A Master’s degree (Merit or Distinction) in Mathematics, Applied Mathematics, Statistics, Theoretical Physics, or a closely related quantitative discipline.

Applicants must also hold a Bachelor’s degree with at least a UK 2:1 (Upper Second-Class Honours) or international equivalent in Mathematics or a related field.

Strong preparation in pure mathematics, applied mathematics, statistics, or computational methods is essential, depending on the research area.

Candidates with backgrounds in Engineering, Physics, or Computer Science may be considered if they demonstrate substantial mathematical or analytical training.

International qualifications must be equivalent to UK academic standards (verification via UK ENIC may be required).

Top universities such as Cambridge, Oxford, Imperial College London, Warwick, and UCL typically expect first-class undergraduate performance and Distinction-level postgraduate results for admission.

Work experience is not required for PhD entry, as admission is based on academic and research excellence.

However, research or teaching experience can enhance an application, particularly if you have served as a research assistant, teaching assistant, or published mathematical work.

Applicants with professional experience in data analysis, quantitative modelling, or computational research may also be considered favourably.

For applied mathematics or statistics pathways, experience in programming (e.g., Python, MATLAB, R, C++) or mathematical software (e.g., Maple, Mathematica) is beneficial.

IELTS (Academic): Overall score of 6.5–7.0, with no component below 6.0.

TOEFL iBT: Overall score of 90–100, with section scores typically above 22.

PTE Academic: Overall score of 62–70, with no skill below 62.

Applicants who completed their previous degrees in English or in a majority English-speaking country may be exempt from testing.

Highly selective research departments (e.g. Oxford or Cambridge) may require IELTS 7.0 or higher.

Official academic transcripts and degree certificates from all higher education institutions attended (with certified English translations if applicable).

Research proposal (usually 1,000–2,000 words) summarising your research interests, problem statement, mathematical methods, and potential supervisor alignment.

Personal statement detailing your academic background, mathematical interests, and motivation for pursuing doctoral research.

Curriculum vitae (CV) listing education, research experience, technical or programming skills, publications, and teaching roles.

Two or three academic references, at least one from a previous supervisor or lecturer familiar with your research ability.

Proof of English language proficiency (if applicable).

Some departments may request a sample of mathematical work (e.g., published paper, dissertation chapter, or theoretical essay).

For highly technical or interdisciplinary projects, applicants may be asked to attend an interview or complete a research aptitude test.