Mathematical Discovery

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 math- ematics 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.

Each chapter begins with a problem and works towards a solution to the problem. The reader participates in discovering the solution. There are also comments about the history of the problems, how answers to questions lead to new problems, how the problems studied relate to other problems that superficially seem to be unrelated, and how some problems that seem similar are still unsolved.