Whenever we try to understand a natural process or to engineer something, we use mathematics to capture those aspects of the system that are relevant for us. This, typically reductionist representation of our system we call “mathematical model” and is the starting point for further analysis, from which we want to obtain more information about the system, make predictions, and possibly want to optimise against certain criteria.
Obviously, if we do not restrict the range of systems we want to understand or engineer, the range of possible mathematical methods to use is enormous.
The most important methods to use for mathematical modelling include but are not limited to ordinary and partial differential equations, variational and optimization principles, methods from statistical physics, agent-based models, Fourier and Laplace transforms, network models, and stochastic and probabilistic models.
Typically, these analytical mathematical tools are intertwined with basic principles from science (like the Molecular Dynamics models depicted on the right, based on Newton’s Second Law) or technology, and need to be evaluated with the help of computers, requiring consequently the use of numerical methods.
Due to the scope of possible applications, the modules on Mathematical Modelling rely on practically any other analytical or numerical module. Since the methods studied in these modules are widely applicable in Science, Engineering, and Economy/Finance, they represent a central part of the curriculum.