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Geometry of Polynomials
 
Geometry of Polynomials
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
Geometry of Polynomials
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Geometry of Polynomials
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
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 31949; 243 pp
    MSC: 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.

  • 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 half-plane or a sector
    • X. The number of zeros in a given circle
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 31949; 243 pp
MSC: 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.

  • 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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.