An ABC of modelling -- I. The Deterministic View. 1. Growth and decay. Dynamical systems. 2. Equilibrium. 3. Optimal control and utility -- II. Validating a Model. 4. Validation: accept, improve, or reject -- III. The Probabilistic View. 5. Birth and death. Probabilistic dynamics. 6. Stationary distributions. 7. Optimal decision and reward -- IV. The Art of Application. 8. Using a model: choice and estimation. 9. Building a model: adapting, extending, and combining -- V. Toward More Advanced Models. 10. Further dynamical systems. 11. Further flow and diffusion. 12. Further optimization -- Appendix 1: A review of probability and statistics -- Appendix 2: Models, sources, and further reading arranged by discipline. Michael Mesterton-Gibbons has done what no author before him could: he has written an in-depth, systematic guide to the art and science of mathematical modelling that's a great read from first page to last. With an abundance of both wit and common sense, he shows readers exactly how the modelling process works, using fascinating real-life examples from virtually every realm of human, machine, natural, and cosmic activity. You'll find models for determining how fast cars drive through a tunnel; how many workers industry should employ; the length of a supermarket checkout line; how birds should select worms; the best methods for avoiding an automobile accident; and when a barber should hire an assistant; just to name a few. Offering more examples, more detailed explanations, and by far, more sheer enjoyment than any other book on the subject, A Concrete Approach to Mathematical Modelling is the ultimate how-to guide for students and professionals in the hard sciences, social sciences, engineering, computers, statistics, economics, politics, business management, and every other discipline in which mathematical modelling plays a role.