A Mathematical Gift, I, II, III: The interplay between topology, functions, geometry, and algebra
, Tokyo Institute of Technology, Japan
, Koji Shiga
, Yokohama, Japan
, Toshikazu Sunada
, Tohoku University, Sendai, Japan
, and Kenji Ueno
, Kyoto University, Japan
| Mathematical World
2005; 392 pp; softcover
ISBN-13: 978-0-8218-3859-4 List Price: US$83
Member Price: US$66.40
Order Code: MAWRLD-GSET
This three-volume set addresses the interplay between topology, functions, geometry, and algebra. Bringing the beauty and fun of mathematics to the classroom, the authors offer serious mathematics in a lively, reader-friendly style. Included are exercises and many figures illustrating the main concepts. It is suitable for advanced high-school students, graduate students, and researchers.
The three-volume set includes A Mathematical Gift I, II, and III.
Advanced high-school students and undergraduates in mathematics.
Table of Contents Part I
Invitation to topology (Viewing figures globally)
The story of dimension
- The Euler characteristic
- Vortices created by winds and the Euler characteristic
- Curvature of a surface and the Euler characteristic
- Learning to appreciate dimension
- What is dimension?
- Three-dimensional figures
- Physics and dimension
The legacy of trigonometric functions
Intersection of geometry and algebra
- Trigonometric functions and infinite series
- Elliptic functions
- 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
- The story of the birth of manifolds
- The prelude to the birth of manifolds
- The birth of manifolds
- The story of area and volume from everyday notions to mathematical concepts
- Transition from the notion of "size" to the concept of "area"
- Scissors-congruent polygons
- Scissors-congruent polyhedra