Statistical Mechanics & Combinatorics
Statistical mechanics involves the understanding of large complex systems by averaging the behaviour of the individual components. For example, one can understand the behaviour of a gas without describing the motion of all the molecules involved, simply by knowing the type and strength of the forces between the molecules, using the principles of statistical mechanics. This powerful idea can be applied to many and varied systems in the natural world and in the human arena. It was not said lightly by a leading scientist that 'a well-trained statistical mechanician can tackle any problem' since, for example, statistical mechanics graduates can be found working in high-end financial organisations, in brain research or working for the Human Genome Project.