Geometry of Surfaces / by John Stillwell.
This text intends to provide the student with the knowledge of a geometry of greater scope than the classical geometry taught today, which is no longer an adequate basis for mathematics or physics, both of which are becoming increasingly geometric. The geometry of surfaces is an ideal starting point...
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| Online Access: |
Full Text (via Springer) |
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| Main Author: | |
| Format: | eBook |
| Language: | English |
| Published: |
New York, NY :
Springer New York,
1992.
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| Series: | Universitext.
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| Subjects: |
| Summary: | This text intends to provide the student with the knowledge of a geometry of greater scope than the classical geometry taught today, which is no longer an adequate basis for mathematics or physics, both of which are becoming increasingly geometric. The geometry of surfaces is an ideal starting point for students learning geometry for the following reasons; first, the extensions offer the simplest possible introduction to fundamentals of modern geometry: curvature, group actions and covering spaces. Second, the prerequisites are modest and standard and include only a little linear algebra, calculus, basic group theory and basic topology. Third and most important, the theory of surfaces of constant curvature has maximal connectivity with the rest of mathematics. They realize all the topological types of compact two-dimensional manifolds, and historically, they are the source of the main concepts of complex analysis, differential geometry, topology, and combinatorial group theory, as well as such hot topics as fractal geometry and string theory. The formal coverage is extended by exercises and informal discussions throughout the text. |
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| Physical Description: | 1 online resource (xi, 236 pages 164 illustrations) |
| ISBN: | 9781461209294 1461209293 |
| ISSN: | 0172-5939. |