PhD Pure Mathematics

Please note for the majority of projects where experimentation requires further resource: higher fee bands (where quoted) will be charged rather than the base rate for supervision, administration and computational costs. The fees quoted above will be fully inclusive and, therefore, you will not be required to pay any additional bench fees or administration costs.

All fees for entry will be subject to yearly review and incremental rises per annum are also likely over the duration of the course for UK/EU students (fees are typically fixed for International students, for the course duration at the year of entry). For general fees information please visit: postgraduate fees . Always contact the Department if you are unsure which fee applies to your project.

Together with EPSRC and other national funding sources, the Department currently provides financial support to some 60 postgraduate students every year (approximately 15 new students per year). EPSRC DTA research studentships are available in all areas for UK and EU students. Students who are normally resident in the EU but not in the UK are eligible for EPSRC PhD studentships, but the awards in such cases currently cover only the course fees, not maintenance stipends.

In addition, about eight departmental scholarships are also available each year to PhD students. PhD students may also have the opportunity to help in teaching undergraduate examples classes, for which they are paid. For details of all available awards, please visit the Department's website .

Studentships are also available from the Heilbronn Doctoral Training Partnership

Applicants should have, or expect to obtain before the start of the course a:

• 1st or upper 2nd class 4 year undergraduate degree (e.g. MMath) degree (or an equivalent overseas qualification) in a mathematical subject
• MSc with Merit or Distinction (or an equivalent overseas qualification) in a mathematical subject.

In some research areas, a background in physics, engineering or computer science is also acceptable.

All applicants will need to demonstrate competency in English language. Applicants who do not already possess an acceptable English Language qualification will need to take a recognised test and attain the required English Language score:

IELTS:  At least 6.5 overall with 6.0 in the written component and no other sub-test below 5.5.

TOEFL iBT:  At least 90 overall with 20 in the written component and no other sub-test below 20. We do not accept 'MyBestScore'.

Pearson Test of English (PTE): At least 58 overall with 50 in the written component and no other sub-test below 42.

Further information on language requirements can be found on our website . 

Pre-sessional English: We also accept successful completion of a pre-sessional English course run by the University Language Centre to meet our English language requirements.

Some English Language test results are only valid for two years. Your English Language test report must be valid on the start date of the course.

We consider your full academic history including which course units you have taken and the marks obtained. Even if you have met our minimum entry requirements, we will take into account your marks in relevant undergraduate and postgraduate taught course units in our final decision making. We pay particular attention to any evidence of research experience, for example, undergraduate projects, summer internships and MSc theses. 

If you graduated more than three years ago, we will also consider the information contained on your CV and any relevant work experience you have to assess if you are still able to fulfil the entry criteria.

An interview is required for entry to this programme of study. Shortlisted applicants will be contacted by the admissions team.

CAS Information

Please upload a copy of your current valid passport with your application showing the photograph page with your application. For CAS purposes, this must show your full name, date of birth, nationality, passport number and the date the passport is valid until, which must be later than the date of your planned arrival in the UK, and the start date of your course.

If you have previously studied in the UK on a Tier 4 visa as an undergraduate or postgraduate student, please send a copy of your previous CAS statement to us as it will assist with the issue of your new CAS statement. This includes study in the UK on study abroad programmes and any study that you did not complete.

You cannot use your CAS to apply for a visa more than three months before the start date of your course. The Admissions Team will contact you at the appropriate time.

Your CAS number is only valid for one Tier 4 application.

Admissions staff will decide whether to offer places to applicants for deferred entry on their courses and you should not assume that they will grant all such requests. If you request deferral for more than one year, you would normally be required to re-apply, as your chosen course, and your suitability for it, would change over time. English Language test results can only be considered to be current for two years from the test date.

If you applied in the previous year and your application was not successful you may apply again. Your application will be considered against the standard course entry criteria for that year of entry. In your new application you should demonstrate how your application has improved. We may draw upon all information from your previous applications or any previous registrations at the University as a student when assessing your suitability for your chosen course.

Manchester is one of the leading centres for pure mathematics in the UK. As well as the core areas of algebra, analysis and dynamical systems, geometry and topology, and mathematical logic, our research spills into mathematical physics and theoretical computer science.

For our research, see the area descriptions . Many of our recent achievements are outlined in the group's RAE2008 submission . A vibrant programme of seminars , a large and lively group of postgraduate students and purpose-designed areas for mathematical interaction, all help create a stimulating environment for creating new mathematics. Other activities of the group include organising international conferences and writing textbooks and research monographs. We are part of the MAGIC consortium which, via the web, presents a range of lecture courses for our postgraduate students far greater than could be provided at any single institution.

Pure Mathematics has a long tradition of excellence at Manchester. The 1920s and 30s saw Manchester become one of the world's leading centres for number theory, with Louis Mordell and Kurt Mahler holding chairs here. In 1945 Max Newman arrived from code-breaking work at Bletchley Park and ensured the growth in eminence of the department, recruiting stars such as the logician Alan Turing , often considered to be the father of artificial intelligence, and the topologist Frank Adams . Manchester also has a long tradition in algebra, through the work of leading figures such as Bernhard Neumann , Hanna Neumann and Brian Hartley .

Practical support and advice for current students and applicants is available from the Disability Advisory and Support Service. Email: dass@manchester.ac.uk