課程資訊
 課程名稱 微分幾何一Differential Geometry (Ⅰ) 開課學期 110-1 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302天數302 備註 總人數上限：40人 Ceiba 課程網頁 http://ceiba.ntu.edu.tw/1101MATH7301_ 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 Hirsch: Differential Topology. Schoen and Yau: Lectures on Differential Geometry. Milnor: Morse Theory. 指定閱讀 待補 評量方式(僅供參考)
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