Written By Dan Rust, Student Research Bursaries and EPSRC Internship Coordinator, and Ethan Shallcross, OU Research Bursary student.
A version of this article will also be available in the OU Open Interval newsletter.
Every summer, the Open University (OU) school of Mathematics and Statistics hosts research placements for undergraduate students from across the world, giving them the opportunity to contribute to contemporary mathematics research. Projects are supervised by one or more experienced researchers in our school, covering topics in pure and applied mathematics, statistics and the history of mathematics. These include our own research bursary scheme and EPSRC DTP Vacation Internships.
This year, we had more students than we’ve ever had before, with a total of 10 undergraduates conducting research in a range of areas including: translating ancient Arabic mathematical texts; understanding the combinatorics of swarms of robots on a network; developing games that teach environmental dynamics; enumerating algebraic objects called ‘friezes’; identifying election fraud in the 2024 Venezuelan presidential election; and statistically analysing air quality data.
While most students met with their supervisors online, having weekly video chats and exchanging regular emails, some were able to visit the OU Milton Keynes campus at Walton Hall to work with their supervisors in person.
At the end of August, we celebrated a successful summer of research by hosting a hybrid event where many of the student researchers gave short presentations about their projects. It really was a joy to see the huge variety of activity that had taken part over just a short couple of months and the school couldn’t be prouder of each of the students that took part.
A great deal of work went into these placements. The students themselves showed incredible resilience in working on challenging problems, most of whom had no previous experience of research, and our school supervisors worked extremely hard to introduce their student researchers to the world of academic research in mathematics, statistics and history, helping them to achieve feats that include a variety of academic papers, talks and posters at international conferences, the awarding of external grants, blog posts for scholarly societies and more.
Below is an account from one of our 2024 students:
Ethan Shallcross
Last December, I gratefully received one of the OU’s student research bursaries to work on a project which can be summarised as follows. Imagine stationing robots on a subset of the nodes in a network, which are permitted to move to adjacent nodes over a sequence of timesteps. You could think of the robots as delivery robots (like those found in Milton Keynes for delivering food) and the nodes as delivery locations. We were investigating the maximum number of robots able to visit all the nodes, whilst requiring that they can always communicate freely. We considered different variants of this problem such as requiring each node to be visited by each robot, allowing all the robots to move at each timestep, and altering the conditions needed for free communication.
Robots exploring a network when using one possible definition of ‘free communication’
As you might expect, I explored lots of fascinating new mathematical ideas. But I also improved my ability to communicate effectively. My supervisor provided helpful advice about writing proofs formally, clearly, and concisely. I enjoyed discussing my work with others during online video calls as well as through emails and texts. Whilst attending meetings with the combinatorics research group, I learned about other people’s work and had the chance to present my findings. I had the pleasure of working with mathematicians from both within the OU and other universities in Indonesia and Slovenia. I am thankful to have had the opportunity to meet and collaborate with so many people.
Over the course of the 8 weeks, I really got a feel for what doing research is like. This even included assisting with peer-reviewing a paper before its publication – an unexpected but very insightful opportunity. I liked learning about the new results and thinking critically about the proofs to provide feedback for the authors.
I experienced the lows of finding an issue with a construction at the final check, but also the highs of solving an open problem from the literature and proving new results. I gave a talk about these results at The International Conference on Graph Theory and Information Security VI – a great experience. The work will hopefully form part of a paper to be published, which I think is very exciting! But the hours spent toiling with different problems were interesting and fulfilling, regardless of the outcome.
A screenshot from a computer program that I wrote during the project.
I thoroughly enjoyed my research bursary experience and have learned a lot. It has confirmed to me that I would like to pursue a PhD after I finish my MSc next year. I would urge any student at the OU thinking of a career in mathematical research to apply for the next round. Finally, I would like to thank James Tuite for his advice and support, all the researchers and students that I have worked with, as well as the School of Mathematics and Statistics for the opportunity.
If you are an undergraduate student and are interested in taking part in a summer research project in 2025, keep an eye out for announcements and updates on the following pages:
Mathematics & Statistics Summer Research Bursaries – https://www5.open.ac.uk/stem/mathematics-and-statistics/research/student-research-bursaries (application deadline approx. December 2024 – OU students only)
EPSRC DTP Vacation Internships – https://stem.open.ac.uk/research/research-degrees/epsrc-dtp-doctoral-training-partnership/epsrc-dtp-vacation-internships (application deadline approx. March 2025 – open to external students)