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課程名稱 |
黎曼面導論
Introduction to Riemann Surfaces |
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開課學期 |
101-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
齊震宇 |
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課號 |
MATH5344 |
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課程識別碼 |
221 U6090 |
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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 |
星期一7,8(14:20~16:20)星期四3,4(10:20~12:10) |
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上課地點 |
新數101新數101 |
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備註 |
3/28暫至天數304教室上課。3/25停課乙次(擇期補課)。
總人數上限：20人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1012riemann |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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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 |
0. Elements of elliptic functions
1. Meromorphic functions and forms on Riemann surfaces
2. Harmonic functions with singularities on Riemann surfaces
3. Construction of holomorphic 1-forms on Riemann surfaces
4. The Riemann-Roch theorem
5. The Abel theorem
6. Jacobi inversion and Abel-Jacobi maps
7. Theta functions and theta divisors
8. Torelli theorem
9. Uniformization theorem
10. (If time permits.)Outline of Moduli spaces and Teichmuler spaces |
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課程目標 |
To introduce the theory of Riemann surfaces in a classical manner and to emphasize the close relation between complex analysis, PDEs, and geometry/topology. |
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課程要求 |
1. General Topology (topological spaces, product topology, quotient topology and quotient maps, continuity, compactness, connectedness, homotopy, etc.)
2. Differentiable manifolds (differential forms, Stokes theorem)
3. Complex analysis (cf. [1], [4], and [6])
4. Fundamental groups, covering spaces, and classification of closed surfaces (cf. [3]) |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
Farkas and Kra, Riemann Surfaces, 2nd edition
Siegel, Topics in Complex Function Theory, Vol. I |
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參考書目 |
[1] Ahlfors, Complex Analysis
[2] Farkas and Kra, Riemann Surfaces, 2nd edition (GTM 71)
[3] Fulton, Algebraic Topology (GTM 153)
[4] Kodaira, Complex Analysis
[5] Mumford, Tata Lectures on Theta, Vol. I-III.
[6] Nevanlinna and Paatero, Introduction to Complex Analysis
[7] Siegel, Topics in Complex Function Theory, Vol. I-III
[8] Weyl, The Concept of a Riemann Surface |
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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. |
Homeworks |
30% |
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2. |
In-class exams (隨堂測驗) |
40% |
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3. |
Final oral presentation/final exam (期末報告/期末考) |
30% |
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