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Essays on Numbers and Figures
 
V. V. Prasolov Independent University of Moscow, Moscow, Russia
Front Cover for Essays on Numbers and Figures
Available Formats:
Softcover ISBN: 978-0-8218-1944-9
Product Code: MAWRLD/16
75 pp 
List Price: $21.00
MAA Member Price: $18.90
AMS Member Price: $16.80
Electronic ISBN: 978-1-4704-2479-4
Product Code: MAWRLD/16.E
75 pp 
List Price: $19.00
MAA Member Price: $17.10
AMS Member Price: $15.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $31.50
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Front Cover for Essays on Numbers and Figures
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  • Front Cover for Essays on Numbers and Figures
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Essays on Numbers and Figures
V. V. Prasolov Independent University of Moscow, Moscow, Russia
Available Formats:
Softcover ISBN:  978-0-8218-1944-9
Product Code:  MAWRLD/16
75 pp 
List Price: $21.00
MAA Member Price: $18.90
AMS Member Price: $16.80
Electronic ISBN:  978-1-4704-2479-4
Product Code:  MAWRLD/16.E
75 pp 
List Price: $19.00
MAA Member Price: $17.10
AMS Member Price: $15.20
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $31.50
MAA Member Price: $28.35
AMS Member Price: $25.20
  • Book Details
     
     
    Mathematical World
    Volume: 162000
    MSC: Primary 00;

    This is the English translation of the book originally published in Russian. It contains 20 essays, each dealing with a separate mathematical topic. The topics range from brilliant mathematical statements with interesting proofs, to simple and effective methods of problem-solving, to interesting properties of polynomials, to exceptional points of the triangle. Many of the topics have a long and interesting history. The author has lectured on them to students worldwide.

    The essays are independent of one another for the most part, and each presents a vivid mathematical result that led to current research in number theory, geometry, polynomial algebra, or topology.

    Readership

    Advanced high school and undergraduate students, mathematics educators at secondary and university level; general mathematical audience.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Conjugate numbers
    • Chapter 2. Rational parametrizations of the circle
    • Chapter 3. Sums of squares of polynomials
    • Chapter 4. Representing numbers as the sum of two squares
    • Chapter 5. Can any knot be unraveled?
    • Chapter 6. Construction of a regular 17-gon
    • Chapter 7. The Markov equation
    • Chapter 8. Integer-valued polynomials
    • Chapter 9. Chebyshev polynomials
    • Chapter 10. Vectors in geometry
    • Chapter 11. The averaging method and geometric inequalities
    • Chapter 12. Intersection points of the diagonals of regular polygons
    • Chapter 13. The chromatic polynomial of a graph
    • Chapter 14. Brocard points
    • Chapter 15. Diophantine equations for polynomials
    • Chapter 16. The Pascal lines
    • Chapter 17. One butterfly and two butterflies theorems
    • Chapter 18. The Van der Waerden theorem on arithmetical progressions
    • Chapter 19. Isogonal conjugate points
    • Chapter 20. Cubic curves related to the triangle
  • Additional Material
     
     
  • Reviews
     
     
    • This volume is quite delightful … Each essay … engages the reader's interest in an immediate and lively manner … can be highly recommended for well-prepared students aspiring to a top-level mathematics degree and will prove a marvelous source for teachers … a good bedtime read for Putnam competitors … a pleasure indeed for the general lover of mathematics.

      Mathematical Reviews
    • A worthwhile resource for mathematics departments to have on hand … this collection serves as a nice resource for accessible topics beyond the standard curriculum around the level of calculus.

      MAA Online
  • Request Review Copy
  • Get Permissions
Volume: 162000
MSC: Primary 00;

This is the English translation of the book originally published in Russian. It contains 20 essays, each dealing with a separate mathematical topic. The topics range from brilliant mathematical statements with interesting proofs, to simple and effective methods of problem-solving, to interesting properties of polynomials, to exceptional points of the triangle. Many of the topics have a long and interesting history. The author has lectured on them to students worldwide.

The essays are independent of one another for the most part, and each presents a vivid mathematical result that led to current research in number theory, geometry, polynomial algebra, or topology.

Readership

Advanced high school and undergraduate students, mathematics educators at secondary and university level; general mathematical audience.

  • Chapters
  • Chapter 1. Conjugate numbers
  • Chapter 2. Rational parametrizations of the circle
  • Chapter 3. Sums of squares of polynomials
  • Chapter 4. Representing numbers as the sum of two squares
  • Chapter 5. Can any knot be unraveled?
  • Chapter 6. Construction of a regular 17-gon
  • Chapter 7. The Markov equation
  • Chapter 8. Integer-valued polynomials
  • Chapter 9. Chebyshev polynomials
  • Chapter 10. Vectors in geometry
  • Chapter 11. The averaging method and geometric inequalities
  • Chapter 12. Intersection points of the diagonals of regular polygons
  • Chapter 13. The chromatic polynomial of a graph
  • Chapter 14. Brocard points
  • Chapter 15. Diophantine equations for polynomials
  • Chapter 16. The Pascal lines
  • Chapter 17. One butterfly and two butterflies theorems
  • Chapter 18. The Van der Waerden theorem on arithmetical progressions
  • Chapter 19. Isogonal conjugate points
  • Chapter 20. Cubic curves related to the triangle
  • This volume is quite delightful … Each essay … engages the reader's interest in an immediate and lively manner … can be highly recommended for well-prepared students aspiring to a top-level mathematics degree and will prove a marvelous source for teachers … a good bedtime read for Putnam competitors … a pleasure indeed for the general lover of mathematics.

    Mathematical Reviews
  • A worthwhile resource for mathematics departments to have on hand … this collection serves as a nice resource for accessible topics beyond the standard curriculum around the level of calculus.

    MAA Online
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