Mathematical Techniques in Crystallography and Materials Science

In the course of 30 years as a practicing crystallographer I have frequently been faced with the necessity of finding out a little bit about some general branch of mathematics with which I was previously unfamiliar. Under these circumstances I have usually followed the common practice of seeking out some colleague who would be expected to have a thorough knowledge of the subject. I would then find myself faced either with an involved lecture in which the colleague would attempt to distill a lifetime of experience into a form that was comprehensible to a novice with a very different background, or with a book about the subject, written by a specialist, that contained far more information than I really wanted to know. I would have to separate the few kernels of useful material from a large volume of what would probably be wheat to someone else, but was chaff to me. In the course of that time I have acquired a collection of books to which I frequently refer. Most of these have a small number of thoroughly dog-eared pages, along with many that have scarcely been opened. During the same period I have been privileged to associate and collabo­ rate with a number of materials scientists who were not trained as crystal­ lographers, but whose interests required them to understand particular details of some structural problem.