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A Mathematical Gift, II: The interplay between topology, functions, geometry, and algebra
Kenji Ueno, Kyoto University, Japan, Koji Shiga, Yokohama, Japan, and Shigeyuki Morita, Tokyo Institute of Technology, Japan
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Mathematical World
2004; 128 pp; softcover
Volume: 20
ISBN-10: 0-8218-3283-2
ISBN-13: 978-0-8218-3283-7
List Price: US$32
Member Price: US$25.60
Order Code: MAWRLD/20
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This item is also sold as part of the following set: MAWRLD-GSET

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.

Table of Contents

The legacy of trigonometric functions
  • Introduction
  • Trigonometric functions and infinite series
  • Elliptic functions
Intersection of geometry and algebra
  • Introduction
  • The Poncelet closure theorem
  • The Poncelet theorem for circles
  • The Poncelet theorem in the world of complex numbers
  • Proof of the Poncelet theorem using plane geometry
  • Conclusion
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