Lecture Notes on Elementary Topology and Geometry (Hardcover)

I.M. Singer

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Langue : anglais

Edité par Springer-Verlag New York Inc., New York, NY, 1976

0387902023 / 9780387902029

Série : Livre 151 sur 170 - Undergraduate Texts in Mathematics

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Hardcover. 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 geomA 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, topolA 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 noteA 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 analys Shipping may be from our Sydney, NSW warehouse or from our UK or US warehouse, depending on stock availability. …

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Titre
Lecture Notes on Elementary Topology and Geometry (Hardcover)
Auteur
I.M. Singer
Éditeur
Springer-Verlag New York Inc., New York, NY
Année de publication
1976
État de l'article
new
Reliure
Hardcover
Langue
anglais
ISBN à 10 chiffres
0387902023
ISBN à 13 chiffres
9780387902029
Édition
Edition originale
Série
Livre 151 sur 170: Undergraduate Texts in Mathematics

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