Masters Degrees (Mathematics and Computer Science Education)
Recent Submissions

Using mathematical and economic epidemiology tools for modelling HIV infection in serodiscordant couples.
(2015)We investigate the appropriate strategies that reduce the HIV transmission rate amongst the serodiscordant married couples. In particular, we formulate two discrete submodels, the formation of married serodiscordant ... 
Exploring preservice teachers' mental constructions of matrix algebra concepts : a South African case study.
At the university where the study was conducted matrix algebra is one of the first advanced mathematics courses that preservice teachers encounter. The transfer of knowledge from a primarily procedural or algorithmic ... 
Modeling the burden of disease for cattle.
(2014)Summary measures of human population health (SMPH) represents approaches to measuring the burden of disease. These approaches are divided into two classes: health expectancies and health gaps. A health gap model approach ... 
Spanning trees : eigenvalues, special numbers, and the treecover ratios, asymptotes and areas of graphs.
(2014)This dissertation deals with spanning trees associated with graphs. The number of spanning trees of a graph can be found by considering the eigenvalues of the Laplacian matrix associated with that graph. Special classes ... 
On the existence of selfdual codes invariant under permutation groups.
(2014)Abstract available in PDF file. 
On minimal degrees of faithful permutation representations of finite groups.
(2014)Abstract available in PDF file. 
Connectedness and the hyperspace of metric spaces.
(2015)One of the prime motivations for studying hyperspaces of a metric space is to understand the original space itself. The hyperspace of a metric space X is the space 2X of all nonempty closed bounded subsets of it, endowed ... 
Mathematical modelling of drug resistance in malignant tumour treatment.
(2014)Resistance to conventional chemotherapies, especially to anticancer agents, is rapidly becoming a global pandemic. Mutations, in combination with genetic instabilities, play an important role in the molecular heterogeneity ... 
On decoupled quasilinearization methods for solving systems of nonlinear boundary value problems.
(20150610)In this dissertation, a comparative study is carried out on three spectral based numerical methods which are the spectral quasilinearization method (SQLM), the spectral relaxation method (SRM) and the spectral local ... 
Chebyshev spectral pertutrbation based method for solving nonlinear fluid flow problems.
(20150303)In this dissertation, a modi cation of the classical perturbation techniques for solving nonlinear ordinary di erential equation (ODEs) and nonlinear partial di erential equations (PDEs) is presented. The method, called ... 
Congestion control based on dynamics pricing scheme and service classbased joint call admission control in heterogeneous wireless networks.
(20150226)Next Generation of Wireless Networks (NGWNs) are heterogeneous and consist of several Radio Access Technologies (RATs) that coexist in the same geographical area. This heterogeneity of wireless networks is supposed to ... 
Using artefacts to support an embodied approach to learning trigonometry : a case study of grade 10 learners.
(2013)The purpose of this study was to explore the role of artefacts (manipulatives) in the teaching and learning of trigonometric ratios in grade 10. The study focused on how the use of manipulatives aided learners’ mathematical ... 
Mathematical analysis of tuberculosis vaccine models and control stategies.
(20141020)The epidemiological study of tuberculosis (TB) has been ongoing for several decades, but the most effective control strategy is yet to be completely understood. The basic reproduction number, R₀, has been found to be ... 
Analysis of coinfection of human immunodeficiency virus with human papillomavirus.
(20140517)We formulate a deterministic mathematical model for the coinfection of HPV with HIV without treatment. Mathematical techniques were used to analyze the stability of the models in terms of basic reproduction numbers for ... 
Representation of regular formal languages.
(20140517)This dissertation presents three different approaches to representing Regular Formal languages, i.e., regular expressions, finite acceptors and regular grammars. We define how each method is used to represent the language, ... 
Exact solutions for spherical relativistic models.
(2011)In this thesis we study relativistic models of gravitating uids with heat ow and electric charge. Firstly, we derive the model of a charged shearfree spherically symmetric cosmological model with heat ow. The ... 
Some models of relativistic radiating stars.
(2012)In this dissertation we study radiating stars in strong gravitational elds. We generate new classes of exact solutions to the Einstein eld equations and the boundary condition applicable to radiating relativistic stars. ... 
The interplay of dynamical systems analysis and group theory.
(2011)We investigate the relationship between the Dynamical Systems analysis and the Lie Symmetry analysis of ordinary differential equations. We undertake this investigation by looking at a relativistic model of selfgravitating ... 
An overview of hidden symmetries.
(2012)Approaches to nding solutions to di erential equations are usually ad hoc. One of the more successful methods is that of group theory, due to Sophus Lie. In the case of ordinary di erential equations, the subsequent ... 
Mathematical analysis of preexposure prophylaxis on HIV infection.
(2012)We develop a mathematical model which seeks to assess the impact of HIV PreExposure Prophylaxis (PrEP) on the prevalence and incidence of HIV infection. Mathematical analysis of the model is carried out to establish the ...