課程名稱 |
代數拓樸導論 Introduction to Algebraic Topology |
開課學期 |
109-2 |
授課對象 |
理學院 數學研究所 |
授課教師 |
于 靖 |
課號 |
MATH5253 |
課程識別碼 |
221 U8920 |
班次 |
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學分 |
3.0 |
全/半年 |
半年 |
必/選修 |
選修 |
上課時間 |
星期三1,2,5(8:10~13:10) |
上課地點 |
天數302 |
備註 |
總人數上限:30人 |
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1092MATH5253_algebra |
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 |
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 |
Fundamental Group, Covering Spaces, Covering Trans, Homology(Betti), Cohomology, de Rham cohomology, Differential Form, Eilenberg-MacLane Spaces, Homotopy Groups, Spheres, Graphs, Surfaces, Galois Theory. |
課程目標 |
Introduction to algebraic topology, fundamental groups and covering spaces, Homotopy Group, Homology functions ad cohomology functions, Cohomology in terms of differential forms, Sheaf cohomology, applications of algebraic topology to other fields of Mathematics. |
課程要求 |
Linear Algebra, Algebra, Analysis, Complex Analysis. |
預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
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參考書目 |
Algebraic Topology, an Introduction by W. Massey GTM; Algebraic Topology, A. Hatcher, 2001, Cambridge.U.Press.; Differential Forms on Algebraic Topology, R. Bott, L. W. Tu, GTM. |
評量方式 (僅供參考) |
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週次 |
日期 |
單元主題 |
Week 1 |
2/24 |
Category |
Week 2 |
3/03 |
Homotopy, Universal objects |
Week 3 |
3/10 |
Fundamental Groups, Functor |
Week 4 |
3/17 |
CW Complexes, Van Kampen |
Week 5 |
3/24 |
Homology, Delta-Complexes |
Week 6 |
3/31 |
Homology Theory, Covering spaces |
Week 7 |
4/07 |
Algebraic Homotopy, Relative Cohomology, Lifting |
Week 8 |
4/14 |
Exact sequence, Action of the Fundamental Groups |
Week 9 |
4/21 |
Barycentric subdivision, Universal Covering Spaces |
Week 11 |
5/05 |
Mayer-Vietoris Sequences, Excision |
Week 12 |
5/12 |
Degree, Cellular Homology |
Week 13 |
5/19 |
Coefficients for Homology, Cohomology, Cochain Complexex |
Week 14 |
5/26 |
Cohomology, Axioms, Naturally, Cellular boundary maps. |
Week 15 |
6/02 |
Cup Product, Cross Product, Cohomology rings |
Week 16 |
06/09 |
Cohomology computations, Kunneth Theorem |
Week 17 |
6/16 |
Poincare Duality, Orientation, Zeta Functions |
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