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Student Mathematical Library
2011; 314 pp; softcover
List Price: US$49
Institutional Members: US$39.20
All Individuals: US$39.20
Order Code: STML/60
Lectures on Surfaces: (Almost) Everything You Wanted to Know about Them - Anatole Katok and Vaughn Climenhaga
Differential Geometry: Curves - Surfaces - Manifolds, Second Edition - Wolfgang Kuhnel
This book presents a number of topics related to surfaces, such as Euclidean, spherical and hyperbolic geometry, the fundamental group, universal covering surfaces, Riemannian manifolds, the Gauss-Bonnet Theorem, and the Riemann mapping theorem. The main idea is to get to some interesting mathematics without too much formality. The book also includes some material only tangentially related to surfaces, such as the Cauchy Rigidity Theorem, the Dehn Dissection Theorem, and the Banach-Tarski Theorem.
The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis.
Undergraduate students interested in geometry and topology of surfaces.
"The book contains a lot of interesting basic and more advanced material which is presented in a nice, intuitive yet rigorous way, and, as such, is perfectly suited as an accompanying text or additional reading for a first course on topology or as a basis for a student seminar."
-- Mathematical Reviews
"This is a novel, eclectic, and ambitious collection of geometric and topological topics developed as they relate to surfaces ... a terrific volume. Highly recommended."
"...a delightful reading. Schwartz gives a beautiful, careful exposition of some of the most elegant ideas, theorems, and proofs in the theory of surfaces. It's an ideal book for casual reading in spare mathematical moments."
-- MAA Reviews
"This highly readable book is an excellent introduction to the theory of surfaces, covering a wide variety of topics with references for further reading. Each chapter contains numerous exercises on the material to get the reader thinking about the subjects covered. There are also many diagrams to aid the reader in understanding the material."
-- Alastair Fletcher, Zentralblatt MATH
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