Research groups
Areas of research focus in the School of Mathematics and Statistics at the University of Melbourne

Algebra
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.

Analysis
Mathematical analysis is a very broad area of mathematics, focusing on the investigation of qualitative and quantitative properties of mathematical 'objects'. Techniques include limits, differentiation and integration, plus tools from functional analysis, harmonic analysis, complex analysis, differential geometry and geometric measure theory.

Applied Mathematics
The Applied Mathematics Group has interests across the fields of colloid science, medicine, chemical engineering and materials processing.

Data Science
Data science combines aspects of statistics, computer science, and mathematics in order to organise, analyse, and extract knowledge from data sets.

Discrete Mathematics
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
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.

Learning and Teaching Innovation
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 Biology
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
Mathematical Physics is the study of the mathematics associated with models of the physical world.

Operations Research
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
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.

Stochastic Processes
This group studies a variety of areas, from the theory of branching processes to applications such as stochastic models of the stock market.