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課程名稱 |
微分幾何一
Differential Geometry (Ⅰ) |
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開課學期 |
105-1 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
馬梓銘 |
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課號 |
MATH7301 |
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課程識別碼 |
221 U2930 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期三9(16:30~17:20)星期五3,4(10:20~12:10) |
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上課地點 |
天數305天數305 |
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備註 |
總人數上限：30人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1051MATH7301_ |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
This is the first semester of an one year course on differential geometry. We will learn about the essential foundations for differential topology and geometry. Knowledge from Calculus and Linear algebra will be integrated to study geometry. |
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課程目標 |
We will cover the following topics in this semester :
1. Differentiable manifolds, tangent spaces, vector fields, differential forms and deRham cohomology, tensors, Frobenius's theorem, stoke's theorem.
2. Riemannian manifolds, Levi-Civita connection, curvature tensors, geodesics, exponential maps, Gauss Lemma.
3. Principle G-bundles and Vector bundles, connections, Chern classes. |
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課程要求 |
待補 |
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預期每週課後學習時數 |
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Office Hours |
備註： Office hours: Wednesday 10, or by appointment, at Astro-Math Rm 404 |
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指定閱讀 |
待補 |
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參考書目 |
1. Clifford Taubes - Differential geometry. Bundles, connections, metrics and curvature.
2. Frank Warner - Foundations of differentiable manifolds and Lie groups
3. Raoul Bott and Loring Tu - Differential forms in algebraic topology.
4. S. S. Chern, W. H. Chen and K. S. Lam - Lectures on Differential Geometry |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Homework |
25% |
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2. |
Midterm |
35% |
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3. |
Final |
40% |
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