Research
The Department of Mathematics and Statistics has a strong postgraduate programme with an enrolment of between 20 and 30 postgraduate students per year over the last five years, and has a national and international reputation for academic excellence and achievement. This is well reflected by the establishment of a Centre of Excellence in Industrial Optimisation and the large number of publications, consultancies and competitive research funds attracted.
The Department has excellent computing and other research infrastructure support. This is further enhanced by the establishment of the Computationally Intensive Optimisation Laboratory under the funding of a Research Infrastructure Equipment and Facilities grant.
The major research foci of the Department include operations research and several areas of applied mathematics, combinatorial mathematics and probability theory and statistics.
Operations Research/Optimisation
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.
Applied Mathematics
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
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 optimization.
Probability Theory and Statistics
A statistical modelling approach is required in order to construct adequate models for numerous real world situations where the only data available contains noise or uncertainty, or when the system itself exhibits stochastic variation. Modern probability theory and statistical methods aim at providing sound methodology and the theoretical and computational tools for dealing with real world statistical and stochastic models. The group's research areas include stochastic processes, Markov processes, financial modelling, survival analysis, advanced statistical inference, industrial statistics and time series analysis.