About this product

Product Identifiers

PublisherSpringer New York

ISBN-100387943390

ISBN-139780387943398

eBay Product ID (ePID)346831

Product Key Features

Number of PagesXii, 289 Pages

Publication NameIntroduction to Hyperbolic Geometry

LanguageEnglish

Publication Year1995

SubjectGeometry / Non-Euclidean, Geometry / Differential, Mathematical Analysis

TypeTextbook

AuthorRobert D. Richtmyer, Arlan Ramsay

Subject AreaMathematics

SeriesUniversitext Ser.

FormatTrade Paperback

Dimensions

Item Weight26.6 Oz

Item Length11 in

Item Width8.3 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN94-025789

Reviews"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

Dewey Edition20

Number of Volumes1 vol.

IllustratedYes

Dewey Decimal516.9

Table Of Content1 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.

SynopsisThis 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., 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., 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.

LC Classification NumberQA641-670