Lecture Notes on Elementary Topology and Geometry (Hardcover)
Language: English
Published by Springer-Verlag New York Inc., New York, NY, 1976
Series: Book 151 of 170 - Undergraduate Texts in Mathematics
- First Edition
- Hardcover
- New
Seller: AussieBookSeller, Truganina, VIC, AustraliaAussieBookSeller
AbeBooks seller since June 22, 2007
Condition: New
£ 96.68
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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. …
Seller Inventory # 9780387902029
- Title
- Lecture Notes on Elementary Topology and Geometry (Hardcover)
- Author
- I.M. Singer
- Publisher
- Springer-Verlag New York Inc., New York, NY
- Publication year
- 1976
- Condition
- new
- Binding
- Hardcover
- Language
- English
- ISBN 10
- 0387902023
- ISBN 13
- 9780387902029
- Edition
- 1st Edition
- Series
- Book 151 of 170: Undergraduate Texts in Mathematics
"Synopsis" may belong to another edition of this title.
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