Preface

Summary

It is always gratifying to discover that it is within one's ability to appreciate a mathematics book and to read it with pleasure. I have often dreamt what a joy it would be to get to know some of the elementary gems that are surely present in every branch of mathematics, only to be dismayed by the literature I have been able to find. Undoubtedly the gems are there, but they often lie buried in textbooks or comprehensive reference works. One is frequently left with the unhappy choice of undertaking a prolonged study of the field or giving up the idea altogether. While it takes a knowledgeable scholar to write something out of the ordinary, the dedicated specialist can get carried away with discussions that one comes to appreciate only after long and serious study. Unfortunately, this makes it very difficult for general readers to disentangle the elementary gems of their heart's desire. On top of this, what passes for a proof is often so concise or sketchy that it is readily understandable only to someone who already knows the subject.

I would dearly love to be able to promise that you will find no such frustrations in the present work. What I can promise is a collection of essays that does not attempt to cover a large amount of material, and that each topic has been extricated from the mass of material in which it is usually found and given as elementary and full a treatment as is reasonably possible.