The aim of the PhD programmes in the Department of Mathematics is to offer an advanced research training in mathematics of high quality and to prepare doctoral students for their future career. The breadth of expertise in the Department, together with a thriving culture of research, international visitors, seminars and workshops, makes the Department one of the best universities in the UK to undertake a postgraduate research programme.

PhD Programmes

The Department offers two PhD programmes, PhD in Mathematics and PhD in Interdisciplinary Mathematics. Other programmes are offered by (maths-related) Doctoral Training Centres who have their own web-sites and are not described here. The PhD in Mathematics is aimed at those students who wish to specialise in Mathematics, whether it be in pure and/or applied mathematics. The PhD in Interdisciplinary Mathematics is aimed at those whose interests lie at an interface between mathematics and its applications. Students studying for this programme will have a supervisor in the Mathematics department as well as in a second University Department in MiR@W (Mathematics Interdisciplinary Research at Warwick) given that the focus of the Interdiciplinary Mathematics PhD is the application of mathematical techniques to problems in another discipline.

PhD Training

All students are required to undergo training in Year 1 and are encouraged to make use of further training opportunities available in subsequent years. Training ranges from gaining a broader knowledge of mathematics through taught modules, seminars and workshops, to enhancing your professional and transferrable skills. Our aim is to produce excellent PhD students who have undertaken high quality original research and who are well-prepared for a career, either in academia or elsewhere.

Supervision and Progression

It is the role of the supervisor(s) to guide the student and discuss the research and progress on a regular basis. A student's progress will additionally be monitored by a PhD Progress Board at various stages during the studies to ensure that supervision and support mechansims are working and that satisfactory progress is being made. The primary purpose of the Board is to help both the student and the supervisor work together so that an excellent PhD thesis is produced by the student in a timely fashion. Membership of the Board comprises the Head of Department (Chair), the Director of Graduate Studies, the Director of MSc Studies and at least one other senior academic. The Board will meet formally three times a year (in March, June and September) to discuss students' progress and provide advice for the supervisors (or students) as required. In the worst case scenario, failure to make satisfactory progress towards the PhD may lead to a recommendation to remain on, or to transfer to the MPhil degree, or to withdraw from postgraduate studies. Such recommendations are made for the mutual benefit of all concerned parties.

Completion

Students are expected to submit their thesis in around 3.5 years which reflects the length of the funding available for many of the funded students. An extension beyond four years of registration will only be given by the University in exceptional circumstances (e.g. medical).

PhD Year 1

The first year of your studies will provide an essential foundation of necessary mathematical and generic tools to enable you to complete a successful and rewarding PhD, as well as preparing you for your future career. During Year 1 you will be required to undergo training ranging from gaining a broader knowledge of mathematics through taught modules, seminars and workshops, to enhancing professional skills. All PhD students are initially registered on the MPhil degree. Subject to satisfactory progress, students will be upgraded to the PhD after approximately 9 months of full time enrolment.

Initial Project Outline

In some cases, it may be possible to clearly define your project at the outset of your studies. In many other cases, a more precise project definition may not emerge until later in your studies. In both cases, the very nature of research means that initial project outlines will necessarily evolve as you gain a deeper understanding of your subject area and as the research proceeds. It is not unusual in mathematics to change the direction of the research if difficulties arise that appear intractable. Nevertheless, it is important that students document an initial project outline/plan in collaboration with the supervisor within the first few weeks of the programme. The outline/plan should identify goals and key tasks for the first year of the PhD studies and should include:

• A brief outline of the project. For some projects this will be initially quite general. For others, it may be possible to define the project in more detail from the outset. As noted above, deviations from the project outline are possible. Nevertheless, documenting the project outline at this stage will enable you to give some initial consideration to your project and concurrently provide focus for the first year of study.
• Taught courses that you will attend (see below). All first year PhD students are required to take 100 hours of training, which typically consists of 3 courses with structured examinations or other assessment. These courses should not be directly related to your specific PhD topic. In some cases, your supervisor may require you to take additional courses due to the specific needs of the project, your individual circumstances or for your general broader training. In all cases, you should discuss the choice of courses with your supervisor before registering for them. Note that Term 1 courses start in week 1 and registration is required by the end of week 3 in the Autumn Term. Satisfactory marks on assessed courses will be required for progression.
• Introductory reading list. These are texts (e.g. journal papers, book chapters, articles) recommended by your supervisor that will help to increase your understanding of the project area and related fields.
• A list of seminars/workshops/conferences etc that you are likely to attend. Again this should be the outcome of the discussions with your supervisor. Attendance at the Postgraduate Seminar and at relevant Friday Colloquia is expected; the Colloquia being aimed at both staff and postgraduate students. In addition, many research groups also hold their own seminar series which you will usually be expected to attend as part of your training.
• Other tasks and milestones. This should briefly document what you plan to do in the Autumn, Spring and Summer terms and could include developing your knowledge about a mathematical technique, or working on a specific problem or set of smaller problems. Transferable skills training could be listed under such a heading.

A standard form to capture the above information can be downloaded here. The form should be signed by both the student and the supervisor and returned to the Postgraduate Coordinator by the end of Week 4.

Taught Courses

All first year PhD students are required to take 3 courses (or modules) with structured examinations or other assessment. These courses can be taken from the following:

• Higher level taught Maths modules (e.g. MA4xx, MA5yy or MA6zz).
• Masters level modules offered by Doctoral Training Centres (MASDOC, Complexity, MOAC, Systems Biology).
• PhD level courses given through the EPSRC sponsored Taught Course Centre (TCC). This is a collaborative project between Bath, Bristol, Imperial, Oxford and Warwick that aims to share postgraduate lectures in all areas of mathematics via Access Grid Technology - an advanced interactive video conferencing facility that enables students from remote sites to participate in a lecture in a specially equipped room (B0.06). Up-to-date timetable and links to module information are available from the web-page.

PhD students may additionally be required to take a small number of undergraduate modules from earlier years (e.g. MA3xx) to complete a gap in the student's knowledge. Whilst these may be formally assessed and a satisfactory mark required for progression, these would not count towards the minimum of 100 hours taught course requirement described above.

Professional and Transferable Skills

In your first year, and to a lesser extent in subsequent years, you will be required to undertake professional and transferable skills training detailed here. The focus in the first year is on communication skills, i.e. how to give an engaging seminar, writing skills, time management, networking and team building. New postgraduate research students are additionally required to maintain a personal web-page.

Progress Report

First year PhD students are required to submit a progress report to the supervisor and the Postgraduate Coordinator by the end of week 2 of the Summer Term. Timings will be adjusted for students who do not begin their studies by October. At this stage it is not expected that students will have completed original research, but they should be able to demonstrate an awareness and understanding of the relevant literature.The full report consists of 2 main components:

[A] A report that demonstrates your understanding of your specific research field and of the progress you have made in the initial period of study. It is not expected that you will have undertaken any original research at this stage, but the report should show an awareness of a research field. Where possible, the report should additionally describe where research might lead in the next one or two years. The report is not expected to exceed 20 pages, it may be shorter if you have taken a large number of taught modules. The precise format of this report can vary from student to student 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.

The report is an important element of your PhD training programme, contributing to for example, the enhancement of both report writing (an essential research skill) and more generic skills (e.g. time management). It is therefore important that the report is well presented and written in LaTeX.

[B] A description of your academic activities including books and papers read, courses and conferences attended (including generic skills training), participation in seminars and study groups, etc. This description should reflect the activities documented in your initial project outline (above).

Progression

The purpose of the progress report ([A] and [B] above) is to provide evidence to third parties about your initial period of study. The report is considered by the supervisor, the Director of Graduate Studies and the PhD Progress Board. The Board meets at the end of Term 3 when it will consider your report together with examination results and other assessments from the courses that you have taken. The primary objective of the exercise is to provide feedback on progress and it is part of the supervisor's role to do this on behalf of the Progress Board. Subject to satisfactory progress, the Board will recommend that students will be upgraded to the PhD.

In some cases, the Board may not feel there is sufficient evidence to take a view on the progress of a student. In these circumstances, a student may be required to undergo an oral examination normally conducted by the supervisor and the Director for Graduate Studies and/or another member of staff, usually by the middle of September. The September PhD Progress Board will consider the results of the oral examination in deciding whether a student should then be upgraded to the PhD or remain on the MPhil. Students who remain on the MPhil will after the September Board have 1 further year to complete their MPhil thesis.

Continued registration is subject to satisfactory progress. In exceptional circumstances, the Board may require that a student withdraw from the programme.

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. 

Progression

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.

YEAR 3

By the beginning of the third year, many PhD students will have a clear idea about the direction of their thesis. Some may have already made significant in-roads into the thesis, for example, by drafting a few chapters. Whatever the situation, students should be thinking about their progress and what they have left to do to complete their thesis. Setting clear achieveable milestones with your supervsior to help you monitor your progress will help you to produce your thesis in a timely fashion.

As for earlier years, you are encouraged to further develop your skills as part of your training. If you have not already presented your work at a formal or informal gathering, then you should do so as this is helpful preparation for your viva and any future career.

Draft Thesis

The normal expectation is that a PhD will be completed within 3.5 years. Given the nature of mathematical research, some students will take a shorter time period, others longer. The University will extend a student's registration beyond 4 years only under exceptional circumstances. If you do not expect to submit before the end of your funded period or you are self-reliant for funding you will also need to have considered how you will support yourself for the duration of your studies.

To help you to complete the thesis in a timely fashion, third year PhD students must submit a draft of their thesis to the supervisor and 2 copies to the Postgraduate Co-ordinator at the end of week 8 of Term 1. It is noted that not many students will be in a position to submit a near to complete draft thesis by this stage. What you do submit should be a matter of discussion between you and your supervisor. However at a minimium one would expect a detailed thesis plan and significant progress in the writing of one or two chapters. The plan should demonstrate that you have carefully considered the contents and structure of the thesis and already have (close to) sufficient material (including original research) for the thesis. Such a plan should contain:

• a list of the chapter (and lower-level) headings, with a description of the content of the chapters where not included
• a rough indication of the number of pages for each section/chapter
• progress made towards each chapter/section e.g. 60% of chapter complete (and included in draft), published in conference proceedings, analysis/results complete, more analysis required
• indication of how long each section/chapter will take i.e. a schedule of work with milestones
• expected submission date

As for previous years, it may also be appropriate to add information about any courses taken, texts read, reading groups, seminars and conferences attended.

Progression

All PhD students will meet a member of staff to discuss the draft/detailed thesis plan as appropriate. The member of staff will be chosen by the Director of Graduate Studies in consultation with the supervisor. The meeting will normally take place by week 5 of Term 2 and feedback will follow within a short period. The meeting will additionally help to develop links between the student and a member of staff other than the supervisor.

In some cases, where further information is required to establish the level of progress of a student, s/he may 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 earlier years continued registration on the PhD is subject to satisfactory progress.

YEAR 4

Students are expected to submit their thesis in around 3.5 years which reflects the length of funding available for many of the funded students. The department makes every effort to ensure that students submit within this time-frame. In particular, the procedures described for year 3 PhD students will also apply to year 4 students who have not yet submitted a PhD thesis. Extensions beyond four years of registration will only be given by the University in exceptional circumstances (e.g. medical).

• Normally at least a first class undergraduate degree (or the equivalent from overseas) in one of the contributing subjects, and a firm background in Mathematics. Clear evidence that the applicant is sufficiently prepared to undertake graduate-level research without further coursework.* At least one member of the department must express a willingness to supervise the applicant's thesis.
• Transcripts from your university-level study
• Research proposal (if you are a MPhil or PhD student)
• Personal statement
• IELTS 6.5

Scholarships

• Chancellor's International Scholarships