The core competencies and research expertise of the Unit of Business Mathematics and Informatics includes:
Basic research in Mathematics: functional analysis (summing multipliers and tensor norms), operator theory (operators defined by probabilistic conditional expectation operators, integral operators with semi-separable kernels), control theory (structured noncommutative multidimensional linear systems) and linear algebra (positive real and real expansive matrices in indefinite inner product spaces and invariant maximal semidefinite subspaces).
Basic research in Statistics: non-parametric analysis (curve estimation), bootstrap resampling methods (the m out of methodology, categorical data analysis), survival analysis, time series analysis, probability theory, goodness of fit tests, non-parametric methods applied to risk analysis.
Basic Research in Applied Mathematics: Financial Economy (Banking, Pension funds, Insurance), Health Economy (Nutrition and Economic Growth).
Basic research in Computer Science and Operations research: data mining, image processing, mathematical programming (decision support systems, computer vision, systems and algorithms, super parallel computing, systems development methodologies, algorithm development for material cuts using artificial intelligence, robust linear regression methods, optimal route planning, tree knapsack solutions for local access networks).
Bank Risk Management: financial risk management, securitisation in SA, Efficiency in bank lending and borrowing, performance evaluation of financial institutions, risk management in agricultural companies and co-operatives.
Risk Analysis: modelling of financial time series (applied to Satrix40), portfolio construction and analysis (applied to Satrix40 in a risk/return framework, statistical research into aspects of modern portfolio theory), pricing of financial derivatives, enterprise wide risk management (Bayesian inference in risk management), regression and depth quantiles with financial applications, data mining and risk analysis.
Foundations and Ethics: The process of conceptualising mathematics and its relation to reality, teaching mathematics from a Christian perspective, Ethics, culture and information technology: a comparative study.