Welcome to the School of Computational & Applied Mathematics

The aim of Computational and Applied Mathematics is to solve problems from the real world. Mathematicians discover mathematical techniques and use these techniques to solve real world problems. Computer scientists study and develop computer hardware and software. Applied mathematicians compute to solve real world problems. What are these problems? They are many and varied, but are linked by a common thread-these problems can be cast in a mathematical form. This process is called mathematical modelling. It may be:

• Mathematical modelling in Finance
• Models to predict movements on the Stock Exchange
• Chaos in Dynamical Systems such as weather forecasting and in mathematical models of the economy
• Rock mechanics in mines; fluid flow in the aircraft industry and wave phenomena in the ocean
• Mathematical modelling of tumours in cancer research and models of the lung
• Reconstruction of a blurred and noisy images with application to mineral exploration and agriculture.
• Models to illustrate continental drift
• A mathematical description of pollution and the environment; forestry, marine resources and grazing patterns of game in a game reserve
• The distribution of goods from warehouses to shops
• Models to predict and help manage the spread of disease in a community
• Near infrared Galaxy Morphology

As long as a mathematical model can be constructed for the problem, we can begin to uncover a solution using a combination of mathematics and the computer. The sources of problems are found in economics, physics, ecology, chemistry, industry, astronomy, engineering, commerce, biology, meteorology... indeed, in any area of knowledge which allows the formulation of mathematical equations. Consider these two examples, one drawn from Operations Research and the other from Cosmology.

Suppose you want to know the best level of production in a factory. That level could be influenced by many factors, such as manpower, available machinery, the sequence in which operations are performed, availability of material, storage space, sales forecasts and the effect of competition. Deciding which of these factors are important and which can be ignored, setting up a mathematical model to describe the system and using computers to find the "best" level, is a typical operations research problem.

Einstein's theory of relativity tells us that our universe exploded into existence in the "Big Bang", billions of years ago. The question is - will the universe carry on expanding forever or will it collapse in a "Big Crunch"? We have to study Einstein's complicated equations and use data from astronomy to tackle this problem related to cosmology.