Seventeen years have passed since the manuscript for the first edition of this
book was submitted to the American Mathematical Society. The preparation of a
new manuscript has presented a welcome opportunity to try to improve the first
edition by rewriting and expanding some of its material, by eliminating known
misprints and errors (with however the pious hope of not introducing too many
new ones) and by including new material developed during the past seventeen
years. It has also led to the replacement of the first edition's title, The Geometry
of the Zeros of a Polynomial in a Complex Variable, by a simpler, more convenient
one, Geometry of Polynomials,
For a subject about 150 years old, the analytic theory of polynomials has
continued to show a surprising degree of vitality. A superficial measure of this is
the extent to which our bibliography has had to be enlarged. Over 300 new titles
have been added to the ones given in the first edition. These include a new,
seventy-six page survey [Specht 7] written as part of the revised Enzyklopadie der
Mathematischen Wissenschaften.
The new material has been incorporated into the text and into the exercises.
Particularly significant is the new material on infrapolynomials beginning with
sec. 5, on abstract polynomials beginning with sec. 14, and on matrix methods
beginning with sec. 31.
The author wishes to express his appreciation to those who have offered correc-
tions and suggestions regarding the first edition and to the following who generously
read all or part of the new manuscript: Dr. Oved Shisha of the Wright Patterson
A.F.B. Aerospace Research Laboratory, Professor Hans Schneider of the University
of Wisconsin at Madison, Professor Robert Vermes of McGill University, and Mr.
G. M. Shah of the University of Wisconsin-Milwaukee. He also wishes to thank
the American Mathematical Society for authorizing the publication of this second
edition and the Society's editorial staff, (Miss Ellen Swanson, Mrs. Patricia Wolf,
Mrs. Fannie S. Balsama) for the patience and care with which they have processed
the manuscript. Finally, he gratefully acknowledges the support given him by the
National Science Foundation through the grants G-16315 and GP-2571.
University of Wisconsin-Milwaukee
December 6, 1965.
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