Applied and Computational Mathematics
Mathematics is the language of Science, and increasingly of many other disciplines. Applied Mathematics takes mathematical structures, ideas and techniques and uses them to understand, explore and predict the behaviour of physical, biological, ecological, technological, industrial, organizational and other systems. In most cases, this now involves modelling and simulation using powerful computers. Applied Mathematics is how Mathematics engages with the world.
Planets, stars, black holes, galaxies, and beyond … all the stuff of Astrophysics. How are they formed, and how do they evolve? What do they tell us about our past, and our future? Observation and modelling form the twin pillars of astronomical research, and mathematics is the tool and the language we use to understand and to probe our data and to build our models.
Pure mathematicians deal with the ideal, the beauty of perfection. They imagine the unimaginable. And magically, such constructions become the basis for applied mathematics to solve the most concrete problems. Research strengths include algebra, analysis, discrete mathematics, and geometry.
Stochastic processes involving randomness dominate in many areas of natural and man made systems. Describing their evolution quantitatively requires powerful theory from the fields of probability, statistics, and other areas of mathematics. Financial mathematics for example seeks to provide guidance in managing risk, and is at the core of modelling carried out by financial institutions and treasuries. The stochastic behaviour of cells, genes, and populations is the subject of Mathematical Biology. Our world is dynamic and complex, and often not deterministic. The mathematics of stochastic processes is crucial in allowing us to understand and manage risk, randomness, and change.