computation.

The Bayes Centre is at the heart of data-driven scientific and mathematical activity in Edinburgh. It provides a dynamic interdisciplinary research environment that will provide a tremendous variety of opportunities for the PhD students to interact with world-leading researchers, visitors and workshops at ICMS, with startup companies, with data scientists and with high performance computing specialists at the Edinburgh Parallel Computing Centre.

These entry requirements are for the 2024/25 academic year and requirements for future academic years may differ. Entry requirements for the 2025/26 academic year will be published on 1 Oct 2024.

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:

English language requirements

Regardless of your nationality or country of residence, you must demonstrate a level of English language competency at a level that 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 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 five years old* at the beginning of your programme of study. (*Revised 05 March 2024 to extend degree validity to five years.)

Find out more about our language requirements:

Read our general information on tuition fees and studying costs:

This programme is associated to the MAC-MIGS Centre for Doctoral Training, which is funded by a grant from the Engineering and Physical Sciences Research Council (EPSRC). UK-based students enrolled in MAC-MIGS will receive their stipends from EPSRC.

There are also supplementary financial resources which can fund the participation of students from other countries. See the programme website for more details.

Search for scholarships and funding opportunities:

  • School of Mathematics
  • James Clerk Maxwell Building
  • Peter Guthrie Tait Road
  • The King's Buildings Campus
  • Edinburgh
  • EH9 3FD

We review applications on a rolling basis. Applications may be submitted at any time, but are mainly considered in the period 1 December to 15 March.

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

Further information

  • School of Mathematics
  • James Clerk Maxwell Building
  • Peter Guthrie Tait Road
  • The King's Buildings Campus
  • Edinburgh
  • EH9 3FD