Magister Scientiae  MSc (Mathematics and Applied Mathematics)
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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. ... 
Multilevel Monte Carlo simulation in options pricing
(University of the Western Cape, 2014)In Monte Carlo path simulations, which are used extensively in computational finance, one is interested in the expected value of a quantity which is a functional of the solution to a stochastic differential equation [M.B. ... 
Mathematical modeling in the sustainable use of natural resources.
(University of the Western Cape, 2015)The sustainable use of natural resources is of utmost importance for every community. In particular, it is important for every given generation to plan in such a way that proper provision is made for future generations. ... 
On the design and implementation of a hybrid numerical method for singularly perturbed twopoint boundary value problems
(University of the Western Cape, 2014)With the development of technology seen in the last few decades, numerous solvers have been developed to provide adequate solutions to the problems that model different aspects of science and engineering. Quite often, these ... 
Codes Related to and Derived from Hamming Graphs
(University of the Western Cape, 2013)Codes Related to and Derived from Hamming Graphs T.R Muthivhi M.Sc thesis, Department of Mathematics, University of Western Cape For integers n; k 1; and k n; the graph k n has vertices the 2n vectors of Fn2 and ...