Undergraduate research experience
Each year undergraduates can apply to work on a research project during the summer. There are a number of schemes that will provide you with a bursary to spend 48 weeks (depending on the scheme) working with one of our academic staff or postgraduate students after the summer exam period. You will be able to get a first taste of what research in Mathematics (Pure or Applied) and Statistics is like, and it is possible that your work will lead to a publication in an academic journal. Even if that doesn’t happen, this research experience can make an excellent addition to your CV.
Our department is devoted to creating an inclusive and welcoming environment to all those who have a passion for mathematics and statistics. In light of this, the Undergraduate Research Internship was set up with the primary goal of offering research experience to students who are typically underrepresented in the mathematical sciences at research level. These underrepresented groups include, but are not limited to: women; people with a disability; people who identify as LGBTQ+; and people in BAME communities.
Undergraduates have the following options for a funded project:
Undergraduate Research InternshipYou can apply to work with one of our postgraduate students for 4 weeks in the summer. We usually offer 6 projects: 2 in Pure Maths, 2 in Applied Maths, and 2 in Statistics. There is a selection process for this scheme which requires that you submit a statement of interest, and, if shortlisted, attend an interview. For Summer 2021, the application is likely to open towards the end of February, which is also when the projects on offer will be advertised. The application is open to students from all years, but students in Levels 2 and Levels 3 will be given priority. The Heilbronn Institute for Mathematical Research, one of the UK's largest mathematics research institutes, has agreed to fund six UGRI projects as part of their commitment to equality and diversity in higher education. Additional funding is possible through the generous bequests of Harry Burkhill, Barry Jackson, and Chris Cannings, which funded all the UGRI projects in 2020. 
Sheffield Undergraduate Research ExperienceYou apply through the Universityrun SURE scheme. The application needs the agreement of a member of staff who will supervise the project. If successful, the scheme will provide you with a bursary for 6 weeks, starting on the week after the summer exam period. The application is typically due at some point in March of April. The SURE scheme is now confirmed to run for summer 2021. Applications are expected to open from Monday 15 February. To apply for the SURE scheme you need to be in your 2nd year (for a 3year degree) or 3rd year (for a 4year degree). It is up to the student to make contact with a potential supervisor and discuss the possibility of a summer project. 
London Mathematical Society  Undergraduate research bursariesYou can also apply for an undergraduate research bursary from the London Mathematical Society. The application for this is already open (deadline February 1st 2021). The typical duration for these projects is 6 weeks, but it is possible to apply for a longer one. For this scheme you are required to apply jointly with an academic supervisor, who will submit the application on your behalf. It is your responsibility to initiate contact with a potential supervisor, and they will then need to alert the Tutor for Undergraduate Research (Dr Dimitrios Roxanas) and the Head of School (Prof. Nick Monk) with their intention to submit an application. Only students in their 2nd year (for a 3year degree) or 3rd year (for a 4year degree) are eligible to apply. 
If you have any questions about the various schemes and the application process, please contact the Tutor for Undergraduate Research, Dr Dimitrios Roxanas, who can also help with putting you in touch with potential supervisors. 
Student stories
Below you can read about some of the research projects our students have completed.
"I'm really happy I was able to complete a short supervised reading project this summer, because it gave me the chance to broaden and deepen my knowledge of group theory and try some challenging problems. Presenting one of the new concepts I learned was also a great opportunity to practice explaining mathematics to an audience and improve my presentation skills." – Jai Schrem, MMath Mathematics Read Jai's research presentation (PDF, 224 KB) 
"As a person who is into pure maths and who has considered getting into research in the future, this was a very enlightening experience for me personally because I got a taste of what research mathematics is like. Also it was incredibly fun and interesting learning about big concepts like natural transformations and fundamental groups." – Kacper Mytnik, BSc Mathematics Read Kacper's research presentation (PDF, 452 KB) 
"It is an excellent insight into what further study would be like. Working hours are flexible and I was able to focus my project on an area of research I am interested in. I really enjoyed myself and learnt a lot from the very best researchers at the University of Sheffield."  Louisa McKenna, BSc Mathematics Read Louisa's research presentation (PDF, 1.06 MB) 
"This project was the perfect chance to explore what postgraduate research could be like. We got to explore the fun, independence and frustrations this sort of stuff has to offer, whilst knowing we were in the reassuring hands of friendly supervisors ready to help at any moment. I am so glad I seized the opportunity."  Elisabetta Dixon, BSc Mathematics with study in Europe Read Elisabetta's research presentation (PDF, 1.60 MB) 
Previous research projects
Below you can find out about research projects from the past academic year, 20192020.
Chameleon mechanism in cosmology 



Rarity of nonconvergence in preferential attachment graphs with three types. 


Representation Theory of Finite Groups and Burnside's Theorem 
Student: Jae Irvine Supervisor: Joseph Martin (PGR) In some sense, simple groups are to groups what prime numbers are to natural numbers. Burnside’s theorem was a large step in the classification of all the simple groups, stating that a group G for which G=p^{a}q^{b} cannot be simple if p and q are primes and a,b are nonnegative integers whose sum is greater than two. It was first proved using representation theory, rather than directly through group theory. A purely group theoretical proof was not completed for another 66 years, which is enough to display representation theory’s effectiveness. 

An Exploration into the Effects of Various Modelling in Chronology Construction in Archaeological Dating 


The Impact of Local Interactions on an Epidemic 
Student: Lydia Wren Supervisor: Dr Alex Best Mathematical modelling has long been used to analyse the dynamics of infectious disease. Since the early twentieth century, the SIR model has been used to track individuals within a population who are either susceptible to, infected with or have recovered from a disease but this model has its shortcomings. One issue with the SIR model is that it assumes every individual has the same likelihood of being infected, whereas, in reality, an individual is much more likely to become infected when they are in close contact with an infected individual, either physically or socially. In my research I have used a pairapproximation model (based on the SIR), which allows for global interactions to be limited, and my results show the impact that local interactions can have on an epidemic. 

ABC methods and their use in ‘step and turn’ animal movement models 


Computational Euclidean Geometry 
Student: Jamie Wright Supervisor: Dr James Cranch In this project me and Dr James Cranch have began development on software which can use polynomial rings and ideals to help deduce certain Euclidean geometrical axioms. Euclidean geometry is a rich source of mathematical problems and is a cornerstone of the school syllabus. Such problems have appeared in competitions for schoolaged students for more than sixty years now. For most of these problems, the range of concepts used is quite limited: nearly everything can be broken down to discussion of points, straight lines, circles, lengths and angles. As a result, it is not difficult to translate these problems into algebra, where we assign variables to the coordinates of all points involved. Such algebraic problems, despite being near impossible for a human to work with, can be used by computers extremely efficiently to do computations on these equations. The main goal of this project was to create a library of Python code which helps convert geometric problems into algebra, enabling that algebra to be solved by existing methods. 

Loops and covers 


Monte Carlo Methods 


Simplicial Sets 


Machine Learning  An Introduction to Gaussian Processes 


Chaos and fractal boundaries 


Finding a strong knot invariant 


Investigating properties of the Solar Corona with Fourier Transforms 


Lagrangian points and spacecrafts 


Direct Systems of Groups: How can the concept of a limit be applied in group theory? 


Using Bayesian thinking to find the law of economic development between nations 
Student: Jialiang Sun Supervisor: Dr Miguel Juarez Economic development is a hot topic in recent years, so the research on the commonness of economic development among developing countries has become a statistical problem worth discussing. This project combined the statistical thinking of Bayes and applied it to the topic of economic development. 