Research
Broad groupings of the department’s research interests are highlighted below. Details of the department’s publications are available in the UC Research Report.
Algebra, Combinatorics, and Logic 
Areas of current research by the department include: algebraic groups; representation theory; clifford algebras; automorphism groups; finite geometry; matroid theory, combinatorial and algorithmic phylogenetics; constructive analysis and topology; foundations of mathematics. Staff actively working in these areas are Prof. Douglas Bridges, Dr Ben Martin, Dr Günter Steinke, Assoc. Prof. Charles Semple, Prof. Mike Steel.
Analysis and Geometry 
The department's research strengths in these areas include: approximation theory; topological geometry; constructive analysis and topology; functional analysis (including applications to quantum theory); harmonic analysis; partial differential equations and potential theory; general topology. Staff active in those areas are Assoc. Prof. Rick Beatson, Prof. Douglas Bridges, Dr Qui Bui, Dr Peter Renaud, Dr Günter Steinke, Assoc. Prof. Neil Watson.
Applied Statistics 
Applied statistics broadly covers research where statistics is being used to help solve real-world problems. Examples include: environmental monitoring; risk assessment and uncertainty analysis; medical and engineering applications; and statistical genetics. Within the department staff who work in this area are Assoc. Prof. Jennifer Brown, Dr James Degnan, Dr Dominic Lee, Dr Marco Reale, Dr Raazesh Sainudiin, Dr Carl Scarrott, Assoc. Prof. Peter Smith.
Computational Mathematics 
Broadly, tool building in the form of the development and analysis of algorithms and methods for numerical computation. Areas of current research in the department include: numerical optimisation; approximation theory; algorithms for surface approximation; inverse problems; numerical linear algebra; and rigorous set processing. Staff currently working in these areas are Assoc. Prof. Ian Coope, Dr Chris Price, Assoc. Prof. Rick Beatson, Prof. David Wall, Mr Bob Broughton, Dr Raazesh Sainudiin.
Dynamical Systems and Differential Equations 
Members of the department have interests in theoretical, computational and applied aspects of nonlinear differential equations and discrete time dynamical systems. Areas of particular activity include: chaotic dynamics; ergodic theory; inverse problems; nonlinear models in ecology and medicine; symmetry methods. Permanent staff include Dr Mark Hickman, Dr Alex James, Dr Michael Plank, Dr Rua Murray, Prof. David Wall.
Financial and Industrial Mathematics 
Broadly, the use of mathematics to understand economics and finance, and processes arising in industrial settings. Specific interests include: econometrics; mathematical economics; fast surface fitting algorithms for applications in geophysics, image processing, computer graphics and custom manufacture; statistical design and analysis of communication systems; signal and image processing; acoustics; industrial applications of spatial statistics, extreme value methods and spectral analysis. Faculty members with interests in this area include Assoc. Prof. Rick Beatson, Prof. Douglas Bridges, Dr Qui Bui, Assoc. Prof. Ian Coope, Dr Dominic Lee, Dr Michael Plank, Dr Chris Price, Dr Marco Reale, Dr Carl Scarrott, Assoc. Prof. Peter Smith, Dr Phil Wilson.
History and Philosophy of Mathematics, and Mathematics Education 
Areas of current research by the department include: mathematics in the ancient Near East, ancient Greece, India, and Islam with an emphasis on editing mathematical texts from these cultures from the original primary sources; mathematics during the Italian renaissance; history of ancient mathematical astronomy; constructive mathematics; foundations of mathematics; mathematics education in the tertiary sector; and mathematics and communication. Staff actively working in these areas are Dr Clemency Montelle, Dr John Hannah, Prof. Douglas Bridges, Dr Phil Wilson, Dr Alex James.
Mathematical Biology 
The department hosts the Biomathematics Research Centre, this focuses on three broad areas: computational molecular biology and phylogenetics; ecological and physiological modelling; and statistical applications in ecology and medicine. Staff actively working in this area include Assoc. Prof. Jennifer Brown, Dr Alex James, Dr Dominic Lee, Dr Michael Plank, Dr Raazesh Sainudiin, Assoc. Prof. Charles Semple, Prof. Mike Steel, Prof. David Wall, Dr Phil Wilson.
Theoretical and Computational Statistics
The Statistics Group within the department has an active research programme in many aspects of theoretical and computational statistics. Particular topics include: stochastic processes; computational methods; Bayesian inference; statistical genetics; sampling theory; random matrices; extreme value theory; graphical models. Staff with research projects in this area include Assoc. Prof. Jennifer Brown, Dr James Degnan, Dr Dominic Lee, Dr Marco Reale, Dr Raazesh Sainudiin, Dr Carl Scarrott, Assoc. Prof. Peter Smith and Prof. Mike Steel.