• The theory of Gröbner bases and applications 

  Davies, Andrew Barnard (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.
• Fragmentation-coagulation equation with growth 

  Poka, Wetsi D (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 ...
• On groups with few 𝑝′-character degrees 

  Mabena, Lehlogonolo Shaun (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 ...
• Application of network filtering techniques in finding hidden structures on the Johannesburg Stock Exchange 

  Gopi, Yashin (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 ...
• Reaction diffusion modelling of bacteria colonies : microbial quiescence and chemotaxis 

  Dumani, Phindile (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 ...
• A guide to the Rado graph : exploring structural and logical properties of the Rado graph 

  Michau, Michelle (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 ...
• Analysis of the vibration of flexible structures 

  Blecher, Tatiana Monique (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 ...
• Beyond the tanh method-looking for explicit travelling wave solutions to partial differential equations 

  Maqele, Khanyisani (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 ...
• Invariant solutions of the Black-Scholes equation 

  Mothiba, Makoba Melidah Kholofelo (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 ...
• Semi-order units in vector lattices 

  Chitanga, Painos (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 ...
• The use of personal response systems to renegotiate the didactical contract in tertiary mathematics education 

  Bothma, Karin (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 ...
• Strong approximation on the Cox-Ingersoll-Ross model 

  Letsoalo, Sabelo Gerald (University of Pretoria, 2022)

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• Analysis of linear and nonlinear mathematical models for beams, cables, columns and rods 

  Hohls, Kirstin (University of Pretoria, 2021)

  The aim of the dissertation was to conduct a literature study on mathematical modelling, numerical computation and mathematical analysis of a linear and nonlinear Timoshenko model for the vibration of a rod with an axial ...
• On the numerical solution of Fisher's and FitzHugh-Nagumo equations using some nite di erence methods 

  Agbavon, Koffi Messan (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 ...
• Convergence analysis of finite element approximations of solutions of hyperbolic equations 

  Stapelberg, Belinda (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 ...
• Involutions on sheaves of endomorphisms of modules over ringed spaces 

  Ng'ambi, Richard (University of Pretoria, 2021)

  The study of Azumaya algebras over schemes has had a comparatively formidable reputation in algebraic geometry over the past decades. In this thesis, we provide in the sheaf-theoretic setting counterparts of results ...
• Finite element analysis of vibrating elastic structures 

  Du Toit, Sonja (University of Pretoria, 2020)

  In this thesis mathematical models for vibrating elastic structures are derived and analysed using finite element approximations where necessary. The most important contribution in this thesis is the development of the ...
• Robust time spectral methods for solving fractional differential equations in finance 

  Bambe Moutsinga, Claude Rodrigue (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 ...
• Comparison theorems for elliptic and parabolic operators in variational form 

  Majozi, Nduduzo Khayelihle (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 ...
• Characterization of reflexive Banach spaces 

  Mbambo, S.P. (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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