《基礎拓撲和幾何講義》是世界圖書出版公司出版的圖書。
基本介紹
- 書名：基礎拓撲和幾何講義
- 作者：(美國)辛格 (Singer.I.M)
- 原版名稱：Lecture Notes on Elementary Topology and Geometry
- ISBN：9787506292818
- 頁數：232頁
- 出版社：世界圖書出版公司
- 出版時間：2009年3月1日
- 開本：24
圖書信息,作者簡介,內容簡介,目錄,
圖書信息
出版社: 世界圖書出版公司; 第1版 (2009年3月1日)
外文書名: Lecture Notes on Elementary Topology and Geometry
平裝: 232頁
正文語種: 英語
開本: 24
ISBN: 9787506292818
條形碼: 9787506292818
尺寸: 22 x 14.8 x 1.6 cm
重量: 322 g
作者簡介
作者：(美國)辛格 (Singer.I.M)
內容簡介
《基礎拓撲和幾何講義》內容為：At the present time, the average undergraduate mathematics major findsmathematics heavily compartmentalized. After the calculus, he takes a coursein analysis and a course in algebra. Depending upon his interests （or those ofhis department）, he takes courses in special topics. If he is exposed to topology,it is usually straightforward point set topology; if he is exposed to geometry, it is usually classical differential geometry.
目錄
Chapter 1 Some point set topology
1.1 Naive set theory
1.2 Topological spaces
1.3 Connected and compact spaces
1.4 Continuous functions
1.5 Product spaces
1.6 The Tychonoff theorem
Chapter 2 More point set topology
2.1 Separation axioms
2.2 Separation by continuous functions
2.3 More separability
2.4 Complete metric spaces
2.5 Applications
Chapter 3 Fundamental group and covering spaces
3.1 Homotopy
3.2 Fundamental group
3.3 Covering spaces
Chapter 4 Simplicial complexes
4.1 Geometry of simplicial complexes
4.2 Baryccntric subdivisions
4.3 Simplicial approximation theorem
4.4 Fundamental group of a simplicial complex
Chapter 5 Manifolds
5.1 Differentiable manifolds
5.2 Differential forms
5.3 Miscellaneous facts
Chapter 6 Homology theory and the De Rham theory
6.1 Simplicial homology
6.2 Do Rham's theorem
Chapter 7 Intrinsic Riemannian geometry of surfaces
7.1 Parallel translation and connections
7.2 Structural equations and curvature
7.3 Interpretation of curvature
7.4 Geodesic coordinate systems
7.5 Isometrics and spaces of constant curvature
Chapter 8 Imbedded manifolds in Ra
Bibliography
Index
