Mathematics and Applied Mathematics
Fields Of Research:

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The main research fields in Mathematics and Applied Mathematics are listed below with brief descriptions of research projects in each field. The Department is particularly strong in Algebra, Combinatorics and Mathematical modelling.

• Combinatorics (C Zaverdinos)
  Generalised matroids, their associated algorithms and relation to NP-complete problems.
• Ecological Modelling (Prof J W Hearne, Prof J Swart, Dr K Koch, Dr P Ewer)
  Evaluation and formulation of policies and strategies for managing ecosystems - with particular focus on multi-species herbivory systems, estuarine ecosystems, biocontrol of crop pests, and population viability of endangered species.
• Financial modelling (Prof J Swart)
  Optimization of risk-adjusted returns in equity markets.
• Finite Groups and Finite Geometries (Prof J Moori)
  Finite Groups, Simple Groups and Sporadic Groups. Representation Theory of Finite Groups, Character Tables of Extension Groups, Clifford-Fisher Matrices. Applications of Finite Groups to Finite Geometries and Combinatorial Designs. Development of a research team for computerised documentation of Finite Groups and Geometries.
• Graph Theory, Graph Algorithms and Complexity (Prof M A Henning, Dr S Bau)
  Domination in graphs, domination functions and distance domination, pancyclicity, average connectivity, Ramsey theory, vertex coverings, graph colourings, cycles in regular graphs, transformation graphs, decycling number, inductive classes of graphs, nonhamiltonian graphs, random regular graphs, oriented graphs, and factorization of graphs.
• Logic (Dr S-A Ng)
  Forking and stability of models. Quantifier elimination in Banach spaces.
• Nonlinear Parabolic Equations (Dr P Ewer)
• Nonstandard Analysis (Dr S-A Ng)
  Application of nonstandard analysis in stochastic calculus and in Banach spaces. Fixed point problems in nonstandard hulls.
• Ring and Module Theory (Dr J E van den Berg)
  Prime and semiprime rings, Torsion Theory.  Representation of algebraic chains by ideals of rings. Bounds of uniform primeness for certain classes of rings. Radicals associated with prime rings.

Six staff members have NRF (National Research Foundation) support and this, together with URF support, enables staff to make known their research findings regularly both locally and overseas.