Doctoral Degrees (Mathematics and Computer Science Education)
Recent Submissions

The pedagogical content knowledge (PCK) of Rwandan grade six mathematics teachers and its relationship to student learning.
(2017)Abstract available in PDF file. 
Mathematics for future engineers : a study of teaching and learning mathematics in an engineering curriculum.
(20160119)This is a study of teaching and learning in the first mathematics module for engineering students at a South African university. The theoretical framing of the study is derived from multiple analytical tools: Bernstein’s ... 

Stellar structure and accretion in gravitating systems.
(2012)In this thesis we study classes of static spherically symmetric solutions to the Einstein and Einstein–Maxwell equations that may be used to model the interior of compact stars. We also study the spherical accretion of ... 
Normalitylike properties, paraconvexity and selections.
(2012)In 1956, E. Michael proved his famous convexvalued selection theorems for l.s.c. mappings de ned on spaces with higher separation axioms (paracompact, collectionwise normal, normal and countably paracompact, normal, and ... 
Linear codes obtained from 2modular representations of some finite simple groups.
(2012)Let F be a finite field of q elements and G be a primitive group on a finite set . Then there is a Gaction on , namely a map G ! , (g; !) 7! !g = g!; satisfying !gg0 = (gg0)! = g(g0!) for all g; g0 2 G and ... 
The role and use of sketchpad as a modeling tool in secondary schools.
(2004)Over the last decade or two, there has been a discernible move to include modeling in the mathematics curricula in schools. This has come as the result of the demand that society is making on educational institutions to ... 
Constructions and justifications of a generalization of Viviani's theorem.
(2013)This qualitative study actively engaged a group of eight preservice mathematics teachers (PMTs) in an evolutionary process of generalizing and justifying. It was conducted in a developmental context and underpinned by a ... 
Exploring master teachers' use of visuals as tools in mathematical classrooms.
(2011)The teaching and learning of mathematics has presented a great challenge for mathematics educationalists over many decades. Researchers have been searching for new strategies and techniques for improving the understanding ... 
Conformally invariant relativistic solutions.
(1993)The study of exact solutions to the Einstein and EinsteinMaxwell field equations, by imposing a symmetry requirement on the manifold, has been the subject of much recent research. In this thesis we consider specifically ... 
Conservation laws models in networks and multiscale flow optimization.
(2011)The flow of fluids in a network is of practical importance in gas, oil and water transport for industrial and domestic use. When the flow dynamics are understood, one may be interested in the control of the flow formulated ... 
Aspects of functional variations of domination in graphs.
(2003)Let G = (V, E) be a graph. For any real valued function f : V >R and SCV, let f (s) = z ues f(u). The weight of f is defined as f(V). A signed ksubdominating function (signed kSF) of G is defined as a function f : V > ... 
Graph and digraph embedding problems.
(1996)This thesis is a study of the symmetry of graphs and digraphs by considering certain homogeneous embedding requirements. Chapter 1 is an introduction to the chapters that follow. In Chapter 2 we present a brief survey ... 
The thermal SunyaevZel'dovich effect as a probe of cluster physics and cosmology.
(2010)The universe is a complex environment playing host to a plethora of macroscopic and microscopic processes. Understanding the interplay and evolution of such processes will help to shed light on the properties and evolution ... 
On purity relative to an hereditary torsion theory.
(1992)The thesis is mainly concerned with properties of the concept "σpurity" introduced by J. Lambek in "Torsion Theories, Additive Semantics and Rings of Quotients", (SpringerVerlag, 1971). In particular we are interested ... 
Aspects of distance and domination in graphs.
(1995)The first half of this thesis deals with an aspect of domination; more specifically, we investigate the vertex integrity of ndistancedomination in a graph, i.e., the extent to which ndistancedomination ... 
Polynomial approximations to functions of operators.
(1994)To solve the linear equation Ax = f, where f is an element of Hilbert space H and A is a positive definite operator such that the spectrum (T (A) ( [m,M] , we approximate 1 the inverse operator A by an operator V which ... 
Amplitudeshape method for the numerical solution of ordinary differential equations.
(1997)In this work, we present an amplitudeshape method for solving evolution problems described by partial differential equations. The method is capable of recognizing the special structure of many evolution problems. ... 
Spherically symmetric cosmological solutions.
(1996)This thesis examines the role of shear in inhomogeneous spherically symmetric spacetimes in the field of general relativity. The Einstein field equations are derived for a perfect fluid source in comoving coordinates. ... 
A modelling approach for determining the freshwater requirements of estuarine macrophytes.
(1998)Increased abstraction of water in the catchment results in a reduced or altered pattern of river flow and this holds serious consequences for the downstream estuarine ecosystem. In South Africa this is a serious concern ...