Even a cursory look at the table of contents of this book will reveal that the material is arranged in an unusual way, starting immediately with the application of techniques (Part I) which are justified and explained in greater detail in later chapters (Parts II and III). Indeed, the book is not meant to be read sequentially and I have not attempted to force the material into a sequential exposition. Rather, I have organized it as a series of modules through which each reader can fashion an individual pathway according to background, needs and interests.

The widespread availability of computers and symbolic manipulation packages has made mathematics relevant to many more people than in the past. A serious problem, however, remains the high “cost of entry” of mathematics. While some might argue that in a perfect world people would spend the time required to learn all the mathematics they might need before applying it, this is a utopia certainly, and probably also a misguided ideal as any user of mathematics – having gone through many cycles of learning and applying – can testify.

Hopefully, the modular structure of the book will serve a variety of users addressing different needs ranging from a quick impression of a mathematical tool to a fairly deep understanding of its basis and “inner workings.” The many cross-references, detailed index and table of contents will render possible a non-systematic “navigation” through the material.