Masters Degrees (Mathematical Sciences)

 

Recent Submissions

  • Ultraproducts and Los’s Theorem: A Category-Theoretic Analysis 

    Chimes, Mark Jonathan (Stellenbosch : Stellenbosch University, 2017-03)
    ENGLISH ABSTRACT : Ultraproducts are an important construction in model theory, especially as applied to algebra. Given some family of structures of a certain type, an ultraproduct of this family is a single structure ...

  • Imaginaries in dense pairs of real-closed fields 

    Rakotonarivo, Tsinjo Odilon (Stellenbosch : Stellenbosch University, 2017-03)
    ENGLISH ABSTRACT : Imaginaries are definable equivalence classes, which play an important role in model theory. In this thesis, we are interested in imaginaries of dense pairs of real-closed fields. More precisely, we ...

  • Immune biomarker reference range estimation for healthy paediatric patients in South Africa 

    Bicko, Steve Cygu (Stellenbosch : Stellenbosch University, 2017-03)
    ENGLISH ABSTRACT : Understanding and quantifying human peripheral blood T-lymphocyte immunophenotypes is necessary for the diagnosis and treatment of immune and haematological disorders. This is only possible if comparison ...

  • Whole body modelling of glucose metabolism in malaria patients 

    Green, Kathleen (Stellenbosch : Stellenbosch University, 2017-03)

  • The double Heston model via filtering methods 

    Namundjebo, Elia N (Stellenbosch : Stellenbosch University, 2016-12)
    ENGLISH ABSTRACT : Stochastic volatility models are well-known for their ability to generate a volatility smile for financial securities. The development of the stochastic volatility models followed shortly after the ...

  • An integrated framework modelling susceptibility to tuberculosis in homogeneous and admixed populations 

    Gebremariam, Zoe Zerihun (Stellenbosch : Stellenbosch University, 2016-12)
    ENGLISH ABSTRACT : In spite of the wide variety of anti-tuberculosis drugs, tuberculosis (TB), caused by mycobacterium tuberculosis (MTB), is the second leading infectious disease after Human Immunode ciency Virus (HIV) ...

  • Elliptic curve cryptography 

    Louw, Gerard Jacques (Stellenbosch : Stellenbosch University, 2016-12)
    ENGLISH ABSTRACT : In this thesis we present a selection of Diffie-Hellman cryptosystems, which were classically formulated using the multiplicative group of a finite field, but which may be generalised to use other group ...

  • A mathematical model for onchocerciasis and its treatment with ivermectin 

    Omondi, Evans Otieno (Stellenbosch : Stellenbosch University, 2016-12)
    ENGLISH ABSTRACT : Onchocerciasis is a human disease that is caused by the filirial worm Onchocerca volvulus. It occurs close to oxygen rich flowing streams and rivers in the inter-tropical zones. The disease is a serious ...

  • Geometry of Complex Polynomials: On Sendov's Conjecture 

    Chalebgwa, Taboka Prince (Stellenbosch : Stellenbosch University, 2016-12)
    ENGLISH ABSTRACT : Sendov’s conjecture states that if all the zeroes of a complex polynomial P(z) of degree at least two lie in the unit disk, then within a unit distance of each zero lies a critical point of P(z). In a ...

  • Modelling of the invasion dynamics of plasmodium falciparum merozoites into red blood cells 

    Meiring, Maynard (Stellenbosch : Stellenbosch University, 2016-03)
    ENGLISH ABSTRACT : BACKGROUND The physiological symptoms of P. falciparum infection are associated with a 48 hour replication cycle whereby parasites (merozoites) invade susceptible red blood cells (RBCs), develop and ...

  • Modelling the transmission of Buruli ulcer in fluctuating environments 

    Assan, Belthasara (Stellenbosch : Stellenbosch University, 2015-12)

  • On commutativity and lie nilpoten y in matrix algebras 

    Sehoana, Mahlare Gerald (Stellenbosch : Stellenbosch University, 2015-12)
    ENGLISH ABSTRACT : In this thesis we first discuss the proof by Mirzakhani [9] of Schur's Theorem which gives the maximum number of linearly independent matrices in a commutative algebra of n×n matrices over a field F. An ...

  • Spectral radii of matrices associated with graphs 

    Dadedzi, Kenneth (Stellenbosch : Stellenbosch University, 2015-12)

  • Calibration and Model Risk in the Pricing of Exotic Options Under Pure-Jump Lévy Dynamics 

    Mboussa Anga, Gael (Stellenbosch : Stellenbosch UniversityStellenbosch University, 2015-12)
    AFRIKAANSE OPSOMMING : Die groeiende belangstelling in kalibrering en modelrisiko is ’n redelik resente ontwikkeling in finansiële wiskunde. Hierdie proefskrif fokusseer op hierdie sake, veral in verband met die prysbepaling ...

  • Analytic methods in combinatorial number theory 

    Baker, Liam Bradwin (Stellenbosch : Stellenbosch University, 2015-12)
    ENGLISH ABSTRACT : Two applications of analytic techniques to combinatorial problems with number-theoretic flavours are shown. The first is an application of the real saddle point method to derive second-order asymptotic ...

  • Modelling Drug Abuse and Drug-related Crime: A Systems Approach 

    Coetzee, Lezanie (Stellenbosch : Stellenbosch University, 2015-12)
    ENGLISH ABSTRACT : In this study we look at the syndemic of substance abuse and drug-related crime in the Western Cape province of South Africa. The intent of this study is to provoke critical thinking about the possibilities ...

  • Modelling the role of HIV and its treatment in non-Hodgkin lymphoma growth dynamics 

    Aogo, Rosemary Akinyi (Stellenbosch : Stellenbosch University, 2015-12)

  • Modelling the potential role of control strategies on Ebola virus disease dynamics 

    Njankou, Sylvie Diane Djiomba (Stellenbosch : Stellenbosch University, 2015-12)
    ENGLISH ABSTRACT : The most deadly Ebola disease epidemic ever was still ongoing as of June 2015 in West Africa. It started in Guinea, where the first cases were recorded in March 2014. Control strategies, aiming at ...

  • Modelling in- and out-patient rehabilitation for substance abuse in dynamic environments 

    Gatyeni, Siphokazi Princess (2015-12)
    ENGLISH ABSTRACT : Substance abuse is a major problem globally with immeasurable consequences to the health of users. Rehabilitation is one of the strategies that can help to fight against substance abuse. It is divided ...

  • On the effciency of code-based steganography 

    Ralaivaosaona, Tanjona Fiononana (Stellenbosch : Stellenbosch University, 2015-03)
    ENGLISH ABSTRACT: Steganography is the art of hiding information inside a data host called the cover. The amount of distortion caused by that embedding can influence the security of the steganographic system. By secrecy ...

  • Quantitative Risk Management and Pricing for Equity Based Insurance Guarantees 

    Leboho, Nakedi Wilson (Stellenbosch : Stellenbosch University, 2015-03)
    ENGLISH ABSTRACT : Equity-based insurance guarantees also known as unit-linked annuities are annuities with embedded exotic, long-term and path-dependent options which can be categorised into variable and equity indexed ...

  • Building Interest Rate Curves and SABR Model Calibration 

    Mbongo Nkounga, Jeffrey Ted Johnattan (Stellenbosch : Stellenbosch University, 2015-03)
    ENGLISH ABSTRACT : In this thesis, we first review the traditional pre-credit crunch approach that considers a single curve to consistently price all instruments. We review the theoretical pricing framework and introduce ...

  • The Levy-LIBOR model with default risk 

    Walljee, Raabia (Stellenbosch : Stellenbosch University, 2015-03)
    ENGLISH ABSTRACT : In recent years, the use of Lévy processes as a modelling tool has come to be viewed more favourably than the use of the classical Brownian motion setup. The reason for this is that these processes provide ...

  • Heath–Jarrow–Morton models with jumps 

    Alfeus, Mesias (Stellenbosch : Stellenbosch University, 2015-03)
    ENGLISH ABSTRACT : The standard-Heath–Jarrow–Morton (HJM) framework is well-known for its application to pricing and hedging interest rate derivatives. This study implemented the extended HJM framework introduced by ...

  • Bifibrational duality in non-abelian algebra and the theory of databases 

    Weighill, Thomas (Stellenbosch : Stellenbosch University, 2014-12)
    ENGLISH ABSTRACT: In this thesis we develop a self-dual categorical approach to some topics in non-abelian algebra, which is based on replacing the framework of a category with that of a category equipped with a functor ...

  • A no-arbitrage macro finance approach to the term structure of interest rates 

    Thafeni, Phumza (Stellenbosch : Stellenbosch University, 2015-03)
    ENGLISH ABSTRACT: This work analysis the main macro-finance models of the term structure of interest rates that determines the joint dynamics of the term structure and the macroeconomic fundamentals under no-arbitrage ...

  • Analysing ranking algorithms and publication trends on scholarly citation networks 

    Dunaiski, Marcel Paul (Stellenbosch : Stellenbosch University, 2014-12)
    ENGLISH ABSTRACT: Citation analysis is an important tool in the academic community. It can aid universities, funding bodies, and individual researchers to evaluate scientific work and direct resources appropriately. With ...

  • Modelling the dynamics of alcohol and methamphetamine co-abuse in the Western Cape Province of South Africa 

    Orwa, Titus Okello (Stellenbosch : Stellenbosch University, 2014-12)
    ENGLISH ABSTRACT: Clinical results have indicated that abuse of multiple drugs/substances has devastating health and social consequences. The combined abuse of alcohol and the highly addictive methamphetamine has worsened ...

  • The risk parity approach to asset allocation 

    Galane, Lesiba Charles (Stellenbosch : Stellenbosch University, 2014-12)
    ENGLISH ABSTRACT: We consider the problem of portfolio's asset allocation characterised by risk and return. Prior to the 2007-2008 financial crisis, this important problem was tackled using mainly the Markowitz mean-variance ...

  • Virtual world accessibility: a multitool approach 

    Kruger, Rynhardt Pieter (Stellenbosch : Stellenbosch University, 2014-12)
    ENGLISH ABSTRACT: Computer-based virtual worlds are increasingly used for activities which previously required physical environments. However, in its mainstream form, such a virtual world provides output on a graphical ...

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