Introduction to Hyperbolic Geometry

  • Arlan Ramsay
  • Robert D. Richtmyer

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Arlan Ramsay, Robert D. Richtmyer
    Pages 1-8
  3. Arlan Ramsay, Robert D. Richtmyer
    Pages 9-29
  4. Arlan Ramsay, Robert D. Richtmyer
    Pages 30-68
  5. Arlan Ramsay, Robert D. Richtmyer
    Pages 69-127
  6. Arlan Ramsay, Robert D. Richtmyer
    Pages 128-148
  7. Arlan Ramsay, Robert D. Richtmyer
    Pages 149-189
  8. Arlan Ramsay, Robert D. Richtmyer
    Pages 190-201
  9. Arlan Ramsay, Robert D. Richtmyer
    Pages 218-231
  10. Arlan Ramsay, Robert D. Richtmyer
    Pages 232-241
  11. Arlan Ramsay, Robert D. Richtmyer
    Pages 242-253
  12. Arlan Ramsay, Robert D. Richtmyer
    Pages 254-282
  13. Back Matter
    Pages 283-289

About this book

Introduction

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.

Keywords

derivation differential equation differential geometry differential geometry of surfaces hyperbolic geometry

Authors and affiliations

  • Arlan Ramsay
    • 1
  • Robert D. Richtmyer
    • 1
  1. 1.Department of MathematicsUniversity of ColoradoBoulderUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-5585-5
  • Copyright Information Springer-Verlag New York 1995
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-94339-8
  • Online ISBN 978-1-4757-5585-5
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book
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