基本素養 Basic Literacy無
課程概述 Course Description這是微分幾何導論的後續課程。課程會講授微分幾何的一些更進階和深入的內容。其中涉及的主題可以包括流形上的微積分、黎曼流形、複流形、辛幾何、纖維叢、李群跟微分拓撲。這個課程的目標是讓學生對現代微分幾何及相關領域的研究有一個較全面的理解，從而幫助發展研究興趣。
This is a sequel to the course "Introduction to differential geometry". We will cover more advanced and specific topics in various aspects of differential geometry. The list of topics may include calculus on manifolds, Riemannian manifolds, complex manifolds, symplectic geometry, fiber bundles, Lie groups, and differential topology. It will enable students to have a comprehensive view on the modern development of differential geometry and its related branches.
課程學習目標 Course Objectives
課程進度 Course Outline
|週次 Week||進度說明 Progress Description|
|2||Tensors, Manifolds, and Vector Bundles|
|3||Definitions and Examples of Riemannian Metrics|
|7||Geodesics and Distance|
|8||Geodesics and Distance|
|13||The Gauss–Bonnet Theorem|
|16||Curvature and Topology|
|17||Curvature and Topology|
有關課程其他調查 Other Surveys of Courses1.本課程是否規劃業界教師參與教學或演講? 否
Is there any industry specialist invited in this course? How many times? No
Are there any internships involved in the course? How many hours? No
Is this course recognized as an academic ethics course? In the course how many hours are regarding academic ethics topics?
Is this course recognized as a Community engagement and Service learning course? Which community will be engaged?