ABSTRACT
Chapter 1, Perfect Partners: Combining Models of Change and Uncertainty with Technology, considers the importance of modeling for change, uncertainty, and machine learning. Mathematical modeling is essential to success in problem solving and analysis at all levels. This chapter presents, explains, and illustrates a modeling process and provides examples of modeling under change, uncertainty, and machine learning. As an introduction to the modeling experience for applied mathematics, management science, and operations research, we present a process for modeling that consists of nine steps to enable a modeler to traverse the entire quantitative decision-making experience. We present numerous examples from business, industry, and government that will be solved in subsequent chapters. Modeling is thought of as a three-prong approach: make assumptions, build the model, and interpret the results. The latter two are self-sufficient, but the first is where a modeler must defend their position. We describe a mathematical model as a mathematical description of a system using the language of mathematics. A mathematical model may be used to help explain a system and to study the effects of different components, and to make predictions about behavior.
