Pure Mathematics is the mathematics that underlies all applications. It has been described as "that part of mathematical activity that is done without explicit or immediate consideration of direct application". However, mathematics that is considered to be "pure" at one time often, later, finds applications. Finance, Computer Science and cryptography are all areas where pure mathematics has currently found significant applications.

The Department of Pure Mathematics at UNSW is one of the most successful pure mathematics departments in Australia. The research interests of its members span a wide spectrum of pure mathematics including modern analysis and its applications, algebra, discrete mathematics, number theory and mathematical physics. There are also strong research links with the Department of Applied Mathematics.

Many members of the department are active researchers and the department has an active visitors program for international research collaboration.

The department has an active seminar program with weekly seminars in algebra, analysis and general pure mathematics seminars. There is a joint colloquium with The University of Sydney. See our seminar page for more details.


Department members are currently grouped into the following research groups:

Functional Analysis:

The use of techniques of functional analysis to study families of operators leads naturally to the concept of an operator algebra. This area of mathematics is at the centre of a host of current applications: quantum mechanics, statistical mechanics, imaging techniques, to name only three.

Interests of the group range from single operator theory in Banach spaces through semigroup theory to von Neumann and C*-algebras. There is significant interaction with the harmonic analysis group.

Harmonic Analysis:

Harmonic analysis may be loosely defined as that branch of mathematics which has its origin in Fourier Series. In the past two centuries, it has become a vast subject with applications in areas as diverse as signals processing and quantum mechanics.

Interests of the harmonic analysis group range from classical problems to analysis on Lie groups.

Algebra and Discrete Mathematics:

Interests of the group span a wide spectrum of homological algebra, group theory, quantum groups, representation theory, geometric number theory, noncommutative algebra, algebraic geometry, graph theory through to computer algebra and its applications in studying various problems in algebra and number theory. These areas are naturally related to coding theory.

Mathematical Physics and Partial Differential Equations:

In the course of their research, members of the Department of Pure Mathematics touch on problems related to physics, including operator algebras, path integrals, quantization and nonlinear PDEs.

The Department of Pure Mathematics is also a key participant in the ARC Centre of Excellence in Mathematical and Statistical Modelling of Complex Systems. In December 2002 the Federal Government announced funding of $11M over five years for the centre. Its mission is to stimulate research in mathematical and statistical modelling of complex systems, and to encourage cross-fertilizaition of ideas and techniques. Special ares of focus for the centre include dynamical systems, Monte Carlo methods, and Scientific Computation.

The Department of Pure Mathematics provides a vigorous postgraduate program and has a substantial enrolment of high-quality postgraduate students. We currently have twelve students enrolled in our research postgraduate programmes, and several have recently completed their degrees.