Lecture Notes on Elementary Topology and Geometry (Undergraduate Texts in Mathematics)

Singer, I.M.; Thorpe, J.A.

ISBN 10: 0387902023 / ISBN 13: 9780387902029

Published by Springer, 1976

About this Item

The item is very worn but is perfectly usable. Signs of wear can include aesthetic issues such as scratches, dents, worn and creased covers, folded page corners and minor liquid stains. All pages and the cover are intact, but the dust cover may be missing. Pages may include moderate to heavy amount of notes and highlighting, but the text is not obscured or unreadable. Page edges may have foxing age related spots and browning . May NOT include discs, access code or other supplemental materials.

Seller Inventory # BVV.0387902023.A

Bibliographic Details

• Title: Lecture Notes on Elementary Topology and Geometry (Undergraduate Texts in Mathematics)
• Publisher: Springer
• Publication Date: 1976
• Language: English
• ISBN 10: 0387902023
• ISBN 13: 9780387902029
• Binding: Hardcover
• Condition: acceptable

About this title

Synopsis

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.