Introduction
xxm
We have included descriptions of many special cases and summarized
the results of many calculations. Most of the nontrivial calculations used
the symbolic manipulation programs MATHEMATICA and/or MAPLE. In
order to excite the reader about the flowers in the beautiful garden we are
cultivating here, we start each chapter with (what we regard as) a handsome
example of what will follow. We have included a number of accessible exer-
cises and research level problems. The latter may be quite challenging and
are at times only conjectures. The reader should also approach the many
special cases we have included as challenges to obtain independent solutions.
They are presented in the spirit of exercises, with solutions supplied by the
authors.
Numbering systems. The book consists of seven chapters and a set of bib-
liographical notes that will be maintained and updated on the web. Chapters
are subdivided into sections; these into subsections. Definitions, lemmas,
propositions, theorems, exercises, problems and remarks are labeled consec-
utively as a single group within each section. A typical item is Theorem
section.number; number starts with 1 for the first item in the section. Thus,
for example, in Chapter 2, Definition 2.32 (in section 2) in our numbering
scheme is followed by Lemma 4.1 (in section 4). Equations that will be ref-
erenced subsequently in the text are labeled by a decimal: chapter.number;
number starts with 1 for the first numbered equation in the chapter. Tables
and figures are numbered consecutively in the book.
Acknowledgments. We thank
1. the mathematicians who have had the patience to listen to our lectures
on the subject of this book: whether our students at the Hebrew University
in Jerusalem or the State University of New York in Stony Brook, who at
times have provided us with constructive criticism, or colleagues at various
institutions who have invited us to speak about this subject;
2. our graduate students who read previous drafts of the book and pointed
out errors and ambiguities (needless to say, the remaining errors and ambi-
guities are the authors' responsibilities);
3. our undergraduate students who helped with the MATHEMATICA cal-
culations and the figures;
4. the editorial and technical staff of the American Mathematical Society,
especially Deborah Smith and Janet Pecorelli who guided us through the
final preparation of the manuscript; and most importantly,
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