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Softcover ISBN:  9780821815038 
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Softcover ISBN:  9780821815038 
Product Code:  SURV/3 
List Price:  $129.00 
MAA Member Price:  $116.10 
AMS Member Price:  $103.20 
eBook ISBN:  9781470412302 
Product Code:  SURV/3.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Softcover ISBN:  9780821815038 
eBook ISBN:  9781470412302 
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 

Book DetailsMathematical Surveys and MonographsVolume: 3; 1949; 243 ppMSC: Primary 30;
During the years since the first edition of this wellknown 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.

Table of Contents

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 halfplane or a sector

X. The number of zeros in a given circle


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During the years since the first edition of this wellknown 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 halfplane or a sector

X. The number of zeros in a given circle