Patrick E. Farrell

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Short biography

On this page I collect some friendly advice for potential applicants for the DPhil (PhD) programme in Mathematics at the Mathematical Institute, Oxford. Most of it applies to any applicant, but it is written from my perspective as a potential supervisor.

Timelines

DPhil applications are typically due in early January each year; the exact date varies, so check the official course page. There are other application windows, but it’s important to apply by the January deadline, as later applications are not considered for funding.

Faculty receive the applications towards the end of January. We then decide whom to interview, and organise online technical interviews for mid-February. The interview results then go into a database for the graduate admissions committee to make offers and allocate funding. Offers are made over the course of the spring and summer for entry the following October.

It is not unusual for applicants to first receive an unfunded offer that subsequently gets upgraded to a funded offer. So don’t be too quick to decline an unfunded offer, and if you hold another offer with a deadline for your decision, let the department know.

Qualifications

Applicants typically require an outstanding first-class undergraduate degree to be competitive for DPhil entry.

The university maintains a list of international qualifications and how they compare with a UK first-class degree. If your degrees are not all from the UK, please consult this to get a sense of how your results will translate.

I have had very good experiences with students whose undergraduate degree was not in mathematics, but rather in a related subject (physics, engineering, etc). However, those students had done MSc courses in mathematics first. If you are interested in applying and have not formally studied a course in a mathematics department, consider first applying to the MSc in Mathematical Modelling and Scientific Computing or the MSc in Mathematical Sciences, both of which are excellent preparation for doctoral study.

Applying

An application consists of:

The best reference letters are written by someone who knows you well (e.g. has worked with you in a research capacity) and can comment directly on your aptitude for research. Few applicants have three such referees, and it is entirely typical that some letters are more detailed than others.

In your personal statement, it is good to try to convey

The best statements point to concrete evidence, such as projects, theses, code, or results.

When you apply, please list me as a potential supervisor. Otherwise, I may not see your file!

Interviews

The interviews are technical, intended to assess your preparedness for doctoral study in the proposed subject (in my case the numerical solution of partial differential equations). The questions do not focus on past projects. More details will be sent if you are invited to interview. The best preparation is to revise the courses you have previously taken on vector calculus, functional analysis, partial differential equations, and numerical analysis.

Funding

At the time of writing (2026), the department has roughly 50 DPhil scholarships to award each year. Some of them are restricted to home students, but many are not. They are very competitive but not impossibly so. If you submit by the January deadline, you are automatically considered for all department-administered funding for which you are eligible.

There are other potential funding sources, not administered by the department. These often depend on nationality, such as the China Oxford Scholarship Fund, Commonwealth Scholarships, and Rhodes Scholarships. These usually require separate applications, often with deadlines well before the department’s January deadline, so check them early.

Project selection

Some funding sources are tied to specific projects (e.g. studentships funded by the European Research Council, UK Atomic Energy Authority, or Science and Technology Facilities Council). These are usually advertised separately.

For other funding sources, the research project is usually decided on together by the supervisor and student over the summer before the DPhil starts. I will send you a list of potential doctoral projects describing my current interests, with references. We can then discuss each one, decide which interests you most, and iterate on it until we are both excited by the idea.

Further questions

Please feel free to reach out if you have questions!

I do not generally reply to generic emails that could be sent to many people; please personalise your message.

If you wish to ask whether your background would be suitable, please include your full CV and any available degree transcripts (including incomplete ones).