課程資訊
課程名稱
微分幾何一
Differential Geometry (Ⅰ) 
開課學期
100-1 
授課對象
理學院  數學系  
授課教師
王文才 
課號
MATH7301 
課程識別碼
221 U2930 
班次
 
學分
全/半年
半年 
必/選修
選修 
上課時間
星期三8(15:30~16:20)星期五3,4(10:20~12:10) 
上課地點
天數305天數305 
備註
研究所數學組基礎課。
總人數上限:30人 
 
課程簡介影片
 
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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, some highlights to be covered are the Gauss-Bonnet theorem, applications of second variational formula, and a sphere theorem.
 

課程目標
Provide an essential foundation in differential geometry for all students, and open a way to pursue work or research in geometry. 
課程要求
Advanced calculus  
預期每週課後學習時數
 
Office Hours
 
參考書目
A Comprehensive Introduction to Differential Geometry, vol. 1, M. Spivak Riemannian Geometry, 3rd edition, P. Petersen, Springer-Verlag  
指定閱讀
Textbook: Riemannian Geometry, M. do Carmo, Birkhäuser 1992 ISBN 3-7643-3490-8 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
作業 
70% 
 
2. 
報告 
10% 
 
3. 
考試 
20% 
 
 
課程進度
週次
日期
單元主題