These internships have been extremely successful and have led not only to excellent research outputs but have also inspired the students to pursue research careers.
Modelling walking droplets
“I really enjoyed my project and it definitely made me realise I want to continue my studies with a PhD.” - Jemima
Jemima Tabeart’s project, working with Professor Paul Milewski, examined the behaviour of bouncing droplets on a vibrated liquid surface. Modelling the behaviour of the droplet is a complex problem that has parallels in quantum mechanics. To do this Jemima used phase plane analysis and MatLab computation to study a differential equation model that reflected the experimental results. She is now building on the results she obtained for her final year MMath project at Bath. Jemima spent part of her internship at Cambridge and said, “it was really interesting to visit another department and meet lots of other mathematicians in the same field who were at various stages in their careers”.
Lévy processes and the Wiener-Hopf factorisation
“I wanted to do a project in order to give me an insight into what research was actually like.” - Emma
Emma Horton is a third year MMath student at Bath who spent the summer working with Professor Andreas Kyprianou on Lévy processes and the Wiener-Hopf factorisation. During the project, Emma was able to extend the existing class of processes and she also computed the potential measures of Wiener-Hopf factors. This is now being written up into a paper which will be submitted for publication later this year. Emma is keen to continue in mathematics research and hopes to do another internship next summer. She highlights how she “obtained a lot of general academic skills from this project, for example, learning how to write a research paper”.
Reducing interference in wireless networks
“I was very interested in the area of Maths, and wanted to expand my knowledge of it beyond what I have studied before.” - Matthew
Also a final year Bath MMath student, Matthew Wiltshire was jointly funded by the University and SAMBa-partner BT, working on finding the optimal algorithm for choosing frequency channels in wireless networks in order to reduce interference. This was modelled as a graph colouring problem and Markov chain theory was used to assess the performance of the algorithms. The initial part of the project was carried out in the Department of Mathematics with Dr Antal Jarai, proving the upper and lower bounds on the Markov chain mixing time for a specific colouring algorithm. Matthew then spent time in the BT research park near Ipswich, programming many different algorithms, computing their stationary distributions and assessing the optimality of each of them. Matthew said, “ I particularly enjoyed the cross-over between the Mathematical side of the work and getting an insight into how it would be applied in the real world when I was at BT.”
Mapping network paths
“I heard a lot that mathematics can actually be used in many fields and industries, but it was very vague to me. This was a good opportunity to see how it can help to solve the real world problem practically.” - Junghoon
Junghoon Yoon, a visiting undergraduate student from Hanyang University in South Korea, also worked on a BT-related research problem although she was wholly based at the University, working with Professor Jonathan Dawes. Junghoon spent her project determining how rapidly the nodes in a network find the shortest path to each other by local message passing, both numerically and analytically. As a Physics student, Junghoon wanted to see how Maths impacted on what she was learning at undergraduate level. She says, “Thanks to this summer project, I could widen my horizon and found that studying dynamical system is super exciting and can be applied to many areas. Now I'm looking for a graduate school to study this area further-which I never imagined doing before this project.”
What's happening next?
The two BT-focussed projects, arose out of a Condensed Integrative Think Thank which SAMBa ran with BT in February 2014. BT are one of the partners attending the first full Integrative Think Tank in January 2015 and it is hoped that more opportunities for summer internships, as well as full PhD projects, will be identified from this event.
All the interns agree undertaking the projects was a useful experience that has helped them to shape their future career plans. Emma says, “The department at Bath is really friendly. It was great to get to know some of the members of staff, postdocs and PhD students and also visitors to the department who were attending conferences and seminars”. Matthew adds, “there was always support and assistance available when I needed it”. Junghoon agrees, “I could feel that everyone in there was very keen on their research. Also they were very friendly and nice” she says. Jemima sums up, “having the experience of working on a longer individual project, I am now confident that I can cope with research, and that carrying on with Maths for another 4 years is definitely something I want to do”.