Magister Scientiae  MSc (Mathematics and Applied Mathematics)
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Ultrafilters and Compactification
(UWC, 2020)In this thesis, we construct the ultrafilter space of a topological space using ultrafilters as points, study some of its properties and describe a method of generating compactifications through the ultrafilter space. As ... 
Design, analysis and simulation of a robust numerical method to solve Zika virus models
(University of the Western Cape, 2019)This thesis deals with the analysis and robust simulation of mathematical models describing Zika virus disease. Some background information about the occurrences of this disease and most recent literature indicating some ... 
Valuation of options for hedging against exchange rate exposure
(University of the Western Cape, 2019)The risk associated with currency exposure is one of the main sources of risk in terms of internationally diversi ed portfolios. Controlling the risk is important for improving the performance of international investments. ... 
Topogenous Structures on Categories
(University of the Western Cape, 2016)Although the interior operators correspond to a special class of neighbourhood operators, the closure operators are not nicely related to the latter. We introduce and study the notion of topogenous orders on a category ... 
On the method of lines for singularly perturbed partial differential equations
(University of the Western Cape, 2017)Many chemical and physical problems are mathematically described by partial differential equations (PDEs). These PDEs are often highly nonlinear and therefore have no closed form solutions. Thus, it is necessary to ... 
On the numerical integration of singularly perturbed Volterra integrodifferential equations
(University of the Western Cape, 2017)Efficient numerical approaches for parameter dependent problems have been an inter esting subject to numerical analysts and engineers over the past decades. This is due to the prominent role that these problems play in ... 
Pricing European options : a modelfree approach
(University of the Western Cape, 2016)This paper focuses on the newly revived interest to model free approach in finance. Instead of postulating some probability measure it emerges in a form of an outermeasure. We review the behavior of a market stock price ... 
Topogenous structures on categories
(University of the Western Cape, 2016)Although the interior operators correspond to a special class of neighbourhood operators, the closure operators are not nicely related to the latter. We introduce and study the notion of topogenous orders on a category ... 
MetaCayley Graphs on Dihedral Groups
(University of the Western Cape, 2017)The pursuit of graphs which are vertextransitive and nonCayley on groups has been ongoing for some time. There has long been evidence to suggest that such graphs are a very rarety in occurrence. Much success has been had ... 
Character tables of some selected groups of extension type using FischerClifford matrices
(University of the Western Cape, 2015)The aim of this dissertation is to calculate character tables of group extensions. There are several well developed methods for calculating the character tables of some selected group extensions. The method we study in ... 
Do money managers outperform their respective benchmark? Evidence from South African Unit Trust industry
(University of the Western Cape, 2015)Motivated by the growing attraction of the mutual fund industries across the world, this research seeks to explore the economic benefits contributed by the South African equity unit trust managers over the period from 1 ... 
Mathematical modeling of the population dynamics of tuberculosis
(University of the Western Cape, 2016)Tuberculosis (TB) is currently one of the major public health challenges in South Africa, and in many countries. Mycobacterium tuberculosis is among the leading causes of morbidity and mortality. It is known that tuberculosis ... 
Mathematical modelling of HIV/AIDS with recruitment of infecteds
(University of the Western Cape, 2015)The influx of infecteds into a population plays a critical role in HIV transmission. These infecteds are known to migrate from one region to another, thereby having some interaction with a host population. This interactive ... 
Test of the overreaction hypothesis in the South African stock market
(University of the Western Cape, 2014)This research undertakes to investigate both longterm and shortterm investor overreaction on the JSE Limited (JSE) over the period from 1 January 2002 to 31 December 2009. The period covers the restructuring and reform ... 
Investigating the difficulties of first year mainstream mathematics students at the University of the Western Cape with “related rates” problems
(University of the Western Cape, 2014)The aim of the thesis is to research the difficulties that first year mainstream mathematics students at UWC experience when solving Related Rates problems in calculus. In chapter 2, an indepth study was made of the nature ... 
Efficient Monte Carlo methods for pricing of electricity derivatives
(University of the Western Cape, 2012)We discuss efficient Monte Carlo methods for pricing of electricity derivatives. Electricity derivatives are risk management tools used in deregulated electricity markets. In the past,research in electricity derivatives ... 
Automorphism groups of some designs of steiner triple systems and the atomorphism groups of their block intersection graphs
(University of the Western Cape, 2014)A Steiner triple system of order v is a collection of subsets of size three from a set of velements such that every pair of the elements of the set is contained in exactly one 3subset. In this study, we discuss some ... 
The Birch and SwinnertonDyer Conjecture for elliptic curves.
(University of the Western Cape, 2014)The aim of this dissertation is to provide an exposition of the Birch and SwinnertonDyer Conjecture, considered by many to be one of the most important unsolved problems in modern Mathematics. A review of topics in Algebraic ... 
Mathematical model of performance measurement of defined contribution pension funds
(University of the Western Cape, 2015)The industry of pension funds has become one of the drivers of today’s economic activity by its important volume of contribution in the financial market and by creating wealth. The increasing importance that pension funds ... 
Numerical techniques for optimal investment consumption models
(University of the Western Cape, 2014)The problem of optimal investment has been extensively studied by numerous researchers in order to generalize the original framework. Those generalizations have been made in different directions and using different techniques. ...