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課程資訊

課程名稱	代數拓樸導論 Introduction to Algebraic Topology
開課學期	109-2
授課對象	理學院數學系
授課教師	于靖
課號	MATH5253
課程識別碼	221 U8920
班次
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
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
Office Hours
指定閱讀
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)

課程進度

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