Lecture Notes on Elementary Topology and Geometry is popular PDF and ePub book, written by I.M. Singer in 2015-05-28, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Lecture Notes on Elementary Topology and Geometry can be Read Online from any device for your convenience.
Lecture Notes on Elementary Topology and Geometry Book PDF Summary
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.
Detail Book of Lecture Notes on Elementary Topology and Geometry PDF
- Author : I.M. Singer
- Release : 28 May 2015
- Publisher : Springer
- ISBN : 9781461573470
- Genre : Mathematics
- Total Page : 240 pages
- Language : English
- PDF File Size : 12,8 Mb
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