Algebra is the study of symmetries and structures that model symmetries. Number theory is the study of the integers and number systems that have properties like the integers. These come together in Representation theory, which is the art of representing algebraic structures as matrices.
Mathematical analysis is a very broad area of mathematics, with strong connections both with other branches of mathematics, such as geometry and mathematical physics, and with other scientific disciplines, such as biology, chemistry, material sciences and finance. Roughly speaking, mathematical analysis focuses on the investigation of qualitative and quantitative properties of mathematical ``objects'' (e.g. functions, series, measures, spaces, solutions of differential equations, etc.). The techniques involved comprise those arising in the elementary calculus, such as limits, differentiation and integration, as well as sophisticated tools from functional analysis, harmonic analysis, complex analysis, differential geometry and geometric measure theory.
The Applied Mathematics Group has interests across the fields of colloid science, medicine, chemical engineering and materials processing.
Complex systems occur in many contexts such as physical, biological or social. It is the collective phenomena occurring as the number of components increase that characterise Complex Systems.
Discrete mathematics is the study of mathematical structures that are by nature discrete rather than continuous. It includes combinatorics and graph theory.
Geometry and topology are the parts of mathematics that study the shapes and properties of lines, curves, surfaces, three dimensional universes, and higher dimensional space.
Innovation in the teaching of mathematics and statistics is a key focus of the department. This group fosters innovations in learning and teaching for tertiary mathematics and statistics.
Mathematical, statistical and computational methods are crucial in many areas of modern biological research. Conversely technological advances in biology allow more data, often of a novel type or at a finer resolution, to be collected resulting in new challenges that are motivating research in mathematics, statistics and computational methods.
Mathematical Physics is the study of the mathematics associated with models of the physical world.
Operations Research (OR) provides a scientific approach to decision making. It involves formulating mathematical models of these problems, and developing mathematical tools to obtain solutions.
Statistics is the science of collecting, organising and interpreting data. Mathematical descriptions of the data collection processes and the statistical analysis are used to determine accurate statistical methods.
This group studies a variety of areas, from the theory of branching processes to applications such as stochastic models of the stock market.