Science of Cities and Regions Lectures on Mathematical Model Design 2012

A ‘science of cities and regions’ seeks an in-depth understanding of their workings and how they evolve over time. This is not only interesting as science, but is also potentially useful in a variety of planning contexts. In common with many other sciences, mathematical modelling provides a valuable approach. There is a history of 50 years or more of serious development and therefore a substantial body of literature and ideas. It is the purpose of these lectures not to review this vast body of work systematically, but rather to elucidate some of the basic principles of model design and to indicate how they can be applied. This can be thought of as the beginnings of assembling a tool kit for model building. Models can be thought of as representations of theories of systems of interest. They offer insight and understanding and potentially provide ‘What if?’ forecasting capabilities for planning and for public policy development. They can be the ‘flight simulators’ for urban and regional planners whether in the public or commercial sectors. The argument can be usefully structured in terms of: systems of interest, and representations of systems; theory; and methods for model building. Hence, the idea of the ‘STM approach’: define a system of interest; decide what theory contributes to the understanding of the system; dip into the tool kit to find appropriate methods for model building. This structure will show that there are many possible ways of approaching model building—hence the idea of a tool kit.
We follow the STM sequence, more or less, to build the argument that follows. We focus first on systems but we illustrate the argument by introducing examples of models at an early stage. These illustrative models also provide an historical context.
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