Introduction to Hyperbolic Geometry

Arlan Ramsay

ISBN 10: 0387943390 / ISBN 13: 9780387943398

Published by Springer, Springer Dez 1995, 1995

About this Item

This item is printed on demand - it takes 3-4 days longer - Neuware -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. 304 pp. Englisch.

Seller Inventory # 9780387943398

Bibliographic Details

• Title: Introduction to Hyperbolic Geometry
• Publisher: Springer, Springer Dez 1995
• Publication Date: 1995
• Language: English
• ISBN 10: 0387943390
• ISBN 13: 9780387943398
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 279W x 210H x 17D millimeters 279 millimeters width by 210 millimeters height by 17 millimeters depth
• Weight: 746 grams

About this title

Synopsis

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.

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