MRes Projects - Mathematics
Master of Research (MRes) Technology is a postgraduate course that will allow you to focus your research interests on one or two areas of technology and work towards translating your learning into research related outputs – such as a submission for a peer-reviewed publication; a peer reviewed research/knowledge transfer grant application, or a presentation.
MRes Technology can be studied either full time (1-year) or part time (2-years), with start dates in September and January each year. You will develop a wide variety of skills, experience and competence on this course, and the MRes will provide a thorough grounding for students moving towards Doctoral (PhD) studies, or pursuing research related activities as a career.
The course is taught within the Faculty of Technology and many of the projects listed on this page are linked to research that is undertaken in our School of Mathematics and Physics. If you'd like to propose your own idea for a research project in the fields of mathematics or technology, email Dr Alexei Nesteruk or Marianna Cerrasuolo to discuss feasibility and potential supervisors.
Supervisor: Dr Alexei Nesteruk
Higher dimensional physics can be confusing as it is full of many strange sounding ideas. The Universe we live in is considered to be four dimensional, with three spatial dimensions and one temporal dimension.
Although there are various ideas such as string theory which claim you can unify the fundamental forces in physics with manifolds in higher dimensions known as strings, as of 2016 research has not found a way to physically interact with them, so they are beyond the scope of this project. This project involves the theoretical construction and modelling of a Universe where the number of spatial dimensions has been changed from three to four, while leaving the number of temporal dimensions as one.
Having an extra spatial dimension will change the way physical objects are able to interact with each other.
How mathematics can help understand the correlation between urinary microbiota and tumour progression in TRAMP mice
Supervisor: Dr Marianna Cerrasuolo
In the last few years mathematics has been extensively used to tackle biological problems. The increasing success of mathematical oncology represent a clear example of the contribution that mathematics can give to the other sciences. Within this MRes project we are going to develop and analyse mathematical models to explore the correlation between the urinary microbiota in TRAMP mice and cancer progression. Experimental data will be statistically analysed to identify the interaction network. The results obtained with the statistical analysis will be incorporated within a differential equation framework. By performing a qualitative study of the mathematical model, sensitivity analysis of the parameters and numerical simulations, it will be possible to identify which parameters mostly affect the tumour-microbiota interaction. The mathematical study will provide novel insights into tumour-related processes associated with urinary microbiota, which would be otherwise impossible to identify, and will support the design of new optimal treatment regimes.
Supervisor: Dr Marianna Cerrasuolo
In epidemiology, there is a broad use of optimal control problems to minimize the number of infections and cost of efforts in controlling disease. Comparative cost-effectiveness analysis – which shows how the cost-benefit of intervention is affected by changes in the variation of model parameters – is also widely performed to assess the most appropriate strategy to eliminate diseases with minimum costs.
In continuous dynamical systems, a classical approach to solving the optimal control problem makes use of Pontryagin's maximum principle. In the case of delayed differential equations, the use of such principles is subject to limitations. Within this project, we are going to solve an optimal control problem applied to a delayed system describing the interaction between plants and viruses. Costs associated either with use of insecticide or with the use of allelopathy (mixed crops) or a combination of both will be analysed.