The Department of Pure Mathematics in the School of Mathematics and Statistics at UNSW is a leading centre of mathematical research and teaching in Australia. The Department of Pure Mathematics provides an outstanding undergraduate, honours and postgraduate education. Our honours and postgraduate programs are at the leading edge of pure mathematics research.
Pure mathematics is mainly concerned with understanding and developing the concepts and principles underlying mathematics, rather than with the mechanics of calculating specific numerical answers or finding exact formulae for the solution of various problems. While an applied mathematician might be looking for the exact value of the sum of a series or for a rapidly converging approximation to the solution of a differential equation, the pure mathematician is more likely to be concerned with whether the series does really converge or whether the differential equation does have a (unique) solution and whether that solution behaves in a particular way.
It's amazing how often the same mathematical principles are found to underlie and unify topics which seem at first to have very little in common. For example, the same mathematical techniques (Fourier analysis, integral geometry and group theory) underlie both medical imaging and mineral exploration, while the idea of chaos links heart attacks with turbulence in fluids and the stability or otherwise of complex ecosystems. Oversimplifying, you could say that pure mathematicians develop the underlying ideas, applied mathematicians apply them to specific problems (taking into account features which a special to each problem) and statisticians try to quantify what happens when random variations are introduced into the picture.