This book is an outgrowth of classes given at the University of California, Santa Barbara, mainly for students who had little mathematical background. Many of the students indicated they never understood what mathematics was all about (beyond what they learned in algebra and geometry). Was there any more mathematics to be discovered or created? How could one actually discover or create new mathematics?

In order to give these students some sort of answers to such questions, we designed a course in which the students could actually participate in the discovery of mathematics. The class was not presented in the usual lecture fashion. And it did not deal with topics that the students had seen before. Ordinary algebra, geometry, and arithmetic played minor roles in most of the problems we addressed. Whatever algebra and geometry that did appear was relatively easy and straightforward.

Our objective was to give the students an appreciation of mathematics, rather than to provide tools they would need in some field that required mathematics. In that sense, the course was like a course in music appreciation or art appreciation. Such courses don’t attempt to train students to become pianists, composers, or artists. Instead, they attempt to give the students a sense of the subject.