First chapter of my thesis reviews recent developments in the theory and practice of volatility measurement. We review the basic theoretical framework and describe the main approaches to volatility measurement in continuous time. In this literature the central parameter of inter…
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The chromatic polynomials of certain families of graphs can be calculated by a transfer matrix method. The transfer matrix commutes with an action of the symmetric group on the colours. Using representation theory, it is shown that the matrix is equivalent to a block-diagonal ma…
This thesis is presented in two parts. In the first part, we study a family of models of random partial orders, called classical sequential growth models, introduced by Rideout and Sorkin as possible models of discrete space-time. We analyse a particular model, called a random b…
Frequency Assignment Problems (FAPs) arise when transmitters need to be allocated frequencies with the aim of minimizing interference, whilst maintaining an efficient use of the radio spectrum. In this thesis FAPs are seen as generalised graph colouring problems, where transmitt…
This thesis has two distinct parts. The second and third chapters concern the theory and practical implementation of computing the value of the (possibly multivariate) distribution function from the known characteristic function. The remaining four chapters consist of a study of…
This thesis explores how small group interactions around problem-solving in secondary school mathematics can be understood using a theoretical framework of Communicative Action inspired by Habermasian Critical Theory. How does cognition express itself socially? What are the tech…
Interest in risk management has increased in recent years. many studies concerning risk and insurance theory have appeared. These have been aimed at defining the risks and finding the most suitable methods to control them and their effects as well as minimizing the costs. The in…
This study reports on a project exploring how a commitment towards teaching mathematics for social justice amongst teachers can be translated into related classroom practice. It recounts how a group of teacher researchers set about achieving this through developing, trying out a…
This thesis explores how small group interactions around problem-solving in secondary school mathematics can be understood using a theoretical framework of Communicative Action inspired by Habermasian Critical Theory. How does cognition express itself socially? What are the tech…
This research explores the complexities of children's everyday experience, examining the common threads and distinctive textures of the lives of four children on their educational journeys from primary to secondary school. Whilst the classroom focus of the empirical work has rem…
This dissertation represents an attempt at increasing the behavioural sophistication of evacuation simulations, through the study of evacuation modelling, the development of new behavioural algorithms, their implementation within an existing evacuation model and the testing of t…
The aim of this thesis is to generalise Bayesian Forecasting processes to models where normality assumptions are, not appropriate. In particular I develop models that can change their minds and I utilise Catastrophe Theory in their description. Under squared-error loss types of …
The first mathematics course for approximately 53 percent of U.S. community college students is a developmental algebra course. Many such students appear to be severely debilitated by their previous encounters with mathematics. Due to numerous misconceptions that dictate against…
This thesis presents the results of an investigation into the flow of several non- Newtonian fluids through two curved gradual planar contractions (contraction ratios 8:1 and 4:1). The objectives were to determine whether a newly discovered effect (velocity overshoots were obser…
Hunt and Kaloshin (1999) proved that it is possible to embed a compact subset X of a Hilbert space with upper box-counting dimension d into RN for any N > 2d+1, using a linear map L whose inverse is Hölder continuous with exponent α < (N - 2d)/N(1 + τ(X)/2), where τ(X) is the 't…
In this thesis we present two different models of Complex Social Systems. The first model represents a vector-borne disease that takes place in a heterogeneous environment composed of areas of different types. Two populations take part in the epidemic process: humans and vectors…
This thesis presents an approach to predicting a 3-dimensional, 3-component velocity field of a fluid ow that possesses a homogeneous dimension. At the core of this approach is the technique of stochastic estimation, which is commonly used to combine a small number of instantane…
In the course of this thesis, several different applications of data assimilation will be looked at. In each case, a rigorous mathematical framework will be constructed, in a Bayesian context, to enable the use of various types of data to infer on various infinite dimensional pa…
Penalized spline regression models are a popular statistical tool for curve fitting problems due to their flexibility and computational efficiency. In particular, penalized cubic spline functions have received a great deal of attention. Cubic splines have good numerical properti…