PhD Pure Mathematics

The programme fee will vary depending on the cost of running the project. Fees quoted are 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 Home students (fees are typically fixed for International students, for the course duration at the year of entry). For general fees information please visit the postgraduate fees page .

Always contact the Admissions team if you are unsure which fees apply to your project.

There are a range of scholarships, studentships and awards at university, faculty and department level to support both UK and overseas postgraduate researchers.

To be considered for many of our scholarships, you’ll need to be nominated by your proposed supervisor. Therefore, we’d highly recommend you discuss potential sources of funding with your supervisor first, so they can advise on your suitability and make sure you meet nomination deadlines.

For more information about our scholarships, visit our funding page to search for scholarships, studentships and awards you may be eligible for.

The standard academic entry requirement for this PhD is an upper second-class (2:1) honours degree in a discipline directly relevant to the PhD (or international equivalent) OR any upper-second class (2:1) honours degree and a Master’s degree at merit in a discipline directly relevant to the PhD (or international equivalent).

Other combinations of qualifications and research or work experience may also be considered. Please contact the admissions team to check.

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 a minimum IELTS 6.5 overall with a minimum of 6 in writing and listening, and 5.5. in all other sub-tests. TOEFL iBT:  At least 90 overall with no subtest below 20. We do not accept 'MyBestScore'.

Pearson Test of English (PTE): At least 70 overall with no subtest below 59. 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 accept a range of qualifications from different countries. For these and general requirements including English language see entry requirements for your country .

An interview is required for entry to this programme of study. Read our interview advice to help you prepare.

It is normally possible to defer entry to another entry point within the academic year, with the approval of your supervisory team and funder (if applicable).

You can request a deferral by contacting the Doctoral Academy Admissions Team by emailing fse.doctoralacademy.admissions@manchester.ac.uk .  If you request deferral for entry in a subsequent academic year you may be required to re-apply.

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), carer support funds for conferences, and peer support networks for parents and carers.

All appointments are made on merit.  The University of Manchester and our external partners are fully committed to equality, diversity and inclusion.

The department has a wide range of expertise in pure mathematics, described in our themes and areas of expertise . 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.

In the Department of Mathematics we offer a range of scholarships, studentships and awards to support UK and overseas postgraduate researchers.

Funding is also available at university and faculty level and can be viewed on our funding page .

We'd recommend you discuss potential sources of funding with your supervisor before applying. They can advise what funding may be available to you, and ensure you meet nomination and application deadlines.

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