PhD Numerical Analysis / Programme details

Year of entry: 2024

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 Mathematics . For more information, please see Numerical Analysis research page or the Numerical Analysis group website and read advice on choosing a project or find out more about specific projects . Please contact the relevant individual members of staff or get in touch with the Numerical Analysis Postgraduate Admissions Tutor .

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.

The Numerical Analysis group is led by Professors Nick Higham, FRS, and David Silvester and comprises nine permanent members of staff, plus research associates and research fellows. In 2007 the group was strengthened by the appointment of Professor Jack Dongarra to a part-time position. The group carries out research in various areas of numerical analysis and provides teaching and supervision at the undergraduate (in all four years) and postgraduate (M.Sc. and Ph.D.) levels. It forms part of the Applied Mathematics Unit.

Activities of the group include organizing international conferences and a Numerical Analysis and Scientific Computing seminar series ; writing textbooks and research monographs ; membership of editorial boards of international journals and book series ; and contributing software to the NAG and LAPACK libraries and MATLAB. The group has a large grant portfolio supported by bodies such as EPSRC, The Royal Society, The British Council, and in the USA (though Dongarra) the NSF and DOE. The strength of numerical analysis in Manchester is indicated by the fact that no less than three of our researchers have been designated Highly Cited Researchers at

Numerical analysis has a long history going back at least to Newton and Gauss, whose names adorn some of today's most-used numerical methods. The UK has a strong tradition of research excellence in the subject, as exemplified by James H. Wilkinson (1919-1986), FRS, who was at the forefront of developments in numerical linear algebra from the days of the first digital computers. In Manchester, numerical analysis has long been an area of strength, and M.Sc. programmes in numerical analysis have run continuously since 1959. See the short historical essay Numerical Analysis at the Victoria University of Manchester, 1957-1979 , by Joan Walsh.

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 .

Disability support

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