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, contact Dr Esmaeil Namvar to discuss feasibility and potential supervisors.
- How mathematics can help understand the correlation between urinary microbiota and tumour progression in TRAMP mice
- Optimal control strategies for delay plant-virus interaction systems
- Shape Matters - Mathematical Foundations in the Geometry of Data
- Studies in Compositionality
- Study of Magnetic Atoms Doped in Quantum Dots (Spintronics)
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 Transgenic Adenocarcinoma of the Mouse Prostate (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 minimise 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.
Supervisor: Dr Ittay Weiss
We live in a world where data is in abundance and the real challenge lies in deciphering data in order to produce useful and insightful information. The mathematical challenges posed by this problem are substantial and require stepping far beyond the well-charted territory of classical statistics and data representation.
Emerging new ideas come from topology and geometry where the fundamental approach is that data represents certain geometric features of the observed phenomenon. The data itself is not of direct interest but rather it is to be used as a proxy for understanding the phenomenon itself. In other words, shape matters and it is the shape of the phenomenon, not the shape of the data, that we care to investigate.
Topology and geometry are the modern mathematical disciplines of the study of shapes and Topological Data Analysis - the use of topological techniques in the analysis of data - draws upon techniques from both realms. The project aims to contribute to the development of a robust mathematical foundation facilitating the study, comparison, and development of new techniques resulting from the interaction between geometry and data science.
Supervisor: Dr Ittay Weiss
The idea of studying a system by understanding how it is composed of simpler sub-systems is as ancient as mathematics itself and has traditionally fuelled much of the development of modern analysis. Category theory is a branch of algebra devised originally with very abstract aims in mind. The theory developed quickly in the past 50 years and has reached a significant level of maturity which now draws the attention of scientists wishing to benefit from its overarching language and impressive expressive power.
The project aims to investigate problems in the context of compositionality including aspects of using category theoretic language as a descriptive tool as well as developing new concepts within category theory that facilitate the understanding of complex systems. An appreciation for the range of scientific problems that can fruitfully be tackled with this approach can be obtained from the online book "Seven Sketches in Compositionality: An Invitation to Applied Category Theory".
Supervisor: Dr Esmaeil Namvar
Quantum Dots (QDs) are crystalline particles at nanometre scale, a domain where the size reduction exposes quantum mechanical effects resulting new unforeseen properties in the bulk matter of the same material. Therefore, QDs have opened a wide range of research and applications opportunities in nanoscience and nanotechnology.
There is no doubt that the current active and live research trend of the field will continue to bring more advantages and capabilities of QDs in everyday life applications. Among them, application to spintronics is of special interest. Spintronics refers to study of the role played by the spin of atomic particles and the possibility of making devices working based on spin properties instead of electrical charge.
The Giant-Magnetoresistance (GMR) phenomena (Nobel Prize award in Physics, 2007) is an example of electron spin contribution to change a device resistance considerably. In this simulation project, you study the implication on the energy level and magnetic properties of a QD where a magnetic atom is added to it as impurity. Therefore, magneto-optical interaction and its applications is the subject of this project. You add a single transition metal ion like Mn or Co as impurities to CdSe QDs. In this way, electronic orbital properties of the d-shell of dopant ions can transfer the ordinary QDs to a new type with spin sensitivity that make it an excellent candidate for applications such as spin memory system.
Other research projects
MRes Technology research projects are offered in the following areas:
Please note, these lists are not exhaustive and you'll need to meet and discuss the project you're interested in with a member of research staff before you apply.