书目名称 | Lecture Notes on Elementary Topology and Geometry | 编辑 | I. M. Singer,J. A. Thorpe | 视频video | http://file.papertrans.cn/584/583420/583420.mp4 | 丛书名称 | Undergraduate Texts in Mathematics | 图书封面 |  | 描述 | 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 exam | 出版日期 | Textbook 1967 | 关键词 | Algebraische Topologie; CON_D030; Differentialgeometrie; Geometry; Topologie; Topology | 版次 | 1 | doi | https://doi.org/10.1007/978-1-4615-7347-0 | isbn_softcover | 978-1-4615-7349-4 | isbn_ebook | 978-1-4615-7347-0Series ISSN 0172-6056 Series E-ISSN 2197-5604 | issn_series | 0172-6056 | copyright | I. M. Singer and John A. Thorpe 1967 |
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