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On this page you can find out about PhD opportunities currently available in Mathematics and Statistics. Click on a project title or research area below to find out more.

Some of these projects come with specific funding (eg, from a research council or Centre for Doctoral Training) to cover your tuition fees and living expenses. If you successfully apply for one of these projects, and you meet the eligibility requirements, you will be automatically awarded the funding. These projects are marked 'FUNDED' in the list below.

If a project does not come with specific funding, that does not mean that there is no funding available. You may be awarded a scholarship after you have submitted your application – let us know if you wish to be considered for a scholarship by including this in your application form. We also accept applications from students who are applying for funding separately, or have funding in place already.

You can find out about scholarships on the following webpage:

Do you have your own idea for a project?

Find a potential supervisor by visiting our research webpages. Contact a member of academic staff to find out about PhD opportunities in their area.


Centres for Doctoral Training

Other funded PhD opportunities are available through the Centres for Doctoral Training or Doctoral Training Partnerships that our staff contribute to.

Visit the webpages for these centres to find out more about their projects.

Centres for Doctoral Training at the University of Sheffield

Once you have identified a potential project and supervisor, please complete the University's postgraduate online application form to apply. If you wish to be considered for a scholarship, you should state this in the form. You should also include any information you have about funding that you are applying for separately, or that you have in place already. It is a good idea to contact the supervisor of any PhD opportunity you want to apply for, before you submit your application.

Postgraduate online application form

Current projects:

Heritage Data Analytics: Sustainable strategies for large and complex stratigraphic and chronometric data

Supervisor: Prof Caitlin Buck

Funding: AHRC and Historic England. Fully funded for up to 3.5 years, this studentship will cover: (i) a tax-free stipend at the standard Research Council rate (£14,777 per annum for 2018-2019), plus an additional CDA maintenance fee of £550 per annum (ii) research costs, and (iii) tuition fees at the RCUK rate (£4260 for 2018/19).

Eligibility: This studentship is available to UK and EU students who meet the UK residency requirements. Students from EU countries who do not meet residency requirements may still be eligible for a fees-only award. International students (non-EU) are not eligible for this studentship.

Our chronological understanding of archaeological sites develops gradually during field and post excavation work. First, we understand the relative chronological and contextual information, as represented by the stratigraphy and cultural finds respectively. Later, scientific (e.g. radiocarbon) dates are obtained and, finally, statistical modelling is used to draw everything together. At present this final stage is extremely laborious and requires considerable expertise because no tools exist to automate anything except the final statistical calculations. The proposed PhD student will develop numerical, analytical and graphical tools to improve this situation, with the goal of semi-automating chronology construction.

Working closely with Prof Caitlin Buck, School of Maths and Stats, Dr Gianna Ayala, Department of Archaeology and Keith May, Historic England, the student will begin by characterizing the most common types of data that heritage practitioners and researchers create and work with, particularly those created by fieldwork investigations. They will consider how the re-use of such datasets could be made easier and more effective by enhancing or developing better standards for digital data archives of excavation records. Working with staff at Historic England, the Government's national agency for managing and caring for the Historic Environment, the student will then focus on protocols and algorithms for interfacing with current and legacy site databases, while Buck and others will work on improvements to the modelling software. Working in this extended team of archaeologists, modellers and programmers, the student will learn techniques and protocols from field and laboratory archaeology, software engineering, graphical and statistical modelling and Bayesian inference.

The project is important because it addresses growing problems caused by a lack of standardized approaches to the archiving of excavation data, especially key stratigraphic and phasing data, often held in hard-copy matrix diagrams or unstructured database tables. The PhD will help inform decisions on digital archiving standards and best practice for stratigraphic data deposition and re-use, while developing our understanding of how statistical and technical approaches can best address the problems involved. It will provide a better understanding of the user requirements for interface tools to make analysis of large sites (especially legacy sites) practical.

Dye and Buck (2015) have recently shown that, by using graph-theoretic algorithms, at least semi-automation of the link between archaeological data and Bayesian chronological modelling is practical. This PhD will extend the tools they have begun to develop, to accommodate a wider range of archaeological site database protocols and complement the developments in Bayesian chronological modelling being undertaken by other members of Buck’s team (e.g. Buck et al, 1996).

Key research questions to be addressed include: What are the most common types of data that heritage practitioners create and work with? How can those various types of data be best characterised? How might adoption of better standards for digital archives of excavation records make re-use of such data sets easier and more useful? How might approaches to excavation data recording and archiving be improved to better enable the use of Big Data technologies?

The proposed PhD research is highly interdisciplinary, and so we are open-minded about the background of the student we appoint. By the end of the project, however, the student must be an independent researcher with skills in archaeology, information science, mathematical and statistical modelling and computer programming. Given this, applicants with formal training in at least one of these areas and who can provide evidence of knowledge and sustained interest in at least one of the others are encouraged to apply.

The student will spend the first year reviewing literature and data (with Historic England support) while learning the basics of several specialist computer protocols and languages (with the support of Buck). In years 2 and 3, the student will work closely with Buck and Dye, extending or rewriting the inputs to Dye and Buck’s prototype software, interfacing it to key file formats and protocols identified in year one. The software developed by Dye and Buck is only a prototype and far from fully functional, so the student will have considerable scope to decide exactly how and in what way the PhD should progress.

Buck C.E., Cavanagh W.G. and Litton C.D. (1996) The Bayesian approach to archaeological data interpretation, Wiley, Chichester, ISBN: 0 471 96197 3.
Dye T.S. & Buck C.E. (2015). Archaeological sequence diagrams and Bayesian chronological models. Journal of Archaeological Science , 83, 84–93.
May, K. 2017 Digital Archaeological Heritage: an introduction, Internet Archaeology 43.

Application deadline
9 March 2018.

Other project opportunities:

If you would like to find out about PhD opportunities in an area that is not covered in the listing above, visit our Research webpages. These pages list the research interests and contact details of our academic staff, so that you can get in touch and discuss other potential projects in their field.


Entry requirements

We usually ask for either a first class or upper second class (2:1) MMath or MSc degree or equivalent in mathematics, statistics, physics or a related subject. We offer a number of MSc courses in mathematics and statistics, if you do not already have a masters degree: Masters courses

Our decision on whether to offer you a place will also be based on the research proposal or personal statement you submit, your degree transcripts (and certificates, if available), your masters dissertation/project (if applicable), your CV and academic references (including your masters dissertation/project supervisor, if applicable), and any interviews and additional tasks we ask you to complete. All documents need to be provided in English, including transcripts and references. Students will also need to meet our English language requirements, and international students will need to get clearance through the Academic Technology Approval Scheme (ATAS). Find out more about English language requirements and ATAS on our webpage for international students:

International students