Zur Startseite gehen
0,00 €*
Cover: 9781461573494 | Lecture Notes on Elementary Topology and Geometry | Thorpe (u. a.)
Dekorationsartikel gehören nicht zum Leistungsumfang.
Lecture Notes on Elementary Topology and Geometry
Taschenbuch von J. A. Thorpe (u. a.)
Sprache: Englisch

50,28 €*

inkl. MwSt.

Versandkostenfrei per Post / DHL

Aktuell nicht verfügbar

Kategorien:
Beschreibung
At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized. After the calculus, he takes a course in analysis and a course in algebra. Depending upon his interests (or those of his department), he takes courses in special topics. Ifhe is exposed to topology, it is usually straightforward point set topology; if he is exposed to geom­ etry, it is usually classical differential geometry. The exciting revelations that there is some unity in mathematics, that fields overlap, that techniques of one field have applications in another, are denied the undergraduate. He must wait until he is well into graduate work to see interconnections, presumably because earlier he doesn't know enough. These notes are an attempt to break up this compartmentalization, at least in topology-geometry. What the student has learned in algebra and advanced calculus are used to prove some fairly deep results relating geometry, topol­ ogy, and group theory. (De Rham's theorem, the Gauss-Bonnet theorem for surfaces, the functorial relation of fundamental group to covering space, and surfaces of constant curvature as homogeneous spaces are the most note­ worthy examples.) In the first two chapters the bare essentials of elementary point set topology are set forth with some hint ofthe subject's application to functional analysis.
At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized. After the calculus, he takes a course in analysis and a course in algebra. Depending upon his interests (or those of his department), he takes courses in special topics. Ifhe is exposed to topology, it is usually straightforward point set topology; if he is exposed to geom­ etry, it is usually classical differential geometry. The exciting revelations that there is some unity in mathematics, that fields overlap, that techniques of one field have applications in another, are denied the undergraduate. He must wait until he is well into graduate work to see interconnections, presumably because earlier he doesn't know enough. These notes are an attempt to break up this compartmentalization, at least in topology-geometry. What the student has learned in algebra and advanced calculus are used to prove some fairly deep results relating geometry, topol­ ogy, and group theory. (De Rham's theorem, the Gauss-Bonnet theorem for surfaces, the functorial relation of fundamental group to covering space, and surfaces of constant curvature as homogeneous spaces are the most note­ worthy examples.) In the first two chapters the bare essentials of elementary point set topology are set forth with some hint ofthe subject's application to functional analysis.
Inhaltsverzeichnis
1 Some point set topology.- 1.1 Naive set theory.- 1.2 Topological spaces.- 1.3 Connected and compact spaces.- 1.4 Continuous functions.- 1.5 Product spaces.- 1.6 The Tychonoff theorem.- 2 More point set topology.- 2.1 Separation axioms.- 2.2 Separation by continuous functions.- 2.3 More separability.- 2.4 Complete metric spaces.- 2.5 Applications.- 3 Fundamental group and covering spaces.- 3.1 Homotopy.- 3.2 Fundamental group.- 3.3 Covering spaces.- 4 Simplicial complexes.- 4.1 Geometry of simplicial complexes.- 4.2 Barycentric subdivisions.- 4.3 Simplicial approximation theorem.- 4.4 Fundamental group of a simplicial complex.- 5 Manifolds.- 5.1 Differentiable manifolds.- 5.2 Differential forms.- 5.3 Miscellaneous facts.- 6 Homology theory and the De Rham theory.- 6.1 Simplicial homology.- 6.2 De Rham's theorem.- 7 Intrinsic Riemannian geometry of surfaces.- 7.1 Parallel translation and connections.- 7.2 Structural equations and curvature.- 7.3 Interpretation of curvature.- 7.4 Geodesic coordinate systems.- 7.5 Isometries and spaces of constant curvature.- 8 Imbedded manifolds in R3.
Details
Erscheinungsjahr: 2012
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Undergraduate Texts in Mathematics
Inhalt: viii
232 S.
ISBN-13: 9781461573494
ISBN-10: 1461573491
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Thorpe, J. A.
Singer, I. M.
Auflage: Softcover reprint of the original 1st ed. 1967
Hersteller: Springer New York
Springer US, New York, N.Y.
Undergraduate Texts in Mathematics
Maße: 235 x 155 x 14 mm
Von/Mit: J. A. Thorpe (u. a.)
Erscheinungsdatum: 11.07.2012
Gewicht: 0,376 kg
Artikel-ID: 105628839
Inhaltsverzeichnis
1 Some point set topology.- 1.1 Naive set theory.- 1.2 Topological spaces.- 1.3 Connected and compact spaces.- 1.4 Continuous functions.- 1.5 Product spaces.- 1.6 The Tychonoff theorem.- 2 More point set topology.- 2.1 Separation axioms.- 2.2 Separation by continuous functions.- 2.3 More separability.- 2.4 Complete metric spaces.- 2.5 Applications.- 3 Fundamental group and covering spaces.- 3.1 Homotopy.- 3.2 Fundamental group.- 3.3 Covering spaces.- 4 Simplicial complexes.- 4.1 Geometry of simplicial complexes.- 4.2 Barycentric subdivisions.- 4.3 Simplicial approximation theorem.- 4.4 Fundamental group of a simplicial complex.- 5 Manifolds.- 5.1 Differentiable manifolds.- 5.2 Differential forms.- 5.3 Miscellaneous facts.- 6 Homology theory and the De Rham theory.- 6.1 Simplicial homology.- 6.2 De Rham's theorem.- 7 Intrinsic Riemannian geometry of surfaces.- 7.1 Parallel translation and connections.- 7.2 Structural equations and curvature.- 7.3 Interpretation of curvature.- 7.4 Geodesic coordinate systems.- 7.5 Isometries and spaces of constant curvature.- 8 Imbedded manifolds in R3.
Details
Erscheinungsjahr: 2012
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Undergraduate Texts in Mathematics
Inhalt: viii
232 S.
ISBN-13: 9781461573494
ISBN-10: 1461573491
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Thorpe, J. A.
Singer, I. M.
Auflage: Softcover reprint of the original 1st ed. 1967
Hersteller: Springer New York
Springer US, New York, N.Y.
Undergraduate Texts in Mathematics
Maße: 235 x 155 x 14 mm
Von/Mit: J. A. Thorpe (u. a.)
Erscheinungsdatum: 11.07.2012
Gewicht: 0,376 kg
Artikel-ID: 105628839
Warnhinweis

Ähnliche Produkte

Ähnliche Produkte

Buch
Cover: 9783110136265 | Maß- und Integrationstheorie | Heinz Bauer | Buch | XVIII | Deutsch
Maß- und Integrationstheorie
EAN: 9783110136265
Sprache: Deutsch
Von/Mit: Heinz Bauer

99,95 €*

Lieferzeit 1-2 Wochen

Taschenbuch
Cover: 9780984422197 | Twenty Lectures About Gaussian Processes | Vladimir Ilich Piterbarg
Twenty Lectures About Gaussian Processes
EAN: 9780984422197
Sprache: Englisch
Von/Mit: Vladimir Ilich Piterbarg

78,75 €*

Lieferzeit 1-2 Wochen

Taschenbuch
Cover: 9783528147181 | Grundlagen des maschinellen Beweisens | Ralf-Detlef Kutsche | Buch
Grundlagen des maschinellen Beweisens
Eine Einführung für Informatiker und Mathematiker
EAN: 9783528147181
Sprache: Deutsch
Von/Mit: Ralf-Detlef Kutsche

44,99 €*

Aktuell nicht verfügbar

Taschenbuch
Cover: 9783709176924 | Vorlesungen über höhere Mathematik | Adalbert Duschek | Taschenbuch
Vorlesungen über höhere Mathematik
Erster Band Integration und Differentiation der Funktionen einer Veränderlichen. Anwendungen. Numerische Methoden....
EAN: 9783709176924
Sprache: Deutsch
Von/Mit: Adalbert Duschek

69,99 €*

Aktuell nicht verfügbar

Taschenbuch
Cover: 9780691005485 | The Topology of Fibre Bundles. (PMS-14), Volume 14 | Norman Steenrod
The Topology of Fibre Bundles
EAN: 9780691005485
Sprache: Englisch
Von/Mit: Norman Steenrod

79,60 €*

Aktuell nicht verfügbar

Buch
Cover: 9789810235550 | Modern Differential Geometry for Physicists | Second Edition | Isham
MODERN DIFF GEOMETRY FOR PHYS (2ED)(V61)
EAN: 9789810235550
Sprache: Englisch
Von/Mit: C J Isham

87,90 €*

Aktuell nicht verfügbar

Taschenbuch
Cover: 9783744667609 | Spuren auf dem Eise | Demeter Diamantidi | Taschenbuch | Paperback
Spuren auf dem Eise
die Entwicklung des Eislaufes auf der Bahn des Wiener Eislauf-Vereines
EAN: 9783744667609
Sprache: Deutsch
Von/Mit: Demeter Diamantidi

26,90 €*

Aktuell nicht verfügbar

Taschenbuch
Cover: 9781119248903 | Anton's Calculus | Early Transcendentals, Global Edition | Taschenbuch
Anton's Calculus
Early Transcendentals, Global Edition
EAN: 9781119248903
Sprache: Englisch
Von/Mit: Howard Anton (u. a.)

69,00 €*

Aktuell nicht verfügbar

Taschenbuch
Cover: 9781446021262 | Apollonius of Perga - Treatise on Conic Sections | Thomas Little Heath
Apollonius of Perga - Treatise on Conic Sections
EAN: 9781446021262
Sprache: Englisch
Von/Mit: Thomas Little Heath

46,65 €*

Lieferzeit 1-2 Wochen

Cover: 9780821843772 | Representations of Algebraic Groups | Kartoniert / Broschiert | 2007
Representations of Algebraic Groups
EAN: 9780821843772

151,14 €*

Aktuell nicht verfügbar

Taschenbuch
Cover: 9780486824499 | Topological Transformation Groups | Deane Montgomery | Taschenbuch
Topological Transformation Groups
EAN: 9780486824499
Sprache: Englisch
Von/Mit: Deane Montgomery

27,10 €*

Lieferzeit 1-2 Wochen

Diese Website verwendet Cookies, um eine bestmögliche Erfahrung bieten zu können. Mehr Informationen ...