| Lecture Notes on Elementary Topology and Geometry Softcover Repri Edition Contributor(s): Singer, I. M. (Author), Thorpe, J. a. (Author) |
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ISBN: 1461573491 ISBN-13: 9781461573494 Publisher: Springer OUR PRICE: $52.24 Product Type: Paperback - Other Formats Published: July 2012 |
| Additional Information |
| BISAC Categories: - Mathematics | Geometry - General - Mathematics | Topology - General |
| Dewey: 514 |
| Series: Undergraduate Texts in Mathematics |
| Physical Information: 0.51" H x 6.14" W x 9.21" (0.76 lbs) 232 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |