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課程名稱 |
代數一
Algebra(Honor Program)(Ⅰ) |
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開課學期 |
104-1 |
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授課對象 |
理學院 數學系 |
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授課教師 |
于 靖 |
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課號 |
MATH5178 |
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課程識別碼 |
221 U6520 |
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班次 |
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學分 |
5 |
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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 |
星期一2,3,4(9:10~12:10)星期四8,9(15:30~17:20) |
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上課地點 |
天數305天數101 |
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備註 |
此課程研究生選修不算學分。
限學士班學生
總人數上限：44人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1041MATH5178_ALGEBRA |
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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 |
http://www.math.ntu.edu.tw/courses/super_pages.php?ID=allcourses |
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課程目標 |
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課程要求 |
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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 |
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參考書目 |
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評量方式
(僅供參考) |
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週次 |
日期 |
單元主題 |
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Week 1 |
9/14,9/17 |
Composition laws, Groups, subgroups, Finite groups, Abelian groups, Symmetric groups, Alternating Groups, Cosets, Multiplication Tables, Lattice of subgroups, |
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Week 2 |
9/21,9/24 |
Dihedral groups, Symmetry, General linear groups, Group actions, Lagrange Theorem, Conjugation, Conjugacy Classes, Orbits, Stabilisers, Class Equations, |
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Week 3 |
9/28,10/01 |
Sylow Theorems I, II, III, Classifications of groups of small order, Normal subgroups, Centralisers, Centers, Isomorphisms, Normalisers, p-groups, Direct Products, |
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Week 4 |
10/05,10/08 |
Homomorphisms, Kernels, Images, First Isomorphism Theorem, Structure of finite abelian groups, Quotient Groups, Semi-Direct Products, Simple groups, Hoelder's Program, |
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Week 5 |
10/12,10/15 |
Automorphism Groups, Generators and Relations, Cayley's Theorem, Maximal subgroups, Nilpotent groups, Frattini's argument, Solvable groups, Symmetric groups |
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Week 6 |
10/19,10/22 |
Free groups, Composition series, The Jordan-Hoelder theorem, elementary abelian groups, The 2nd isomorphism theorem, The 3rd isomorphism theorem, Lattices of subgroups |
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Week 7 |
10/26,10/29 |
Rings and homomorphisms, The Chinese reminder theorem |
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