PhD Pure Mathematics / Programme details

Year of entry: 2023

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.

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 .


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

Disability support

Practical support and advice for current students and applicants is available from the Disability Advisory and Support Service. Email: