
Overview
- Degree awarded
- Doctor of Philosophy
- Duration
- 36 or 48 Months. [Full-Time]
- Entry requirements
-
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.
- How to apply
- Apply online
Please include details of your previous study, your area of interest (or research project title, if known) and the name of the academic member of staff you would like to supervise your research.
We strongly recommend that you make contact with your proposed supervisor before submitting an application.
To apply for this programme, select Academic Program: PhD Mathematical Sciences and Academic Plan: PhD Pure Mathematics.
Equality, diversity and inclusion is fundamental to the success of The University of Manchester, and is at the heart of all of our activities. We know that diversity strengthens our research community, leading to enhanced research creativity, productivity and quality, and societal and economic impact. We actively encourage applicants from diverse career paths and backgrounds and from all sections of the community, regardless of age, disability, ethnicity, gender, gender expression, sexual orientation and transgender status.
We also support applications from those returning from a career break or other roles. We consider offering flexible study arrangements (including part-time: 50%, 60% or 80%, depending on the project/funder).
Programme options
Full-time | Part-time | Full-time distance learning | Part-time distance learning | |
---|---|---|---|---|
PhD | Y | Y | N | N |
Programme description
The Department of Mathematics has an outstanding research reputation. The research facilities include one of the finest libraries in the country, the John Rylands University Library. This library has recently made a very large commitment of resources to providing comprehensive online facilities for the free use of the University's research community. Postgraduate students in the Department benefit from direct access to all the Library electronic resources from their offices.
Many research seminars are held in the Department on a weekly basis and allow staff and research students to stay in touch with the latest developments in their fields. The Department is one of the lead partners in the MAGIC project and research students can attend any of the postgraduate courses offered by the MAGIC consortium.
Opportunities for PhD research are available in a wide range of topics in Pure Mathematics. For some of the available areas of possible PhD research see the current Pure Mathematics research areas . For more details about the specific projects, please contact the relevant individual members of staff or get in touch with the Pure Mathematics Postgraduate Admissions Tutor .
Students may enter our graduate programme in Pure Mathematics by initially taking our taught M.Sc. course over 1 year. This, subject to satisfactory progress, can lead to admission to the PhD programme.
Open days
Fees
Fees for entry in 2023 have not yet been set. For reference, the fees for the academic year beginning September 2022 were as follows:
-
PhD (full-time)
UK students (per annum): Band A £4,596; Band B £6,000; Band C £9,000; Band D £11,000
International, including EU, students (per annum): Band A £25,500; Band B £27,000; Band C £30,000; Band D £32,000 -
PhD (part-time)
UK students (per annum): Band A: TBC; Band B £3,000; Band C £4,500; Band D £5,500
International, including EU, students (per annum): Band A £12,750; Band B £13,500; Band C £15,000; Band D £16,000
Further information for EU students can be found on our dedicated EU page.
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.
Scholarships/sponsorships
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
Contact details
- Department
- Department of Mathematics
- Contact name
- Postgraduate Research Admissions Team
- Telephone
- +44 (0)161 275 0178
- fse.doctoralacademy.admissions@manchester.ac.uk
- Website
- https://www.maths.manchester.ac.uk/
- School/Faculty
-
Our internationally-renowned expertise across the School of Natural Sciences informs research led teaching with strong collaboration across disciplines, unlocking new and exciting fields and translating science into reality. Our multidisciplinary learning and research activities advance the boundaries of science for the wider benefit of society, inspiring students to promote positive change through educating future leaders in the true fundamentals of science. Find out more about Science and Engineering at Manchester .
Programmes in related subject areas
Use the links below to view lists of programmes in related subject areas.
Entry requirements
Academic entry qualification overview
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.
English language
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.
English language test validity
Application and selection
How to apply
Please include details of your previous study, your area of interest (or research project title, if known) and the name of the academic member of staff you would like to supervise your research.
We strongly recommend that you make contact with your proposed supervisor before submitting an application.
To apply for this programme, select Academic Program: PhD Mathematical Sciences and Academic Plan: PhD Pure Mathematics.
Equality, diversity and inclusion is fundamental to the success of The University of Manchester, and is at the heart of all of our activities. We know that diversity strengthens our research community, leading to enhanced research creativity, productivity and quality, and societal and economic impact. We actively encourage applicants from diverse career paths and backgrounds and from all sections of the community, regardless of age, disability, ethnicity, gender, gender expression, sexual orientation and transgender status.
We also support applications from those returning from a career break or other roles. We consider offering flexible study arrangements (including part-time: 50%, 60% or 80%, depending on the project/funder).
Advice to applicants
- A personal statement in which you elaborate on your research interests and display a clear motivation to study for a PhD,
- Bachelor's transcripts and certificates.
- Master's transcripts and certificates (where available).
- CV
If English is not your first language, we also require proof of your English language ability. If you have already taken an English language qualification, please include your certificate with your application. We may be willing to consider your application without this document, but if we choose to make you an offer, the conditions will include IELTS (or equivalent qualification).
How your application is considered
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.
Interview requirements
Overseas (non-UK) applicants
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.
Deferrals
Re-applications
Programme details
Programme description
The Department of Mathematics has an outstanding research reputation. The research facilities include one of the finest libraries in the country, the John Rylands University Library. This library has recently made a very large commitment of resources to providing comprehensive online facilities for the free use of the University's research community. Postgraduate students in the Department benefit from direct access to all the Library electronic resources from their offices.
Many research seminars are held in the Department on a weekly basis and allow staff and research students to stay in touch with the latest developments in their fields. The Department is one of the lead partners in the MAGIC project and research students can attend any of the postgraduate courses offered by the MAGIC consortium.
Opportunities for PhD research are available in a wide range of topics in Pure Mathematics. For some of the available areas of possible PhD research see the current Pure Mathematics research areas . For more details about the specific projects, please contact the relevant individual members of staff or get in touch with the Pure Mathematics Postgraduate Admissions Tutor .
Students may enter our graduate programme in Pure Mathematics by initially taking our taught M.Sc. course over 1 year. This, subject to satisfactory progress, can lead to admission to the PhD programme.
Related research
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 .
Facilities
The Department of Mathematics is the largest in the UK with an outstanding research reputation and facilities .