phd maths manchester

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PhD Pure Mathematics

Year of entry: 2024

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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.

Full entry requirements

Apply online

In your application you’ll need to include:

• The name of this programme
• Your research project title (i.e. the advertised project name or proposed project name) or area of research
• Your proposed supervisor’s name
• If you already have funding or you wish to be considered for any of the available funding
• A supporting statement (see 'Advice to Applicants for what to include)
• Details of your previous university level study
• Names and contact details of your two referees.

Programme options

Programme description

The 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.

For entry in the academic year beginning September 2024, the tuition fees are as follows:

• PhD (full-time) UK students (per annum): Band A £4,786; Band B £7,000; Band C £10,000; Band D £14,500; Band E £24,500 International, including EU, students (per annum): Band A £28,000; Band B £30,000; Band C £35,500; Band D £43,000; Band E £57,000
• PhD (part-time) UK students (per annum): Band A £2393; Band B £3,500; Band C £5,000; Band D £7,250; Band E 12,250 International, including EU, students (per annum): Band A £14,000; Band B £15,000; Band C £17,750; Band D £21,500; Band E £28,500

Further information for EU students can be found on our dedicated EU page.

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.

Scholarships/sponsorships

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 or use our funding database to search for scholarships, studentships and awards you may be eligible for.

Contact details

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.

• Mathematics

Entry requirements

Academic entry qualification overview, 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 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.  

English language test validity

Other international entry requirements, application and selection, how to apply, advice to applicants.

• Identified the specific research project, CDT or dual-award you'd like to apply for or, if you already have funding, determined your own research project and title and discussed this with a supervisor.
• Contacted the project supervisor and spoken to them about your suitability for the project.  
• Browsed funding you are eligible for and discussed this with your supervisor, if you don't already have your own funding.  
• Supporting statement: A one or two page statement outlining your motivation to pursue postgraduate research, the area(s) of research you’re interested in, why you want to undertake postgraduate research at Manchester, any relevant research or work experience, the key findings of your previous research experience, and techniques and skills you’ve developed.
• Certificates and transcripts: Certificates and final transcripts of any completed university-level qualifications and interim transcripts for qualifications in progress. If your transcripts are in a language other than English, you must provide an official English translation. If your current weighted average mark or GPA is not included on these documents, please also include an official document from your university verifying this information.
• CV : Summarising your academic record and highlighting experience that demonstrates your potential to conduct research.  
• English language proof: A certificate or evidence demonstrating your English language ability and proficiency. Applications can be considered without this evidence but any offer would be conditional on meeting minimum requirements.  
• Referees: Names and contact details of two academic referees who we can get in contact with and will support your application.

Interview requirements

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 [email protected] .  If you request deferral for entry in a subsequent academic year you may be required to re-apply.

Programme details

Additional programme information.

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.

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 .

Scholarships and bursaries

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 . Alternatively, you can use our funding database to find scholarships, studentships and awards you may be eligible for.

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.

The Department of Mathematics is the largest in the UK with an outstanding research reputation and facilities .

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