# Category Archives: BSc projects

## Studying varieties with computer algebra

A variety is the solution set of a system of polynomial equations, usually in several unknowns. For instance, some famous plane curves are described by one polynomial equation in x and y. A possible project is to discuss how computer algebra, e.g., Maple, can be applied to work with varieties. Interesting operations are, e.g., taking

## Regression modelling of competing risks

Motivation: Survival analysis takes into account of whether an event occurs as well as the time to such an event. Right censoring can be due to the occurrence of another event, which is called competing risks. An example of competing risk is disease progression due to a local relapse or a distant relapse. Analysis assuming

## Network meta-analysis of randomized controlled trials

Motivation: A number of treatments may be available to patients with the same health condition. Policy-maker, clinicians and patients may want to know what the optimal treatment is. This requires comparing the benefits and harms of all available treatments. However, not all the direct comparisons are available from randomized trials. This makes the multiple comparisons

## Theory and Application of Evolutionary Algorithms

Evolutionary algorithms are iterative stochastic optimisation algorithms which achieve approximate solutions of a problem through use of naturally inspired ‘random’ operations such as crossover, mutation and natural selection. They act on a population of individuals, each one an approximation to a solution of the problem. Analysis of the algorithm is based upon analysis of how

## Hybrid mesons from a potential model

The elementary particle called quarks combine together to form mesons. For heavy quarks the masses of the mesons can be obtained by numerically solving Schrodinger’s equation (from quantum mechanics) with a suitable potential (see http://de.arxiv.org/abs/0805.2704 for example). The potential can be modified to predict the masses of hybrid mesons. The aim of the project is

## Cryptography

Cryptography is an eminently applicable area of mathematics. The problems come in several different flavours and utilise distinct areas of mathematics, giving available projects in at least the following two areas. a. Number-theoretic cryptography: Number-theoretic cryptosystems depend upon numerical base problems such as the discrete logarithm problem and integer factorisation problem. RSA is one example

## Game theory

Game theory, popularised by von Neumann and Morgenstern in 1944, is used to study a large variety of real-life situations concerning strategic decision making. It models conflict and cooperative strategies in business, economics, politics and cybersecurity, to name but a few, and may be used to predict short-term and long-term behaviours in a competitive environment.

## Avalanches

An avalanche is an example of a system displaying “self-organisation”. On a clear day, the great mass of snow on a mountain may appear to be in equilibrium, but the slightest change such as a gentle breeze or the drop of a snowflake can trigger the release a dramatic amount of energy as the system

## Fireflies

Fireflies provide an example from nature of the phenomenon of synchronisation. When one firefly flashes near another, it can cause another to match the frequency of its flashing. Using analytical and/or numerical methods, the project will investigate models for synchronising oscillators, covering topics such as phase-locking and entrainment.   Supervisor: Dr Ben King

## Shock waves: Burgers’ Equation

Shock waves occur throughout nature: in fluids, gases and plasmas. A classic example is the “sonic boom” produced around an aircraft when it exceeds the speed of sound. This project will involve the study of Burgers’ equation, which is a fundamental partial differential equation that demonstrates shock wave behaviour. Using analytical and/or numerical methods, the

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