Objectives

This chapter gives a very basic introduction to practical mathematical and arithmetic principles. Some readers who can recall their earlier training in high school and elsewhere may want to skip it or merely skim over the vocabulary. However, many often find that the various other interests in life push out the assorted artifacts of functional expressions, logarithms, and other principles.

Usually what happens is that we vaguely remember the basic ideas without specific properties, in the same way that we might remember that the assigned reading of Steinbeck's Grapes of Wrath included poor people traveling West without remembering all of the unfortunate details. To use mathematics effectively in the social sciences, however, it is necessary to have a thorough command over the basic mathematical principles in this chapter.

Why is mathematics important to social scientists? There are two basic reasons, where one is more philosophical than the other. A pragmatic reason is that it simply allows us to communicate with each other in an orderly and systematic way; that is, ideas expressed mathematically can be more carefully defined and more directly communicated than with narrative language, which is more susceptible to vagueness and misinterpretation. The causes of these effects include multiple interpretations of words and phrases, near-synonyms, cultural effects, and even poor writing quality.

The second reason is less obvious, and perhaps more debatable in social science disciplines. Plato said “God ever geometrizes” (by extension, the nineteenth-century French mathematician Carl Jacobi said “God ever arithmetizes”). The meaning is something that humans have appreciated since before the building of the pyramids: Mathematics is obviously an effective way to describe our world.