Lecture Notes on Elementary Topology and Geometry

Lecture Notes on Elementary Topology and Geometry

English | ISBN: 0387902023 | | 240 Pages | PDF | 8 MB

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.



[Fast Download] Lecture Notes on Elementary Topology and Geometry

Related eBooks:
Digital Signal Processing: System Analysis and Design
Ultra Wideband Signals and Systems in Communication Engineering
Conceptual Digital Signal Processing with MATLAB
Tracking Differentiator Algorithms
Tensors and the Clifford Algebra
Audio Signal Processing for Next-Generation Multimedia Communication Systems
Compressed Sensing with Side Information on the Feasible Region
Sustainable Green Technologies for Environmental Management
Principles of Digital Transmission: With Wireless Applications
Electroporation Protocols: Microorganism, Mammalian System, and Nanodevice Ed 3
Problems of High Altitude Medicine and Biology
Synthesis and Optimization of DSP Algorithms (Кузщые)
Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.