Postgraduate study

Mathematical Analysis & its Applications

Awards: PhD

Study modes: Full-time

Mathematical Analysis & its Applications is the four-year programme associated with the Maxwell Institute Graduate School in Analysis and its Applications (MIGSAA), a Centre for Doctoral Training that provides high quality instruction in analysis and the applications of analysis to a wide range of areas.

MIGSAA has been made possible by a grant from the UK's Engineering and Physical Sciences Research Council and the Scottish Funding Council. The programme is delivered in collaboration with Heriot-Watt University.

PhD study in MIGSAA may be undertaken with over 40 supervisors and on topics ranging from pure analysis to applied mathematics relevant for scientific, engineering, environmental or social challenges.

Most projects will relate to one of the following themes:

  • Harmonic Analysis
  • Partial Differential Equations (PDEs)
  • Stochastic Processes
  • Mathematical Modelling
  • Atomic and Molecular Systems
  • Fluid Dynamics
  • Applied Probability

As opposed to a standard PhD, MIGSAA students are admitted to the programme (rather than with a specific supervisor), and take PhD training courses and projects over their first year, which help shape their perspective, leading to a match with a supervisor in the second half of Year 1.

The research project directed by the supervisor is still the centrepiece of the PhD, but this is augmented by an on-going training programme in Years 2-4 of the student’s studies.

The MIGSAA cohort will consist of approximately 12 students per year, however students are also part of the larger PhD community at both the University of Edinburgh and Heriot-Watt University, with access to supervisors from both institutions as well as MIGSAA's industrial partners.

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. The collaboration between MIGSAA's partner institutions maximises the opportunities available for students to gain a breadth of knowledge from leading experts.

Our intention is that all MIGSAA students gain awareness of the full intellectual spectrum of research in analysis and its applications, including familiarity with theoretical issues, stochastic techniques, numerical methods and examples of how analysis problems impact the sciences and engineering. Therefore we expect all students to take some training spanning these areas – even though their eventual PhD thesis may specialise in only one or two.

More details of the training available on the programme are available on the MIGSAA website.

In the first year, the MIGSAA cohort is based at the International Centre for Mathematical Sciences in the centre of Edinburgh. This affords a number of opportunities to engage with the international mathematical community.

MIGSAA students 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 collaborating institutions and the various collaborative centres based here. You’ll find opportunities for networking that could have far-reaching effects on your career in mathematics.

Further, MIGSAA students are fully registered at both collaborating institutions and entitled to use the facilities of both.

A UK 2:1 honours degree, or its international equivalent, in an relevant subject, or relevant qualifications and experience.

International qualifications

Check whether your international qualifications meet our general entry requirements:

English language requirements

All applicants must have one of the following qualifications as evidence of their English language ability:

  • an undergraduate or masters degree, that was taught and assessed in English in a majority English speaking country as defined by UK Visas and Immigration

  • 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(A): 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

Degrees taught and assessed in English must be no more than two and a half years old at the beginning of your degree programme. Language tests must be no more than two years old at the beginning of your degree programme.

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.

See Scholarships and Student Funding Services for other funding opportunities:

  • 15 South College Street
  • Central Campus
  • Edinburgh
  • EH8 9AA

We encourage you to apply at least one month prior to entry so that we have enough time to process your application. If you are also applying for funding or will require a visa then we strongly recommend you apply as early as possible. We may consider late applications if we have places available, but you should contact the relevant Admissions Office for advice first.

You must submit two references with your application.

MIGSAA is able to offer a number of fully-funded places to well-qualified applicants. To maximise your chances of securing funding, we recommend you apply before 15 December, and in any case by 31 January. Applicants successful in the initial screening will be called to interview.

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

Further information

  • 15 South College Street
  • Central Campus
  • Edinburgh
  • EH8 9AA