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A Mathematical Gift, I: The interplay between topology, functions, geometry, and algebra


About this Title

Kenji Ueno, Kyoto University, Kyoto, Japan, Koji Shiga, , Yokohama, Japan and Shigeyuki Morita, Tokyo Institute of Technology, Tokyo, Japan. Translated by Eiko Tyler

Publication: Mathematical World
Publication Year 2003: Volume 19
ISBN: 978-0-8218-3282-0 (print)
DOI: http://dx.doi.org/10.1090/mawrld/019
MathSciNet review: MR2013039
MSC: Primary 57-01; Secondary 53-01

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Table of Contents


Invitation to topology (Viewing figures globally)

  • 1. Introduction
  • 2. The Euler characteristic
  • 3. Vortices created by winds and the Euler characteristic
  • 4. Curvature of a surface and the Euler characteristic

The story of dimension

  • 5. Introduction
  • 6. Learning to appreciate dimension
  • 7. What is dimension?
  • 8. Three-dimensional figures
  • 9. Physics and dimension