This short textbook introduces students to the concept of describing natural systems using mathematical models. We highlight the variety of ways in which natural systems lend themselves to mathematical description and the importance of models in revealing fundamental processes. The process of science via the building, testing and use of models (theories) is described and forms the structure of the book. The book covers a broad range from the molecular to ecosystems and whole-Earth phenomena. Themes running through the chapters include scale (temporal and spatial), change (linear and nonlinear), emergent phenomena and uncertainty. Mathematical descriptions are kept to a minimum and we illustrate mechanisms and results in graphical form wherever possible. Essential mathematical details are described fully, with the use of boxes. The mathematics supports but does not lead the text.

The use of mathematical models is a fundamental aspect of modern science. With computers now allowing previously difficult calculations to be done quickly and easily, an understanding of mathematics and an appreciation for modelling is possible even in fields with traditionally less mathematical content. Modelling Nature introduces basic concepts in mathematical modelling applied to natural systems to tackle real-world problems from fields such as physics, ecology, geology and epidemiology. It shows how using models can help to unravel complex issues such as the melting of the Arctic ice, the spread of infectious disease and the age of the Earth. The text helps students to build steadily upon a basic level of mathematics, to a more advanced understanding of mathematical concepts, for a thorough understanding of a variety of mathematical techniques. Key features include: Worked through calculations, with clear steps that can be followed with just a calculator, pen and paper or popular software packages. Intuitive introduction of advanced mathematical techniques in the context of model building, for an understanding of real-life application. An emphasis on an overall philosophy of building models, drawing repeatedly from the key elements of data, physical processes and mathematical methods to develop and refine models.