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 recentlyestablished 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.
Structure
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.
Assessment

Compulsory modules SR5101. 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 pseudodifferential operators
 Wavelets
 Locally convex cones
 Linear approximation
 Integral representations
 Choquet theory
 Numerical Analysis: Spline functions on triangulations, Refinable stable local spline basis functions, Macroelement 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, Longranged 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, Goodnessoffit 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