課程資訊
課程名稱
微分幾何一
Differential Geometry (Ⅰ) 
開課學期
108-1 
授課對象
理學院  數學研究所  
授課教師
蔡宜洵 
課號
MATH7301 
課程識別碼
221 U2930 
班次
 
學分
3.0 
全/半年
半年 
必/選修
選修 
上課時間
星期三9(16:30~17:20)星期五3,4(10:20~12:10) 
上課地點
天數101天數102 
備註
總人數上限:80人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1081MATH7301_ 
課程簡介影片
 
核心能力關聯
核心能力與課程規劃關聯圖
課程大綱
為確保您我的權利,請尊重智慧財產權及不得非法影印
課程概述

Modern differential geometry encompasses a wide array of techniques and results. Beginning with an overview of smooth differential manifolds (including coordinates, vector fields, tangent bundles, differential forms, tensors) we will then discuss Riemannian manifolds (those for which metric notions such as length, volume, etc. are defined), connections (leading to Hessian and Laplacian), exponential map, geodesics, submanifolds, and curvature.
A significant part of the remainder of the course will study the effects curvature has on geometry and topology. In particular, this includes the linear theory of de Rham theorem and Hodge theory of harmonic forms, Bochner principles, and the non-linear theory on applications of second variational formula for geodesics and minimal sub-manifolds. 

課程目標
Provide an essential foundation in differential geometry for students aiming at using it in various kind of further applications in mathematics or modern sciences, and open a way to pursue work or research in modern geometry. 
課程要求
Undergraduate required courses: Linear algebra, advanced calculus, algebra, geometry, complex analysis, introduction to ODE, introduction to PDE.
Optional (not absolutely required): Topology, algebraic topology. 
預期每週課後學習時數
 
Office Hours
 
參考書目
1. Jurgen, Jost: Riemannian Geometry and Geometric Analysis.
2. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, I and II.
3. Schoen and Yau: Lectures on Differential Geometry.
4. Y. Matsushima, Differentiable Manifolds.
5. M. Spivak : A Comprehensive Introduction to Differential Geometry, I-II. 
指定閱讀
待補 
評量方式
(僅供參考)
   
課程進度
週次
日期
單元主題