Department of Mathematics
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Mathematical models for optimal management of bank capital, reserves and liquidity
(University of the Western Cape, 2019)The aim of this study is to construct and propose continuoustime mathematical models for optimal management of bank capital, reserves and liquidity. This aim emanates from the global financial crisis of 2007 − 2009. In ... 
Codes, graphs and designs from maximal subgroups of alternating groups
(University of the Western Cape, 2018)The main theme of this thesis is the construction of linear codes from adjacency matrices or submatrices of adjacency matrices of regular graphs. We first examine the binary codes from the row span of biadjacency ... 
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 ... 
A mathematical model for studying the impact of climate variability on malaria epidemics in South Africa
(University of the Western Cape, 2017)Malaria is most prevalent in tropical climates, where there are sufficient rainfall for mosquitoes to breed and conducive temperatures for both the mosquito and protozoa to live. A slight change in temperature can ... 
Fischerclifford matrices and character tables of inertia groups of maximal subgroups of finite simple groups of extension type
(University of the Western Cape, 2011)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 group extensions. In this dissertation we study the method ... 
Analysis of errors in derivatives of trigonometric functions: a case study in an extended curriculum programme
(University of the Western Cape, 2012)The purpose of this study was to explore errors that are displayed by students when learning derivatives of trigonometric functions in an extended curriculum programme. The first aim was to identify errors that are displayed ... 
The role of visualization in the teaching and learning of multivariate calculus and systems of ordinary differential equations
(University of the Western Cape, 2015)The purpose of this study was to investigate the role of visualization in the conceptualisation and solution of problems in multivariate calculus and dynamical systems. The theoretical basis, and the visual and analytical ... 
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 ... 
Optimal asset allocation and capital adequacy management strategies for Basel III compliant banks
(University of the Western Cape, 2015)In this thesis we study a range of related commercial banking problems in discrete and continuous time settings. The ﬁrst problem is about a capital allocation strategy that optimizes the expected future value of a commercial ... 
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 ...