Magister Scientiae  MSc (Mathematics and Applied Mathematics)
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Variances of purity within torsionfree Abelian groups
(University of the Western Cape, 1994)In 1921, Prufer introduced the concept of a pure subgroup of an abelian group. This concept, which is applicable only to abelian groups, proved to be a very useful one. Subsequently, this concept has sparked off numerous ... 
Pairings of binary reflexive relational structures
(University of the Western Cape, 2007)The main purpose of this thesis is to study the interplay between relational structures and topology, and to portray pairings in terms of some finite poset models and order preserving maps. We show the interrelations between ... 
Analysis and Implementation of a Positivity Preserving Numerical Method for an HIV model
(University of the Western Cape, 2007)This thesis deals with analysis and implementation of a positivity preserving numerical method for a vaccination model for the transmission dynamics of two HIV subtypes in a given community. The continuous model is analyzed ... 
Numerical treatment of nonlinear singular perturbation problems
(University of the Western Cape, 2007)This thesis deals with the design and implementation of some novel numerical methods for nonlinear singular perturbations problems (NSPPs). We provide a survey of asymptotic and numerical methods for some NSPPs in past ... 
Analysis and simulation of nonlinear option pricing problems
(University of Western Cape, 2021)We present the BlackScholes Merton partial differential equation (BSMPDE) and its analytical solution. We present the BlackScholes option pricing model and list some limitations of this model. We also present a nonlinear ... 
Throughput of UWC students who did at least one semester of thirdyear Statistics
(University of the Western Cape, 2005)The study explores the completion rates (the number of years a student takes to complete a degree) of graduates at the University of the Western Cape (UWC) in South Africa. The graduates in the study all did at least one ... 
Codes, graphs and designs related to iterated line graphs of complete graphs
(University of the Western Cape, 2011)In this thesis, we describe linear codes over prime fields obtained from incidence designs of iterated line graphs of complete graphs Li(Kn) where i = 1,2. In the binary case, results are extended to codes from ... 
Codes Related to and Derived from Hamming Graphs
(University of the Western Cape, 2013)For integers n, k 2:: 1, and k ~ n, the graph r~has vertices the 2n vectors of lF2 and adjacency defined by two vectors being adjacent if they differ in k coordinate positions. In particular, r~is the classical ncube, ... 
Elementary Logic as a Tool in Proving Mathematical Statements
(University of the Western Cape, 2008)An analysis of South African school mathematics results indicates that one of the problem areas in the mathematical performance of learners is proof and proving. In an endeavour to improve the mathematical proving ability ... 
The noncancellation groups of certain groups which are split extensions of a finite abelian group by a finite rank free abelian group
(University of the Western Cape, 2008)The groups we consider in this study belong to the class Xo of all finitely generated groups with finite commutator subgroups. We shall eventually narrow down to the groups of the form T)<lw zn for some nE N and some finite ... 
Pairings of binary reflexive relational structures
(University of the Western Cape, 2007)The main purpose of this thesis is to study the interplay between relational structures and topology, and to portray pairings in terms of some finite poset models and order preserving maps. We show the interrelations between ... 
The impact of using technology through cooperative learning on learners’ performance on grade 11 circle geometry
(University of the Western Cape, 201911)Euclidean geometry was recently reintroduced as a compulsory topic in the Mathematics Curriculum for learners in the Further Education and Training (FET) band in 2012. The diagnostic analysis reports on the National ... 
Model theory of algebraically closed fields and the AxGrothendieck Theorem
(University of Western Cape, 2020)We introduce the concept of an algebraically closed field with emphasis of the basic modeltheoretic results concerning the theory of algebraically closed fields. One of these nice results about algebraically closed ... 
Boundedness and pseudocompactness in pointfree topology
(University of Western Cape, 2019)This dissertation is a presentation to generalize boundedness and pseudocompactness in pointfree topology. We rst obtain and introduce a boundedness notion for elements of a frame. This is then further inspiration to ... 
Estimating the cost of deposit insurance for a commercial bank following an optimal investment strategy
(University of Western Cape, 2020)Commercial banks play a dominant role in facilitating the economic growth of a country by acting as an intermediary between the de cit spending unit (borrowers) and the surplus spending unit (lenders). In particular, ... 
The paradox of enrichment in predatorprey systems
(University of Western Cape, 2020)In principle, an enrichment of resources in predatorprey systems show prompts destabilisation of a framework, accordingly, falling trophic communication, a phenomenon known to as the \Paradox of Enrichment" [54]. After ... 
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 ...