Introduction to Hyperbolic Geometry by Arlan Ramsay (English) Paperback Book

The Nile on eBay   Introduction to Hyperbolic Geometry by Arlan Ramsay, Robert D. Richtmyer

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. The book goes well beyond the standard course in later chapters, and there is enough material for an honors course, or for supplementary reading.

FORMATPaperback LANGUAGEEnglish CONDITIONBrand New Publisher Description

This text for advanced undergraduates emphasizes the logical connections of the subject. The derivations of formulas from the axioms do not make use of models of the hyperbolic plane until the axioms are shown to be categorical; the differential geometry of surfaces is developed far enough to establish its connections to the hyperbolic plane; and the axioms and proofs use the properties of the real number system to avoid the tedium of a completely synthetic approach. The development includes properties of the isometry group of the hyperbolic plane, tilings, and applications to special relativity. Elementary techniques from complex analysis, matrix theory, and group theory are used, and some mathematical sophistication on the part of students is thus required, but a formal course in these topics is not a prerequisite.

Table of Contents

1 Axioms for Plane Geometry.- 2 Some Neutral Theorems of Plane Geometry.- 3 Qualitative Description of the Hyperbolic Plane.- 4 ?3 and Euclidean Approximations in ?2.- 5 Differential Geometry of Surfaces.- 6 Quantitative Considerations.- 7 Consistency and Categoricalness of the Hyperbolic Axioms; The Classical Models.- 8 Matrix Representation of the Isometry Group.- 9 Differential and Hyperbolic Geometry in More Dimensions.- 10 Connections with the Lorentz Group of Special Relativity.- 11 Constructions by Straightedge and Compass in the Hyperbolic Plane.

Review

"The book is well laid out with no shortage of diagrams and with each chapter prefaced with its own useful introduction...Also well written, it makes pleasurable reading." Proceedings of the Edinburgh Mathematical Society

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Long 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

Review Text

"The book is well laid out with no shortage of diagrams and with each chapter prefaced with its own useful introduction...Also well written, it makes pleasurable reading." Proceedings of the Edinburgh Mathematical Society

Review Quote

"The book is well laid out with no shortage of diagrams and with each chapter prefaced with its own useful introduction...Also well written, it makes pleasurable reading." Proceedings of the Edinburgh Mathematical Society

Description for Sales People

This text for advanced undergraduates emphasizes the logical connections of the subject. Elementary techniques from complex analysis, matrix theory, and group theory are used, and some mathematical sophistication on the part of students is thus required, but a formal course in these topics is not a prerequisite.

Details ISBN0387943390 Author Robert D. Richtmyer Language English ISBN-10 0387943390 ISBN-13 9780387943398 Media Book Format Paperback DEWEY 516.9 Year 1995 Imprint Springer-Verlag New York Inc. Country of Publication United States Place of Publication New York, NY Short Title INTRO TO HYPERBOLIC GEOMETRY 1 Pages 289 DOI 10.1007/b48423;10.1007/978-1-4757-5585-5 AU Release Date 1995-12-16 NZ Release Date 1995-12-16 US Release Date 1995-12-16 UK Release Date 1995-12-16 Publisher Springer-Verlag New York Inc. Edition Description 1995 ed. Series Universitext Edition 1995th Publication Date 1995-12-16 Replaced by 9780387745329 Illustrations 6 Illustrations, black and white; XII, 289 p. 6 illus. Audience Undergraduate We've got this

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