The Department of Mathematics and Statistics has a strong postgraduate program with an average enrolment of 20-30 postgraduate students per year.
It has a national and international reputation for academic excellence and achievement.
The Department has excellent computing and other research infrastructure support, including the Curtin Institute for Computation. The major research focus of the Department includes operations research and several areas of applied mathematics, combinatorial mathematics and probability theory and statistics.
Major Research Foci
Operations Research deals with scientific methods for solving problems, concerning operational efficiency, that arise in business, government and industry operations. It provides a quantitative evaluation of alternative policies, plans and decisions. Through mathematical modelling and scientific investigation of the model, operations research/optimisation seeks an optimum strategy under several interacting constraints and well defined objectives. The major projects in the Department involve the application of operations research techniques to problems arising in telecommunications engineering, transport, agriculture, mining and the defence industries.
Control Theory is concerned with the controllability and observability properties of dynamical systems and with the study of suitable control strategies for these systems. Optimal Control involves the optimisation of some objective function over time subject to a given dynamical system. The decision variables are known as the controls and the solution of the dynamical system for a given control is called the state. Various types of constraints may be imposed on both the control and the state. Department staff are actively involved with both theoretical and applied research in these areas with particular emphasis on the development of efficient computational algorithm.
Solutions to many real world problems require mathematical modelling and computer simulation. The applied mathematics group in the Departments is particularly interested in the areas of financial mathematics, computational techniques, industrial and applied mathematics modelling, which include modern numerical techniques for partial differential equations, computational fluid dynamics, heat transfer, granular flows and mathematical models in geophysics. These problems may be formulated either as direct or inverse boundary value problems and research in this area is expected to have a wide range of applications in engineering, medical sciences and process control. Other areas of research include genetic algorithms, mathematics in sport and modelling of brain function.
Combinatorial mathematics is concerned with the study of arrangements, patterns, designs, assignments, schedules, connections and configurations. It encompasses the areas of graph theory, coding theory, combinatorial designs, enumeration, number theory and polyhedra. The group’s main foci are on characterising graphs with prescribed properties and using these properties to devise computational algorithms and investigating various combinatorial properties of dynamical positive systems. The work of this group interfaces with the work of the optimisation group, particularly in the area of combinatorial optimisation.
Statistics is the science of variability. It has solid mathematical foundations in the theory of probability and the mathematical theory of statistical inference; it also has close connections to computer science. Statistical science plays a key role in many modern sciences, especially genetics, public health, information and communication, economics and finance, and the analysis of Big Data.
A major new focus for the research group is spatial statistics, the statistical analysis of spatial information. For example, maps of the locations of road accidents or mineral deposits can be analysed using statistical methodology to identify areas of high risk (for accidents) or high prospectivity (for gold) and to discover unexpected relationships. The group’s research activities include advanced theoretical study of spatial random processes, development of new statistical methodology for spatial data, development of efficient computational methods for large spatial datasets, and collaboration with government and academic
partners on real applications.
The group also has research interests in Markov processes, financial modelling, advanced statistical inference, industrial statistics and time series analysis.