Mathematics: Fully Funded EPSRC PhD Scholarship: Non(computability) in Linear Algebra

Closing date: Apply as soon as possible

Key Information

This scholarship is funded by the Engineering and Physical Sciences Research Council (EPSRC).

*The deadline for full consideration of applications is 1 August 2021. We will accept applications until the position is filled.

Start date: October 2021 or January 2022

Project Supervisor: Dr Arno Pauly

Project description:

Algorithmic questions pertaining to linear algebra are predominately studied by either taking the underlying field to be discrete (e.g. the rationals) or by forgoing a rigorous model of computation and instead focussing on the development of concrete numerical algorithms. Computable analysis provides a convenient framework to simultaneously consider non-discrete fields (e.g. real or complex numbers) and a rigorous model of computation (ultimately founded on Turing machines). However, only few initial investigations have been undertaken so far, and the field is wide open for research by an ambitious PhD student.

Many interesting computational problems in linear algebra will not be computable in general (this holds e.g. for solving systems of linear equations, finding the rank of a matrix or computing the orthogonal complement of a subspace in infinite dimensions). In these cases, it is very interesting to determine how non-computable the problem is, using the framework of Weihrauch degrees. Such results let us draw conclusions to what extent additional input information or a relaxed notion of algorithm can resolve the non-computability.


Candidates must have a First, Upper Second Class Honours or a Master’s degree with Merit, in a relevant discipline.

For candidates whose first language is not English, we require IELTS 6.5 (with 6.0 in each component) or equivalent. Please visit our website for a list of acceptable English language tests. We prefer candidates to have already met the English Language requirements at the point of application, although this is not a requirement.

This scholarship is open to candidates of any nationality.

NB: If you are holding a non-UK degree, please see Swansea University degree comparisons to find out if you meet the eligibility. 

If you have any questions regarding your academic eligibility based on the above comparison, please email with the web-link to the scholarship(s) you are interested in. 


This four-year fully funded scholarship covers UK tuition fees and an annual stipend of £15,245.

Research Training Support Grant of £1,000 per annum is also provided. 

How to Apply

To apply, please complete and submit the following documents to

  • Research Scholarship Application Form 2021
  • Equality, Diversity and Inclusion Monitoring Form_Ffurflen Monitro
  • Academic References – all scholarship applications require two supporting references to be submitted. Please ensure that your chosen referees are aware of the funding deadline, as their references form a vital part of the evaluation process. Please either include these with your scholarship application or ask your referees to send them directly to
  • Academic Transcripts and Degree Certificates – academic transcripts and degree certificates must be submitted along with the scholarship application by the funding deadline. We will be using these to verify your academic qualifications.
  • A recent CV
  • Candidates should use the ‘Supplementary Personal Statement’ section of the application form to explain why the award they are applying for particularly matches their skills and experience and how they would choose to develop the project.

Please email the documents with ‘EPSRC DTP 21 LINEAR ALGEBRA SCHOLARSHIP 2021-2022’ in the email subject header.

Informal enquiries are welcome by emailing Dr Arno Pauly (