Despite attempts to decrease university drop-out rates, the graduation rate remains low both internationally and locally. Internationally, up to 40% of students who enter higher education do not graduate; in South Africa, the number is higher at 55%. Several studies have found that growth mindset interventions help improve performance in mathematics and language courses. However, most of these studies are carried out outside of South Africa and on children and adolescents. Very little is known about whether and how the growth mindset theory can help improve performance in first-year university courses in South Africa. In this study, the correlation between mindset and performance in first-year mathematics courses is investigated. First-year science, commerce, and engineering students (N=745) enrolled in four different introductory calculus courses participated in this study. Their mindsets were assessed using a survey questionnaire known as the Mindset Assessment Profile (MAP) tool. The reliability of the Mindset Assessment Profile was assessed using Cronbach's alpha coefficient. This was followed by a comparison of mindset scores of students enrolled in different degree programs. Moreover, the participants' average mindset scores in the current study were compared with international mindset scores. The participants' mathematics grades were collected for different assessments during the academic year. The changes in mathematics grades were compared with the mindset scores to examine the relationship between the two variables. The mathematics grade changes were used instead of the grades themselves; this is because the aim was to measure the improvement in mathematics grades rather than the final grade. In the face of failure, students with a growth mindset are predicted to put more effort and seek feedback to improve their grades in subsequent assessments. On average, the participants of this study were growth mindset oriented according to the Mindset Assessment Profile tool. The MAP was moderately reliable, with Cronbach's alpha coefficients ranging between 0.501 and 0.642. Item-by-item analysis showed that reliability could not be improved by the removal of any item in the Mindset Assessment Profile. There was a significant difference between the mindset scores of commerce students and the mindset scores of science and engineering students. Students enrolled in commerce degree programs scored significantly lower than students enrolled in science and engineering degree programs on the MAP. The University of Cape Town students scored higher than Hong Kong university students on the mindset scale but lower than the students in the US. There was no statistically significant correlation between mindset scores and academic performance in any of the degree programs. The correlations were assessed for (a) all the students, (b) students who failed their first mathematics test, and (c) students who scored 75% and above for their first mathematics test. The findings of this study provide a baseline of mindset scores for a South African university population. The tool for measuring mindset may need to be adapted to be better suited for the population outside of the United States. Furthermore, future research should investigate the effects of a growth mindset intervention on academic performance in mathematics grades at the University of Cape Town.

The presence of periodic oscillations in the earth's atmosphere has been confirmed in recent years by analysis of satellite drag data. The amplitudes of these oscillations vary with height and time in a complex manner with the underlying physical mechanism of this behaviour not fully understood. Classical studies have been limited to the lower levels of the atmosphere, but these have neglected to include the damping effects of heat conduction and viscosity. These also ignored the second order terms in the equations of motion which, in effect, treats an otherwise singular perturbation problem as regular. Upper atmosphere studies of the diurnal density oscillations were discussed by Nicolet, on the basis of the mutual diffusion of the components of a binary gas system, where he compared different equilibrium configurations. This statical treatment again ignores the damping effects on mass flow. D.G. Parkyn reduced the problem in idealised form to that of investigating the effect of a travelling temperature wave at the base of a viscous, heat conducting, diffusing gas atmosphere. This model excludes molecular dissociation and ionization in the upper regions and absorption of solar energy. Incorporation of all these properties would render the problem impossibly difficult . As a first step to the development of the analysis for the complex spherical atmosphere, Parkyn simplified the model to that of a cylindrical homogeneous atmosphere, and he considered the effect of forced oscillations about an isothermal equilibrium state. Parkyn showed that this idealised problem is capable of explicit solution and, contrary to the result of Wilkes, he found that the amplitudes of the forced osciliations decrease with height in the lower atmospheric regions. This implies the importance of heat conduction and viscosity as damping effects in these regions. It is proposed to extend the analysis of Parkyn by simplifying the geometry, treating one space dimension, so giving more flexibility to the assumed physical properties. Continuum equations of motion will be taken to hold throughout the range of investigation.

Includes bibliography. / The main focus of this thesis is to study the properties of null geodesics in general relativistic models. This thesis is divided into two parts. In the first part, we introduce the (1+3)-covariant approach which will be used in our study of null geodesics and their applications to gravitational lensing. The dynamics of the null congruence can be better understood through the propagation and constraint equations in the direction of the congruence. Thus, we derive these equations after describing the geomentry of a ray. We also derive a general from of the null geodesic deviation equation (NGDE) which can be used in any given space-time. Various applications of this equation are studied, including its role in determining area-distance relations in an Friedmann-Lemaitre-Robertson-Walker (FLRW) cosmological model. We also use the NGDE in deriving a covariant form of the angle of deflection, showing its versatile applications in gravitational lensing theory.

Genetic Programming is a type of machine learning that employs a stochastic search of a solutions space, genetic operators, a fitness function, and multiple generations of evolved programs to resolve a user-defined task, such as the classification of data. At the time of this research, the application of machine learning to radio astronomy was relatively new, with a limited number of publications on the subject. Genetic Programming had never been applied, and as such, was a novel approach to this challenging arena. Foundational to this body of research, the application Karoo GP was developed in the programming language Python following the fundamentals of tree-based Genetic Programming described in "A Field Guide to Genetic Programming" by Poli, et al. Karoo GP was tasked with the classification of data points as signal or radio frequency interference (RFI) generated by instruments and machinery which makes challenging astronomers' ability to discern the desired targets. The training data was derived from the output of an observation run of the KAT-7 radio telescope array built by the South African Square Kilometre Array (SKA-SA). Karoo GP, kNN, and SVM were comparatively employed, the outcome of which provided noteworthy correlations between input parameters, the complexity of the evolved hypotheses, and performance of raw data versus engineered features. This dissertation includes description of novel approaches to GP, such as upper and lower limits to the size of syntax trees, an auto-scaling multiclass classifier, and a Numpy array element manager. In addition to the research conducted at the SKA-SA, it is described how Karoo GP was applied to fine-tuning parameters of a weather prediction model at the South African Astronomical Observatory (SAAO), to glitch classification at the Laser Interferometer Gravitational-wave Observatory (LIGO), and to astro-particle physics at The Ohio State University.

No description available.

Includes abstract. / Includes bibliographical references (p. 69-73). / The objective of this thesis is to explore several hotly debated current issues in modern cosmology, with a focus on f(R) gravity. In chapter 1 we present a review of modern theoretical cosmology. We begin by introducing some fundamental cosmological concepts, followed by a discussion of the field equations of general relativity, which underlie both the behavior of global cosmological models and the isolated gravitating systems such as stars, black holes and galaxies. In particular we focus on the solutions for the Friedmann-Robertson-Walker Universe. Next we present a detailed discussion of the dark matter problem. Astrophysical observations indicate that the two components account for 25% of the total mass/energy of the observable Universe. We then present the big bang model, which represents the current standard model for the origin and the evolution of the Universe. In our discussion we introduce the inflationary scenario in some detail; specifically we present an example of quadratic inflation to demonstrate how this scenario provides a solution to some of the problems with the standard model. Next we discussed the dark energy model, which as been introduced to address the late-time acceleration problem. We then present the quintessence model, which as been proposed to address the coincidence and the magnitude problems. We conclude this chapter by a detailed discussion of the higher order theories of gravity with a particular we focus on f(R)-gravity, which is based on the idea of introducing corrections to the Einstein-Hilbert action that are negligible in the early Universe and only become effective at late times when the Ricci curvature R decreases. In our discussion we indicate how these corrections can be interpreted as an effective fluid of purely geometrical origin; we also discuss the phase space and stability of deSitter space in f(R) gravity.

Bibliography: pages 78-81. / In the nineteenth century no distinction was drawn between maximal and nonmaximal orders in a numberfield. Most of the work on orders in this period was done by Dedekind and Kronecker. The twentieth century has witnessed a relative neglect of the nonmaximal orders of a numberfield, which are the algebraic analogues of singular curves, although a few texts, for example the one by Borevich and Shafarevich, do discuss arbitrary orders. In this dissertation we attempt to present a connected account of the theory of nonmaximal orders, highlighting some of their important properties.

This thesis is intended to critically review the standard black holes. In this thesis, we used the intractability of the black hole Information loss problem and the current crisis stirred up by the black hole Firewall paradox to support the argument that nature is better off without black holes.

Includes bibliographical references. / The Copernican principle asserts homogeneity on very large scales, however, this scale is still not well defined; and in reality homogeneity is assumed. Recent galaxy redshift surveys have brought in a large amount of cosmological data out to redshift 0.3 or more, that is now available for analysis; and their accuracy has been improved dramatically. With future surveys expected to achieve a high degree of completeness out to redshift exceeding 1, and a dramatic increase in the amount of data harvested, it will soon be practical to have a numerical programme for determining the metric of the universe from standard observations. This project is the beginning of a series of developments on such a numerical implementation. It is sensible to start with a simple case - that of spherical symmetry and a dust equation of state. Using observational data from out post light cone, consisting of galaxy redshifts, apparent luminosities, angular diameters and number densities, together with chosen source evolution functions, viz absolute luminosities, true diameters and masses of sources; and applying the algorithm in [43], a set of Lemaître-Tolman-Bondi (LTB) arbitrary functions can be found. This set will specify the LTB model that reproduces the given observations, and hence provides a metric that describes the geometry of the observed universe. We briefly review the theoretical development of this topic from the fundamental paper by Kristian and Sachs, to the ideal observational cosmology programme by Ellis and Stoeger and others. We also discuss some of the most crucial issues that we are currently facing in the study of observational cosmology, for example, the problem of source evolution and selection effects. We then briefly introduce a few recent galaxy redshift surveys, that are available for analysis, or will be available in the near future, and the data that we may use from them. We also discuss how one can obtain the diameter distance, luminosity distance and number density, the observables that are essential to our project. We introduce the LTB metric, the null cone solution and the notation that we use, and thus relate the LTB model to be observables.

Bibliography: pages 92-95. / A lattice gas is a species of cellular automaton used for numerically simulating fluid flows. TransGas [9], the lattice gas code currently in use at the CSIR, is based on the FHP-I model [5], and is used to perform various two-dimensional flow simulations. In order to broaden the scope of the applications in which lattice gases can be used locally, the development of a three-dimensional lattice gas capability is required. The first major task in setting up a three dimensional-lattice gas is the construction of an efficient collision rule generator which will determine collision outcomes. For suitability to local applications, the collision rules should be chosen in such a way as to maximise the Reynolds coefficient of the flow, while conserving quantities such as mass and momentum. Part of the task thus becomes an optimisation problem. When expanding from two to three dimensions, the number of possible collision rules increases from 64 to 16777216. If a complete collision rule table is used for determining collision outcomes, storage problems are encountered on the available hardware. Selection and optimisation of collision rules cannot be done by hand when there are so many rules to choose from. Selection of rules is thus non-trivial. The work outlined in this thesis provides the CSIR with a 3-D lattice gas collision table which is well suited to the available hardware capabilities. The necessary theoretical background is considered, and a survey of the literature is presented. Based on the findings of this literature study, various methods of collision outcome determination are implemented which are considered to be suitable to the local needs, while remaining within the constraints set by hardware availability. An isometric collision algorithm, and a reduced collision table are generated and tested. A measure of the overall efficiency of a lattice gas model is determined by two factors, namely the computational efficiency and the implementation efficiency. In testing a collision table, the first is characterised by the rate at which post-collision states can be determined, and depends on the hardware and programming techniques. The second factor can be expressed by means of a number called the Reynolds coefficient, which is defined and discussed in the following chapters. The higher the Reynolds coefficient of a model, the greater the scope of flow regimes which may be simulated using it. Another advantage of having a high Reynolds coefficient is that the simulation time required for a given flow regime decreases as the Reynolds coefficient of the model increases. The overall efficiency of the isometric model is too low to be of practical use, but a significant improvement is obtained by using the method of reduced tables. In the isometric case, the number of collision outcomes that can be determined per second is similar to that of the reduced table, but the Reynolds coefficient is very much lower. Simulation of a flow regime with a Reynolds number of about 100, on a lattice of size 128³, over 20 thousand timesteps, making use of the isometric model, would take of the order of a few years to complete on the currently available hardware. Since the simulation parameters mentioned above are typical of the local requirements for lattice gas simulations, this method is obviously unsatisfactory. The isometric method does however serve as a useful introduction to three-dimensional lattice gas collision rule methods. The reduced collision table has been constructed so that it maintains semi-detailed balance, and the Boltzmann Reynolds coefficient has been calculated. In the reduced collision table model, the efficiency is higher than the isometric case in respect of both the rate at which collision outcomes can be determined, and in terms of the Reynolds coefficient. As a result of these improvements, the simulation time for the exact case mentioned above would reduce to the order of days, on the same hardware. This simulation time is sufficiently low for immediate practical application in the local environment.