| Softcover ISBN: | 978-0-8218-1944-9 |
| Product Code: | MAWRLD/16 |
| List Price: | $39.00 |
| MAA Member Price: | $35.10 |
| AMS Member Price: | $31.20 |
| eBook ISBN: | 978-1-4704-2479-4 |
| Product Code: | MAWRLD/16.E |
| List Price: | $35.00 |
| MAA Member Price: | $31.50 |
| AMS Member Price: | $28.00 |
| Softcover ISBN: | 978-0-8218-1944-9 |
| eBook: ISBN: | 978-1-4704-2479-4 |
| Product Code: | MAWRLD/16.B |
| List Price: | $74.00 $56.50 |
| MAA Member Price: | $66.60 $50.85 |
| AMS Member Price: | $59.20 $45.20 |
| Softcover ISBN: | 978-0-8218-1944-9 |
| Product Code: | MAWRLD/16 |
| List Price: | $39.00 |
| MAA Member Price: | $35.10 |
| AMS Member Price: | $31.20 |
| eBook ISBN: | 978-1-4704-2479-4 |
| Product Code: | MAWRLD/16.E |
| List Price: | $35.00 |
| MAA Member Price: | $31.50 |
| AMS Member Price: | $28.00 |
| Softcover ISBN: | 978-0-8218-1944-9 |
| eBook ISBN: | 978-1-4704-2479-4 |
| Product Code: | MAWRLD/16.B |
| List Price: | $74.00 $56.50 |
| MAA Member Price: | $66.60 $50.85 |
| AMS Member Price: | $59.20 $45.20 |
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Book DetailsMathematical WorldVolume: 16; 2000; 75 ppMSC: 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.
ReadershipAdvanced high school and undergraduate students, mathematics educators at secondary and university level; general mathematical audience.
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Table of Contents
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Chapters
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Chapter 1. Conjugate numbers
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Chapter 2. Rational parametrizations of the circle
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Chapter 3. Sums of squares of polynomials
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Chapter 4. Representing numbers as the sum of two squares
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Chapter 5. Can any knot be unraveled?
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Chapter 6. Construction of a regular 17-gon
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Chapter 7. The Markov equation
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Chapter 8. Integer-valued polynomials
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Chapter 9. Chebyshev polynomials
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Chapter 10. Vectors in geometry
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Chapter 11. The averaging method and geometric inequalities
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Chapter 12. Intersection points of the diagonals of regular polygons
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Chapter 13. The chromatic polynomial of a graph
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Chapter 14. Brocard points
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Chapter 15. Diophantine equations for polynomials
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Chapter 16. The Pascal lines
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Chapter 17. One butterfly and two butterflies theorems
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Chapter 18. The Van der Waerden theorem on arithmetical progressions
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Chapter 19. Isogonal conjugate points
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Chapter 20. Cubic curves related to the triangle
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Additional Material
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Reviews
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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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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Reviews
- Requests
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.
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
