PhD Numerical Analysis

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 or use our funding database 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.  

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 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 ISIHighlyCited.com.

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.

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.