A mathematical gift : the interplay between topology, functions, geometry, and algebra

Author(s)

• 上野, 健爾 ウエノ, ケンジ
• 志賀, 浩二 シガ, コウジ
• 森田, 茂之 モリタ, シゲユキ
• Tyler, Eiko
• 砂田, 利一 スナダ, トシカズ

Bibliographic Information

A mathematical gift : the interplay between topology, functions, geometry, and algebra

Kenji Ueno, Koji Shiga, Shigeyuki Morita ; translated by Eiko Tyler

（Mathematical world, v. 19-20, 23）

American Mathematical Society, c2003-

• 1
• 2
• 3

Other Title

Kokosei ni okuru sugaku

高校生に贈る数学

Note

"Originally published in Japanese by Iwanami Shoten, Publishers, Tokyo, Japan"--T.p. verso

Statement of responsibility on 3: Koji Shiga, Toshikazu Sunada ; translated by Eiko Tyler

Description and Table of Contents

Volume

1 ISBN 9780821832820

Description

This book will bring 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 presents the geometry and topology of surfaces. Among other topics, the authors discuss the Poincare-Hopf theorem on critical points of vector fields on surfaces and the Gauss-Bonnet theorem on the relation between curvature and topology (the Euler characteristic).The second chapter addresses various aspects of the concept of dimension, including the Peano curve and the Poincare approach. Also addressed is the structure of three-dimensional manifolds. In particular, it is proved that the three-dimensional sphere is the union of two doughnuts. This is the first of three volumes 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 undergraduate mathematics courses in the sciences and liberal arts. The second volume is available as Volume 20 in the AMS series, ""Mathematical World"". A third volume is forthcoming.

Table of Contents

Invitation to topology (Viewing figures globally): Introduction The Euler characteristic Vortices created by winds and the Euler characteristic Curvature of a surface and the Euler characteristic The story of dimension: Introduction Learning to appreciate dimension What is dimension? Three-dimensional figures Physics and dimension.

Volume

2 ISBN 9780821832837

Description

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"".

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.

by "Nielsen BookData"

Details

• NCID: BA64717053
• ISBN:
  • 0821832824
  • 0821832832
  • 0821832840
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Original Language Code: jpn
• Place of Publication: Providence, R.I.
• Pages/Volumes: v.
• Size: 26 cm
• Parent Bibliography ID:
  • BA12396627