Department of Mathematics

Variances of purity within torsion-free Abelian groups

Van Ster, Lynnette (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 ...

Reliable numerical simulations of problems for pricing real estate derivatives

Dube, Mbakisi (University of the Western Cape, 2023)

The globalisation of nancial systems has presented new challenges to investing in real estate assets. For example, any crisis occurring in one real estate market will have an adverse e ect on other markets regardless ...

Analysis and simulation of some ecological models describing weed-water hyacinth dynamics in Lake Tana, Ethiopia

Belay, Yeshambel Azene (University of the Western Cape, 2023)

The water hyacinth plant is notorious for being the world’s worst aquatic weed. In Ethiopia, it invades lake Tana which is the largest lake in Ethiopia. This is attracting attention of many researchers including mathematical ...

Analysis and robust simulation of mathematical models of HIV and Leishmaniasis co-infection

Adamu, Elias M. (University of the Western Cape, 2022)

The purpose of this thesis is the theoretical and numerical study of epidemiological models of Visceral Leishmaniasis (VL) and human immunode ciency virus (HIV) coinfection. We study these models theoretically and design ...

Analysis and simulation of mathematical models governing HIV-TB co-infection dynamics in Ethiopia

Affesa, Getachew Tilahun (University of the Western Cape, 2022)

Among the most prominent health challenges of the 21st century is the impact of the TB and HIV twin epidemics on the globe. In addition to being one of the main factors that contribute to morbidity and mortality, HIV and ...

Pairings of binary reflexive relational structures

Chishwashwa, Nyumbu (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

Wyngaardt, Jo-Anne (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 ...

Mesh Free Methods for Differential Models In Financial Mathematics

Sidahmed, Abdelmgid Osman Mohammed (University of the Western Cape, 2011)

Many problems in financial world are being modeled by means of differential equation. These problems are time dependent, highly nonlinear, stochastic and heavily depend on the previous history of time. A variety of financial ...

Numerical treatment of non-linear singular perturbation problems

Shikongo, Albert (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

Tawe, Tarla Divine (University of Western Cape, 2021)

We present the Black-Scholes Merton partial differential equation (BSMPDE) and its analytical solution. We present the Black-Scholes 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 third-year Statistics

Latief, Abduraghiem (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

Kumwenda, Khumbo (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 ...

Numerical singular perturbation approaches based on spline approximation methods for solving problems in computational finance

Kabir, Mohmed Hassan Mohmed (University of the Western Cape, 2011)

Options are a special type of derivative securities because their values are derived from the value of some underlying security. Most options can be grouped into either of the two categories: European options which can ...

Codes Related to and Derived from Hamming Graphs

Muthivhi, Thifhelimbilu Ronald (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 n-cube, ...

Elementary Logic as a Tool in Proving Mathematical Statements

May, Bruce Matthew (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 non-cancellation groups of certain groups which are split extensions of a finite abelian group by a finite rank free abelian group

Mkiva, Soga Loyiso Tiyo (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 ...