搜搜做题作业网自学微分几何需要哪些数学基础
来源：学生作业帮 编辑：搜搜做题作业网作业帮 分类：英语作业 时间：2024/05/27 03:43:40
自学微分几何需要哪些数学基础
我是学力学的,目前研二.已经有线性代数和高等数学的基础,偏微分方程也学过,不过学到不好.想自学微分几何,还要哪些数学基础课啊?
我是学力学的,目前研二.已经有线性代数和高等数学的基础,偏微分方程也学过,不过学到不好.想自学微分几何,还要哪些数学基础课啊?
微分几何,非数学系的线代和微积分很浅,建议自学数学分析,高等代数,注意是数学系的而不是非数学的课本,可以用北大版的高等代数,数学分析可以用复旦版的,但是这些东西对于非数学系有一些难度.
另外,学完这两门之后（注意,一定要学完这两门之后）需要学习的是实变函数,拓扑学,这两门很重要.然后就差不多了
这些是微分几何的相关的英文教材
1.Michael Spivak (1999),A Comprehensive Introduction to Differential Geometry,(5 Volumes),3rd Edition.
2.Manfredo Do Carmo (1976),Differential Geometry of Curves and Surfaces.Prentice Hall.
3.Manfredo Perdigao do Carmo,Francis Flaherty (1994),Riemannian Geometry.
4.John McCleary (1994),Geometry from a Differentiable Viewpoint
5.Ethan D.Bloch (1996),A First Course in Geometric Topology and Differential Geometry
6.Alfred Gray (1998),Modern Differential Geometry of Curves and Surfaces with Mathematica,2nd ed.
另外,学完这两门之后（注意,一定要学完这两门之后）需要学习的是实变函数,拓扑学,这两门很重要.然后就差不多了
这些是微分几何的相关的英文教材
1.Michael Spivak (1999),A Comprehensive Introduction to Differential Geometry,(5 Volumes),3rd Edition.
2.Manfredo Do Carmo (1976),Differential Geometry of Curves and Surfaces.Prentice Hall.
3.Manfredo Perdigao do Carmo,Francis Flaherty (1994),Riemannian Geometry.
4.John McCleary (1994),Geometry from a Differentiable Viewpoint
5.Ethan D.Bloch (1996),A First Course in Geometric Topology and Differential Geometry
6.Alfred Gray (1998),Modern Differential Geometry of Curves and Surfaces with Mathematica,2nd ed.