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Theses and Dissertations (Mathematics and Applied Mathematics): Recent submissions
Now showing items 1-20 of 157
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(University of Pretoria, 2023)In this dissertation we explore the theory and applications of Gröbner bases, and the algorithms that allow us to compute them.
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(University of Pretoria, 2023)The theory of fragmentation-coagulation equations began around 1916 with a series of papers by Smoluchowski on pure coagulation and since then continued to incorporate other processes into the model. The intention was to ...
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(University of Pretoria, 2022)Seitz’s theorem asserts that a finite group has exactly one non-linear irreducible character of degree greater than one if and only if the group is either an extraspecial 2-group or the group is isomorphic to a one-dimensional ...
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(University of Pretoria, 2023)Researchers from the field of econophysics have favoured the idea that financial markets are a complex adaptive system, consisting of entities that behave and interact in a diverse manner, leading to non-linear, emergent ...
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(University of Pretoria, 2022)The physiological structure of microbial communities in natural environments is typically a response to changes in internal and external conditions. External conditions may include the availability or depletion of ...
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(University of Pretoria, 2023)The Rado graph, denoted R, is the unique (up to isomorphism) countably infinite random graph. It satisfies the extension property, that is, for two finite sets U and V of vertices of R there is a vertex outside of both U ...
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(University of Pretoria, 2022)Research on vibrations of flexible structures is ongoing in engineering and applied mathematics fields. Flexible structures in practice can be considered as systems of interconnected rod-like components. This dissertation ...
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(University of Pretoria, 2022)In this work, we focus on a general procedure for finding exact travelling wave solutions for evolution equations with polynomial nonlinearites. Mathematically, looking for travelling wave solutions is asking the question ...
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(University of Pretoria, 2022)In this study, we discuss derivatives, Lie symmetries and invariant solutions of the Black Scholes equation. We combine the Lie group methods with the Adomian decomposition method to solve the Black and Scholes equation ...
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(University of Pretoria, 2021)The space C(X) of real-valued continuous functions on a topological space X is a vector lattice and a locally convex topological vector space, but what is the interaction between these structures? In the case of a compact ...
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(University of Pretoria, 2020)Challenges experienced by first year students transitioning from secondary to tertiary mathematics education are examined through the lens of the didactical contract or agreement between the lecturer and students that is ...
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(University of Pretoria, 2020)In this thesis, we make use of numerical schemes in order to solve Fisher’s and FitzHugh-Nagumo equations with specified initial conditions. The thesis is made up of six chapters. Chapter 1 gives some literatures on partial ...
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(University of Pretoria, 2015-01)The vibration of elastic bodies and structures consisting of elastic bodies is an active research field in engineering and applied mathematics. Typically, a mathematical model is a complex system of partial differential ...
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(University of Pretoria, 2021)In this work, we construct numerical methods to solve a wide range of problems in finance. This includes the valuation under affine jump diffusion processes, chaotic and hyperchaotic systems, and pricing fractional ...
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(University of Pretoria, 2020)Order properties are normally derived from maximum principles associated with an operator, say $P$, in classical formulation. This result is often formulated as a comparison theorem for solutions of linear elliptic PDEs ...
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(University of Pretoria, 2020-12)A cone K in a vector space X is a subset which is closed under addition, positive scalar multiplication and the only element with additive inverse is zero. The pair (X, K) is called an ordered vector space. In this study, ...
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(University of Pretoria, 2021)In this thesis, we study the representation of dynamic risk measures based on backward stochastic differential equations (BSDEs) and ergodic-BSDEs, and capital allocation. We consider the equations driven by the ...
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(University of Pretoria, 2020-10-20)Maximising investment returns is the primary goal of asset management but managing and mitigating portfolio risk also plays a significant role. Successful active investing requires outperformance of a benchmark through ...
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(University of Pretoria, 2019)Mosquitoes are long-legged, two winged flies that are responsible for the transmission of many diseases such as Zika fever, malaria, yellow fever, chikungunya and dengue hemorrhagic fever. Mosquito borne diseases account ...
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(University of Pretoria, 2019)This study investigates the cryptocurrency called bitcoin. A cryptocurrency is a type of currency that depends on cryptography to issue new units instead of depending on government decree like fiat currencies. The study ...
Now showing items 1-20 of 157