Most quantitative problems involve several different interrelated objects: market forces determine the price of a commodity, steps in a manufacturing process depend on other steps, virus-infected computers can slow network traffic. In order to analyze these relationships, it helps to think mathematically about them.
In this chapter we will explore different ways that the elements of a set can be related to each other or to the elements of another set. These relationships can be described by mathematical objects such as functions, relations, and graphs. Our goal is to develop the ability to see mathematical relationships between objects, which in turn will enable us to apply tools from discrete mathematics.