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Department of Mathematics - Research Interests and Current Projects

As its name suggests, the Department of Mathematics and Applied Mathematics engages in research across the spectrum of our subject.  At the "pure mathematics" end of the spectrum the active academic staff members have established expertise and current research projects in abstract algebra, number theory, topology, analysis, category theory, graph theory and discrete mathematics.  Those whose expertise leans towards "applied mathematics" are involved in research covering control theory, numerical linear algebra, numerical analysis, mathematical biology and computational finance.  There is ongoing research work involving the application of mathematical models in a range of collaborative projects across the university, particularly in the biological sciences.  A number of our staff are involved in mathematics education research in collaboration with colleagues in the faculty of education.

Professor Jennifer Key

Professor Key's research interests lie in finite geometries and designs, and the use of algebraic coding theory in their classification. This work includes permutation decoding methods for linear codes from these structures, and also from graphs.

Current Projects

  • Codes from adjacency matrices related to classes of uniform subset graphs.

  • Hulls of codes from incidence matrices of some strongly regular graphs.

  • Minimum words in codes from non-desarguesian finite affine planes.

  • Codes from a class of quasi-symmetric 2-designs. 

Professor Peter Witbooi

Professor Witbooi's interestes straddle pure mathematics and mathematical modeling.  In pure mathematics he engages in research in Algebraic Topology; Quasifibration theory and applications; and Localization of homotopy types and groups. His activities in mathematical modeling are in stochastic or deterministic differential equations, mainly focusing on biological and financial problems.

Current Projects

  • Prevalence of malaria under climate change.

  • MTB-human protein-protein interactions.

  • Homotopy of finite topological spaces. 

Professor Kailash Patidar

Prof Patidar's research is focused on Numerical Methods and Scientific Computing for the applied problems that arise from interactions between natural and life sciences as well as engineering.  His research is a well balanced combination of the analytical investigations and numerical experiments using finite difference, finite element and spline approximation methods. The overall idea behind all these approaches is to design robust solvers for the parameter sensitive differential models described by means of ordinary and/or partial differential equations that arise in various fields in sciences and engineering.

Current Projects

  • The development of reliable numerical methods for the mathematical models arising in population biology.

  • The development of efficient numerical methods for option pricing problems in computational finance.

  • Construction, analysis and implementation of numerical methods for singular perturbation problems.

  • High order numerical methods for singular perturbation problems. 

Professor David Holgate

Professor Holgate's principal research interest is in category theory and topology, pursuing a deeper categorical analysis of methods and constructions in topology and set theory. He also has an interest in education research, in particular the use of technology in undergraduate mathematics teaching and in academic staff development.

Current Projects

    • ·         Compactness and sequential compactness in frames (locales).
    • ·         Neighbourhood, closure and interior operators in categories.
    • ·         (Syn)topogenous structures in categories
    • ·         Boundedness in frames (locales)


Professor Francis Benyah

Professor Benyah conducts research in the areas of Optimal Control Theory and Applications, Mathematical Biology, Optimization and Numerical Analysis.

DR Justin Munyakazi

Dr Munyakazi’s research interests include numerical methods for differential equations, integro-

differential equations, scientific computing and applications of mathematics in biology.

Current Projects:

  • Higher order numerical methods for singularly perturbed systems of differential equations.
  • Design, analysis and implementation of numerical methods for integro-differential equations
  • Mathematical epidemiology and analysis of malaria enhancer and reducer factors

Dr Deon Solomons

Dr Deon Solomons currently does research in Differential Geometry, Gravitation, and Cosmology

Current Projects:

  • Exterior Calculus and its applications in Gravitation and Cosmology
  • Tensor analysis
  • The role of vacuum energy in physics and cosmology

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