Introduction to Hyperbolic Geometry (Universitext) 1995th Edition by Arlan Ramsay (PDF)

Description

This book is an introduction to hyperbolic and differential geometry that provides material in the early chapters that can serve as a textbook for a standard upper division course on hyperbolic geometry. For that material, the students need to be familiar with calculus and linear algebra and willing to accept one advanced theorem from analysis without proof. The book goes well beyond the standard course in later chapters, and there is enough material for an honors course, or for supplementary reading. Indeed, parts of the book have been used for both kinds of courses. Even some of what is in the early chapters would surely not be nec­ essary for a standard course. For example, detailed proofs are given of the Jordan Curve Theorem for Polygons and of the decomposability of poly­ gons into triangles, These proofs are included for the sake of completeness, but the results themselves are so believable that most students should skip the proofs on a first reading. The axioms used are modern in character and more “user friendly” than the traditional ones. The familiar real number system is used as an in­ gredient rather than appearing as a result of the axioms. However, it should not be thought that the geometric treatment is in terms of models: this is an axiomatic approach that is just more convenient than the traditional ones.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Thank you very much Dr. Marvin J. Greenberg Professor of Mathematics and Geometry expert with a specialty in Algebraic Topology. With all due respect, so glad you enjoyed it.I have not read this text but doubt that they took the time to provide solutions.

⭐This review is of the first edition.For me the highlight of this treatment is the indication of a new model of the Euclidean plane within the hyperbolic plane. I have named that model after these authors in my March 2010 American Mathematical MONTHLY survey article. Previously, only a model within hyperbolic three-space was known.The material relating hyperbolic geometry to special relativity is also very valuable.

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