I teach mostly pure mathematics at a liberal arts college so I might be thought a dreamy, impractical, type. Wrong! Nothing is more “useful” than college mathematics. An analogy with language explains why. Like French, mathematics has lots of uses, but they all require knowledge of the language itself—lots of vocabulary and grammar, and a glance at the literature. Conveying all those things is my job. With a working knowledge of the language of mathematics, one can go anywhere: to concrete applications, to teaching, to more study of mathematics itself.

Since the appearance of the first addition of this book, some things have changed. For instance, the internet would now join digital music and widebody jets on any short list of popular wonders of science and mathematics. Cryptography—itself driven largely by the growth of the internet—is now a leading application of number theory, a mathematical field traditionally seen as the purest of the pure. (Not all the mathematical news is computer-driven: in the mid-90s, Andrew Wiles solved the 350-year-old problem known as Fermat's Last Theorem.)

Another current of change in mathematics, related to but not entirely driven by computing, has come to be known as “calculus reform.” That loaded phrase means quite different things to different people, but many college mathematicians agree that the elementary calculus course, historically the foundation of a mathematics major, needs some shoring up.