Postgraduate study

Mathematical Modelling, Analysis and Computation PhD

Awards: PhD

Study modes: Full-time

Funding opportunities

Placements/internships

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

You will benefit from:

  1. 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
  2. extensive experience of collaborative and interdisciplinary work through projects, modelling camps, industrial sandpits and internships
  3. outstanding early-career training, with a strong focus on entrepreneurship
  4. 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 comprised of mathematicians from the University of Edinburgh and Heriot-Watt University, as well as computer scientists, biologists, engineers, physicists and chemists providing their own disciplinary expertise, and these are also complemented by many industrial and government partners.

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.

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

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: total 92 with at least 20 in each section

  • PTE Academic: total 61 with at least 56 in each of the Communicative Skills scores

  • CAE and CPE: total 176 with at least 169 in each paper

  • Trinity ISE: ISE II with distinctions in all four components

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, PTE Academic or Trinity ISE, 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.

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.*

(*Revised 8/11/2018 to provide more accurate information on English language qualifications expiry dates. Revised 22/03/2019 to provide more accurate/comprehensive information.)

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:

  • Graduate School
  • 5319, James Clerk Maxwell Building
  • School of Mathematics
  • 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

  • Graduate School
  • 5319, James Clerk Maxwell Building
  • School of Mathematics
  • The King's Buildings Campus
  • Edinburgh
  • EH9 3FD