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| Product Code: | SURV/3 |
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| Softcover ISBN: | 978-0-8218-1503-8 |
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| AMS Member Price: | $203.20 $153.20 |
| Softcover ISBN: | 978-0-8218-1503-8 |
| Product Code: | SURV/3 |
| List Price: | $129.00 |
| MAA Member Price: | $116.10 |
| AMS Member Price: | $103.20 |
| eBook ISBN: | 978-1-4704-1230-2 |
| Product Code: | SURV/3.E |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
| Softcover ISBN: | 978-0-8218-1503-8 |
| eBook ISBN: | 978-1-4704-1230-2 |
| Product Code: | SURV/3.B |
| List Price: | $254.00 $191.50 |
| MAA Member Price: | $228.60 $172.35 |
| AMS Member Price: | $203.20 $153.20 |
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Book DetailsMathematical Surveys and MonographsVolume: 3; 1949; 243 ppMSC: Primary 30
During the years since the first edition of this well-known monograph appeared, the subject (the geometry of the zeros of a complex polynomial) has continued to display the same outstanding vitality as it did in the first 150 years of its history, beginning with the contributions of Cauchy and Gauss. Thus, the number of entries in the bibliography of this edition had to be increased from about 300 to about 600 and the book enlarged by one third. It now includes a more extensive treatment of Hurwitz polynomials and other topics. The new material on infrapolynomials, abstract polynomials, and matrix methods is of particular interest.
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Table of Contents
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Chapters
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I. Introduction
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II. The critical points of a polynomial
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III. Invariantive formulation
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IV. Composite polynomials
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V. The critical points of a rational function which has its zeros and poles in prescribed circular regions
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VI. The critical points of a polynomial which has only some prescribed zeros
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VII. Bounds for the zeros as functions of all the coefficients
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VIII. Bounds for $p$ zeros as functions of $p$ + 1 coefficients
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IX. The number of zeros in a half-plane or a sector
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X. The number of zeros in a given circle
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During the years since the first edition of this well-known monograph appeared, the subject (the geometry of the zeros of a complex polynomial) has continued to display the same outstanding vitality as it did in the first 150 years of its history, beginning with the contributions of Cauchy and Gauss. Thus, the number of entries in the bibliography of this edition had to be increased from about 300 to about 600 and the book enlarged by one third. It now includes a more extensive treatment of Hurwitz polynomials and other topics. The new material on infrapolynomials, abstract polynomials, and matrix methods is of particular interest.
-
Chapters
-
I. Introduction
-
II. The critical points of a polynomial
-
III. Invariantive formulation
-
IV. Composite polynomials
-
V. The critical points of a rational function which has its zeros and poles in prescribed circular regions
-
VI. The critical points of a polynomial which has only some prescribed zeros
-
VII. Bounds for the zeros as functions of all the coefficients
-
VIII. Bounds for $p$ zeros as functions of $p$ + 1 coefficients
-
IX. The number of zeros in a half-plane or a sector
-
X. The number of zeros in a given circle
