Ein erster Kurs in geometrischer Topologie und Differentialgeometrie (moderne Birkh�us,

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“Used book in good condition. Shows typical wear. Quick shipping. Satisfaction guaranteed!”
Book Title
A First Course in Geometric Topology and Differential Geometry (,
Topic
Differential Geometry
Narrative Type
Differential Geometry
Genre
N/A
Intended Audience
N/A
ISBN
9780817638405
Kategorie

Über dieses Produkt

Product Identifiers

Publisher
Birkhäuser Boston
ISBN-10
0817638407
ISBN-13
9780817638405
eBay Product ID (ePID)
913796

Product Key Features

Number of Pages
Xii, 421 Pages
Language
English
Publication Name
First Course in Geometric Topology and Differential Geometry
Subject
Geometry / Differential, Geometry / General, Topology
Publication Year
1996
Type
Textbook
Author
Ethan D. Bloch
Subject Area
Mathematics
Series
Modern Birkhäuser Classics Ser.
Format
Hardcover

Dimensions

Item Height
0.4 in
Item Weight
61.7 Oz
Item Length
9.3 in
Item Width
6.1 in

Additional Product Features

Intended Audience
Scholarly & Professional
LCCN
96-015470
Reviews
"[The author] avoids aimless wandering among the topics by explicitly heading towards milestone theorems... [His] directed path through these topics should make an effective course on the mathematics of surfaces. The exercises and hints are well chosen to clarify the central threads rather than diverting into byways." - Computing Reviews "Many examples and illustrations as well as exercises and hints to solutions are providing great support... By well-placed appendices the reader is relieved of the strain to immediately understand some extensive proofs or to learn adjoining mathematical factsa? The book is suitable for students of mathematics, physics and of the teaching profession as well as university teachers who might be interested in using certain chapters...to present the topic in a seminar or in not too advanced special lectures about the topic...It is the great clarity of thought in this book, the simplicity and concreteness of the representation with respect to the capacity for teaching of students, and some other aspects that make this work stand out from comparable efforts." - ZAA, "[The author] avoids aimless wandering among the topics by explicitly heading towards milestone theorems... [His] directed path through these topics should make an effective course on the mathematics of surfaces. The exercises and hints are well chosen to clarify the central threads rather than diverting into byways." - Computing Reviews "Many examples and illustrations as well as exercises and hints to solutions are providing great support... By well-placed appendices the reader is relieved of the strain to immediately understand some extensive proofs or to learn adjoining mathematical facts... The book is suitable for students of mathematics, physics and of the teaching profession as well as university teachers who might be interested in using certain chapters...to present the topic in a seminar or in not too advanced special lectures about the topic...It is the great clarity of thought in this book, the simplicity and concreteness of the representation with respect to the capacity for teaching of students, and some other aspects that make this work stand out from comparable efforts." - ZAA "The exposition is clear, nicely organized, and generally easy to read." ---Zentralblatt Math, "[The author] avoids aimless wandering among the topics by explicitly heading towards milestone theorems... [His] directed path through these topics should make an effective course on the mathematics of surfaces. The exercises and hints are well chosen to clarify the central threads rather than diverting into byways."- Computing Reviews"Many examples and illustrations as well as exercises and hints to solutions are providing great support... By well-placed appendices the reader is relieved of the strain to immediately understand some extensive proofs or to learn adjoining mathematical facts… The book is suitable for students of mathematics, physics and of the teaching profession as well as university teachers who might be interested in using certain chapters...to present the topic in a seminar or in not too advanced special lectures about the topic...It is the great clarity of thought in this book, the simplicity and concreteness of the representation with respect to the capacity for teaching of students, and some other aspects that make this work stand out from comparable efforts."- ZAA"The exposition is clear, nicely organized, and generally easy to read." ---Zentralblatt Math
Dewey Edition
20
TitleLeading
A
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
516.3/63
Table Of Content
I. Topology of Subsets of Euclidean Space.- 1.1 Introduction.- 1.2 Open and Closed Subsets of Sets in ?n.- 1.3 Continuous Maps.- 1.4 Homeomorphisms and Quotient Maps.- 1.5 Connectedness.- 1.6 Compactness.- II. Topological Surfaces.- 2.1 Introduction.- 2.2 Arcs, Disks and 1-spheres.- 2.3 Surfaces in ?n.- 2.4 Surfaces Via Gluing.- 2.5 Properties of Surfaces.- 2.6 Connected Sum and the Classification of Compact Connected Surfaces.- Appendix A2.1 Proof of Theorem 2.4.3 (i).- Appendix A2.2 Proof of Theorem 2.6.1.- III. Simplicial Surfaces.- 3.1 Introduction.- 3.2 Simplices.- 3.3 Simplicial Complexes.- 3.4 Simplicial Surfaces.- 3.5 The Euler Characteristic.- 3.6 Proof of the Classification of Compact Connected Surfaces.- 3.7 Simplicial Curvature and the Simplicial Gauss-Bonnet Theorem.- 3.8 Simplicial Disks and the Brouwer Fixed Point Theorem.- IV. Curves in ?3.- 4.1 Introduction.- 4.2 Smooth Functions.- 4.3 Curves in ?3.- 4.4 Tangent, Normal and Binormal Vectors.- 4.5 Curvature and Torsion.- 4.6 Fundamental Theorem of Curves.- 4.7 Plane Curves.- V. Smooth Surfaces.- 5.1 Introduction.- 5.2 Smooth Surfaces.- 5.3 Examples of Smooth Surfaces.- 5.4 Tangent and Normal Vectors.- 5.5 First Fundamental Form.- 5.6 Directional Derivatives -- Coordinate Free.- 5.7 Directional Derivatives -- Coordinates.- 5.8 Length and Area.- 5.9 Isometries.- Appendix A5.1 Proof of Proposition 5.3.1.- VI. Curvature of Smooth Surfaces.- 6.1 Introduction and First Attempt.- 6.2 The Weingarten Map and the Second Fundamental Form.- 6.3 Curvature -- Second Attempt.- 6.4 Computations of Curvature Using Coordinates.- 6.5 Theorema Egregium and the Fundamental Theorem of Surfaces.- VII. Geodesics.- 7.1 Introduction -- "Straight Lines" on Surfaces.- 7.2 Geodesics.- 7.3 Shortest Paths.- VIII. TheGauss-Bonnet Theorem.- 8.1 Introduction.- 8.2 The Exponential Map.- 8.3 Geodesic Polar Coordinates.- 8.4 Proof of the Gauss-Bonnet Theorem.- 8.5 Non-Euclidean Geometry.- Appendix A8.1 Geodesic Convexity.- Appendix A8.2 Geodesic Triangulations.- Further Study.- References.- Hints for Selected Exercises.- Index of Notation.
LC Classification Number
QA440-699

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