Articoli correlati a Introduction to Hyperbolic Geometry (Universitext)

Introduction to Hyperbolic Geometry (Universitext) - Brossura

Libro 149 di 261: Universitext

Ramsay, Arlan; Richtmyer, Robert D.

 
9780387943398: Introduction to Hyperbolic Geometry (Universitext)
Brossura
ISBN 10: 0387943390 ISBN 13: 9780387943398
Casa editrice: Springer, 1995

Sinossi

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.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Dalla quarta di copertina

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.

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

Editore
Springer
Data di pubblicazione
1995
Lingua
Inglese
ISBN 10 
0387943390
ISBN 13 
9780387943398
Rilegatura
Copertina flessibile
Numero di pagine
289
Contatto del produttore
ProductSafety@springernature.com
ProductSafety@springernature.com

Europaplatz 3
Heidelberg
69115
Germania