These projects represent just a few of the things that our researchers are thinking about just now, that might be good starters for a PhD project. They sound pretty open-ended because that's what research is like, it usually starts with a hunch that something might be a good idea rather than a careful detailed plan. A typical PhD student would start with one of these projects, or one they came up with for themselves, and spend the first few months reading, thinking and experimenting around the problem before focussing their ideas on a specific aspect of it. Exact arithmetic . Mathematical modelling is the basis of computation in many branches of science, yet models can sometimes give the wrong answer because of software flaws.
Exact arithmetic is a new technique for getting arbitrary precison results to numeric computations.
A new research project at St Andrews investigates how to conbine this with symbolic computation systems like Maple. You will extend the work by looking at applications in mathematical modelling, investigating the strengths and weaknesses of the approach when compared with traditional numerical methods. Mathematical modelling is the basis of computation in many branches of science, yet models can sometimes give the wrong answer because of imprecise understanding of requirements. Light formal methods is a new technique for tracking and documenting requirements, investigated at St Andrews by Martin Dunstan with support from NAG Ltd . You will extend the work by looking at applications of light formal methods in mathematical modelling, investigating the strengths and weaknesses of the approach when compared with traditional methods.