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 for students learning geometry for the following reasons; first, the extensions offer the simplest possible introduction to fundamentals of modern 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.

Genres: Mathematics, Geometry

228 pages, Paperback

First published June 24, 1992

About the author

John Colin Stillwell (born 1942) is an Australian mathematician on the faculties of the University of San Francisco and Monash University

Reviews

[Kouver · Rating 1 out of 5]

Don't read this book. Great for a sloppy misunderstanding of its topics.