# Author Archives: Place Holder

## Bayesian Methods for Analysing Historic Data

This project will concern (Bayesian) models for the survival time of historic populations.  Such models can provide interesting historical insights.  For example, we can understand how survival times have increased across the centuries and how they differ between sexes.  In this project will will  develop  survival analysis methodology for populations for which good data are

## Dynamic Social Media Information Extraction

This project concerns the extraction of information from Social Media such as Facebook and Twitter. It will develop methodology to provide an understanding of how sentiments expressed on social media change over time.  A Shiny app that will, for example, provide a user who inputs a topic and a time frame  with a detailed understanding

## The Numerical Solution of the p-Laplace Equation in a Geometry with Sharp Corners

Certain types of fluids do not respond in a linear way to external forces – they are called non-Newtonian fluids. A simple model of a non-Newtonian fluid which is widely used in industrial applications (e.g. food processing) is the so-called power-law model. In very slow flows, the governing equation turns out to be the p-Laplace

## Perturbation Methods

Perturbation methods are used to investigate solutions to mathematical problems in which exact solutions can’t be found but in which there is a parameter whose size (usually very small) allows approximate solutions to be found. In this project the aim would be to look at a range of perturbation methods and the types of problems

## The Inverted Pendulum

Why is it that a solid pendulum can be made to stand on its end when it’s other end is made to oscillate? This project will investigate the underlying mathematics behind this very strange phenomena. You could also try modelling this in Maple or even building your own control system to do it. Supervisor: Dr

## Mondromy of Abelian Integrals

This project is related to the change in an complex integral as its defining parameters change. You will need to learn some theory about Riemann surfaces and integrals on them, but I would like this project to have more of a research nature with plenty of experiments (and pictures) in Maple to find out what

## Hilbert’s 10th Problem

How complicated can it be to find all the integer solutions to a set of polynomial equations? In fact, as complicated as you like! Given any output from a computer program (a list of all prime numbers, for example), you can find a set of equations whose only solutions occur when one of the variables

## Algebraic Curves

We know that x2+y2=1 is the equation of a circle, but what happens when the degree of the equation is greater than two? In this project we investigate some of the geometry of algebraic curves – that is, solutions of polynomial equations P(x,y)=0. In particular, when P is a cubic polynomial, the resulting curve is

## Symmetry Groups and Space

This project will look at the interplay between group theory and symmetry in different spaces. It is deliberately left open for you to explore the areas that you like best – but you will be expected to understand the mathematics behind the pretty pictures too! Supervisor: Dr Colin Christopher

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