Doctor of Philosophy in Mathematics

PhD in Mathematics, Faculty of Science (FOS), is a programme that fosters pure and applied research in different branches of Mathematics. The Mathematics Group offers postgraduate research opportunities in a number of areas of Pure and Applied Mathematics, Statistics, Operations Research and Financial Mathematics. A particular focus initiative of the Group is the recently-established Mathematical Modelling and Simulation Cluster, which aims to pursue research in areas such as mathematical epidemiology, inventory analysis, hydrology, crop production and the properties of nanoparticles. One important resource available to the Modelling and Simulation Cluster is UBD’s BlueGene supercomputer, which is currently the only supercomputer in South East Asia. The Programme is designed for qualified individuals, who wish to acquire advanced knowledge, as well as analytical and research skills in Pure and Applied Mathematics. Students interested in starting a Masters or Doctoral degree in Mathematics at UBD should in the first instance contact one or more of the staff members, and liaise with them to design a suitable research project.

Aims and Scope

The PhD Programme in Mathematics aims to make researchers and scientists with high level specialised skills in order to cope with the increased demands of governments, industries, banks, hospitals etc. The scope of the Programme is to provide students the necessary specific scientific information, as well as to train them to develop their skills and analytical capabilities.


Students conduct research on an approved research topic, under the supervision of one or more staff members. Upon completion of their research, they submit a Thesis, which normally does not exceed 100,000 words.


  • Compulsory modules SR-5101. These are modules that all postgraduate students must read and pass to satisfy their graduation requirement.

  • Assessment includes examination of the thesis by internal and external examiners. As stipulated in the relevant UBD regulations the examiners may subject a candidate to an oral examination or any other test they think necessary to assess the acceptability of the thesis. Periodic assessment of the progress of the candidate is carried out as stipulated in the relevant UBD regulations.

Areas of Research

  • Operator theory
  • Integral equations
  • Approximation of pseudo-differential operators
  • Wavelets
  • Locally convex cones
  • Linear approximation
  • Integral representations
  • Choquet theory
  • Numerical Analysis: Spline functions on triangulations, Refinable stable local spline basis functions, Macro-element Riesz bases
  • Functional differential equations, and Impulsive differential equations
  • Stability and oscillations in dynamical systems, Computer (or numerical) simulations of differential equations
  • Mathematical models of neural networks, population dynamics, epidemics, etc.
  • Characterization of probability models, Bivariate statistical analysis, Parametric Estimation
  • Mathematical physics and cosmology, Petrophysics modelling, Differential geometry, Population dynamics and epidemiology
  • Modelling and simulation, High performance computing
  • Stochastic volatility, Study of Brunei’s healthcare insurance claims
  • Numerical solutions of partial differential equation involving options
  • Time series models, Long-ranged dependence stochastic processes
  • Extension of Markowitz’s portfolio optimisation method
  • Dynamical systems and chaos, Mathematical modelling: medicine, ecology, epidemiology, Bifurcation Theory, Numerical computation
  • Renewable/Solar energy technology, Approximant methods
  • Health and medical statistics, Applied statistics, Goodness-of-fit tests; Biostatistics, Survival analysis, Longitudinal data analysis
  • Mathematical modelling of air quality and pollution, atmospheric transport, population and traffic flows
  • Functional differential equations, Impulsive differential/difference equations
  • Computational fluid dynamics (CFD), Modelling and simulation of the application of nanofluids on heat transfer problems
  • Production and inventory control, Supply chain management, Transportation and logistics, Optimization and heuristic techniques
  • Road Safety and driving behavior, Intelligent traffic system