Preface to the Second
As is usual in a second edition, various minor flaws that had crept into
the ﬁrst edition have been corrected. Certain topics are now presented more
clearly, it is hoped, after being rewritten and/or reorganized. The treatment
has been expanded only slightly: there is now a section on division of power
series, and a brief discussion of homotopy. (The latter topic was relegated
to a couple of exercises in the ﬁrst edition.) Four appendices have been
added; they contain needed background which, experience has shown, is not
possessed nowadays by all students taking introductory complex analysis.
In this edition, the numbers of certain exercises are preceded by an
asterisk. The asterisk indicates that the exercise will be referred to later in
the text. In many cases the result established in the exercise will be needed
as part of a proof.
I am indebted to a number of students for detecting minor errors in
the ﬁrst edition, and to Robert Burckel and Bjorn Poonen for their valuable
comments. Special thanks go to George Bergman and his eagle eye. George,
while teaching from the ﬁrst edition, read it carefully and provided a long
list of suggested improvements, both in exposition and in typography. I owe
my colleague Henry Helson, the publisher of the ﬁrst edition, thanks for
encouraging me to publish these Notes in the ﬁrst place, and for his many
kindnesses during our forty-plus years together at Berkeley.