ABSTRACT
Two tools have come to occupy a central role in dealing with the complexity: mathematics and computers. The first provides a powerful language and framework for the conceptualization of the relationships, and the second provides a powerful technique for exploring the relationships encoded mathematically. This chapter explores the process of representing physical reality using mathematics and the process of extracting insights from these representations. It reviews the process scientists use to conceptualize the regularities of nature for predictive purposes. The process of applying mathematics to the solution of engineering problems is an old art form that is enjoying increased attention at the interface between engineering and biology. The chapter discusses the role of mathematical models in connecting the conceptual and experimental tasks. It also discusses the practical steps engineers have found useful in formulating, validating, and interpreting mathematical models. The chapter considers a representative problem to illustrate and to make the discussion of the traditional modeling process more concrete.
