Universitext

Geometry of Surfaces

Authors: Stillwell, John

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About this Textbook

Geometry used to be the basis of a mathematical education; today it is not even a standard undergraduate topic. Much as I deplore this situation, I welcome the opportunity to make a fresh start. Classical geometry is no longer an adequate basis for mathematics or physics-both of which are becoming increasingly geometric-and geometry can no longer be divorced from algebra, topology, and analysis. Students need a geometry of greater scope, and the fact that there is no room for geometry in the curriculum un­ til the third or fourth year at least allows us to assume some mathematical background. What geometry should be taught? I believe that the geometry of surfaces of constant curvature is an ideal choice, for the following reasons: 1. It is basically simple and traditional. We are not forgetting euclidean geometry but extending it enough to be interesting and useful. The extensions offer the simplest possible introduction to fundamentals of modem geometry: curvature, group actions, and covering spaces. 2. The prerequisites are modest and standard. A little linear algebra (mostly 2 x 2 matrices), calculus as far as hyperbolic functions, ba­ sic group theory (subgroups and cosets), and basic topology (open, closed, and compact sets).

Table of contents (8 chapters)

Table of contents (8 chapters)

Buy this book

eBook $44.99
price for USA in USD (gross)
  • ISBN 978-1-4612-0929-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-0-387-97743-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Geometry of Surfaces
Authors
Series Title
Universitext
Copyright
1992
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4612-0929-4
DOI
10.1007/978-1-4612-0929-4
Softcover ISBN
978-0-387-97743-0
Series ISSN
0172-5939
Edition Number
1
Number of Pages
XI, 236
Topics