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A Mathematical Gift, II: The interplay between topology, functions, geometry, and algebra
 
Kenji Ueno Kyoto University, Kyoto, Japan
Koji Shiga Yokohama, Japan
Shigeyuki Morita Tokyo Institute of Technology, Tokyo, Japan
Front Cover for A Mathematical Gift, II
Available Formats:
Softcover ISBN: 978-0-8218-3283-7
Product Code: MAWRLD/20
List Price: $37.00
MAA Member Price: $33.30
AMS Member Price: $29.60
Front Cover for A Mathematical Gift, II
Click above image for expanded view
A Mathematical Gift, II: The interplay between topology, functions, geometry, and algebra
Kenji Ueno Kyoto University, Kyoto, Japan
Koji Shiga Yokohama, Japan
Shigeyuki Morita Tokyo Institute of Technology, Tokyo, Japan
Available Formats:
Softcover ISBN:  978-0-8218-3283-7
Product Code:  MAWRLD/20
List Price: $37.00
MAA Member Price: $33.30
AMS Member Price: $29.60
  • Book Details
     
     
    Mathematical World
    Volume: 202004; 128 pp
    MSC: Primary 00;

    This book brings the beauty and fun of mathematics to the classroom. It offers serious mathematics in a lively, reader-friendly style. Included are exercises and many figures illustrating the main concepts.

    The first chapter talks about the theory of trigonometric and elliptic functions. It includes subjects such as power series expansions, addition and multiple-angle formulas, and arithmetic-geometric means. The second chapter discusses various aspects of the Poncelet Closure Theorem. This discussion illustrates to the reader the idea of algebraic geometry as a method of studying geometric properties of figures using algebra as a tool.

    This is the second volume originating from a series of lectures given by the authors at Kyoto University (Japan). It is suitable for classroom use for high school mathematics teachers and for undergraduate mathematics courses in the sciences and liberal arts. The first volume is available as Volume 19 in the AMS series, Mathematical World.

    Readership

    Advanced high-school students and undergraduates in mathematics.

    This item is also available as part of a set:
  • Table of Contents
     
     
    • The legacy of trigonometric functions
    • 1. Introduction
    • 2. Trigonometric functions and infinite series
    • 3. Elliptic functions
    • Intersection of geometry and algebra
    • 4. Introduction
    • 5. The Poncelet closure theorem
    • 6. The Poncelet theorem for circles
    • 7. The Poncelet theorem in the world of complex numbers
    • 8. Proof of the Poncelet theorem using plane geometry
    • 9. Conclusion
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Volume: 202004; 128 pp
MSC: Primary 00;

This book brings the beauty and fun of mathematics to the classroom. It offers serious mathematics in a lively, reader-friendly style. Included are exercises and many figures illustrating the main concepts.

The first chapter talks about the theory of trigonometric and elliptic functions. It includes subjects such as power series expansions, addition and multiple-angle formulas, and arithmetic-geometric means. The second chapter discusses various aspects of the Poncelet Closure Theorem. This discussion illustrates to the reader the idea of algebraic geometry as a method of studying geometric properties of figures using algebra as a tool.

This is the second volume originating from a series of lectures given by the authors at Kyoto University (Japan). It is suitable for classroom use for high school mathematics teachers and for undergraduate mathematics courses in the sciences and liberal arts. The first volume is available as Volume 19 in the AMS series, Mathematical World.

Readership

Advanced high-school students and undergraduates in mathematics.

This item is also available as part of a set:
  • The legacy of trigonometric functions
  • 1. Introduction
  • 2. Trigonometric functions and infinite series
  • 3. Elliptic functions
  • Intersection of geometry and algebra
  • 4. Introduction
  • 5. The Poncelet closure theorem
  • 6. The Poncelet theorem for circles
  • 7. The Poncelet theorem in the world of complex numbers
  • 8. Proof of the Poncelet theorem using plane geometry
  • 9. Conclusion
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