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PhD Year 2

The second year can often be the most difficult. Whereas the first year provides you with a more structured training with background reading required, broader and research-specific courses available, initial problems to work on and/or mathematical tools to learn or enhance, the second year should be when you use your acquired skills in earnest and make progress on your PhD topic. Mathematical research is not however always that straightforward and despite the best of your efforts and your supervisor's guidance, you may need to take a step back before making further progress. It is therefore essential that you meet regularly with your supervisor to discuss your progress.

As for your first year, you are strongly encouraged to continue enhancing your research and more generic skills. Opportunities will arise (e.g. presenting you work at a seminar group or workshop or externally at conferences) and these should be discussed with your supervisor. Opportunities for generic skills training are available from various sources and taking advantage of these should help you in your future career (see Transferable Skills).

Taught Courses

PhD level courses are still available through the Taught Course Centre (TCC). A range of other taught modules can also be taken on the advice of your supervisor.

Progress Report

Second year PhD students are required to submit a report to their supervisor an 2 copies to the Postgraduate Co-ordinator by the end of week 2 of Term 2. The full report consists of four main components:

[A] A report, approximately 20 pages, that demonstrates your understanding of your research topic and of the progress you have made to date. The precise format of this report can vary and could include one or more of the items from the non-exhaustive list below:

  • review of a book or mathematical papers,
  • notes on a proof of a difficult theorem,
  • description of conducted experiments or simulations,
  • computed examples,
  • draft of a proof of a new theorem,
  • a research paper.

The report is an important element of your PhD training programme and should be well presented and written in LaTeX.

[B] A description of your academic activities including texts read, courses and conferences attended (including generic skills training), participation in seminars and study groups, etc. (approximately 5 pages).

[C] A proposed title of the future thesis

[D] A brief description of the anticipated content of the thesis, for instance titles of chapters, abstract, etc.

The precise format of the report will be defined by the supervisor in consultation with the student.


The purpose of the report ([A] to [D] above) is to provide evidence to a third party about:

  • progress towards more precisely defining and embarking upon a subject suitable for a PhD thesis
  • to facilitate communication between the student and another member of staff different to the supervisor(s)
  • suitability for the PhD programme.

All students will meet a member of staff to discuss the report by week 5 of Term 2. The staff member will be chosen by the Director of Graduate Studies in consultation with the supervisor. Feedback will follow within a short period.

In some cases, the report may not provide sufficient evidence to come to a clear positive conclusion about a student's progress. In these circumstances, the student will be required to undergo an oral examination normally conducted by the supervisor and the Director for Graduate Studies. The outcome of the oral examination will be reported to the PhD Progress Board. As in the first year, continued registration on the PhD is subject to satisfactory progress. In exceptional circumstances, the Board may recommend that a student should transfer to the MPhil degree, or withdraw from the programme.