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課程名稱 |
代數二
Algebra(Ⅱ) |
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開課學期 |
99-2 |
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授課對象 |
理學院 數學系 |
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授課教師 |
林惠雯 |
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課號 |
MATH7106 |
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課程識別碼 |
221 U3840 |
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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 |
星期一3,4(10:20~12:10)星期四7,8(14:20~16:20) |
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上課地點 |
天數305天數305 |
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備註 |
研究所數學組基礎課。
總人數上限：40人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/992alg2 |
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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 |
1. Field theory (II):
Transcendental extensions; purely inseparable extensions; infinite Galois theory; calculations of Galois groups.
2. Module theory:
Tensor product; free, projective, injective and flat modules; symmetric and exterior algebras; modules over PID.
3. Introduction to the representation theory of finite groups:
Wedderburn's structure theorem; character theory; Burnside's theorem, the theory of induced characters. |
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課程目標 |
We would like to provide a solid foundation for students who are interested in advanced studies in the fields related to algebra, such as algebraic number theory, algebraic geometry and representation theory. |
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課程要求 |
Grading scheme:
1. Homework 30%
2. Midterm 35%
3. Final Examination 35%
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預期每週課後學習時數 |
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Office Hours |
另約時間 |
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指定閱讀 |
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參考書目 |
Dummit-Foote:Abstract Algebra |
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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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第1週 |
2/21,2/24 |
Transcendental extensions(I)/transcendental extensions(II) & purely inseparable extensions (I) |
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第2週 |
2/28,3/03 |
和平紀念日/purely inseparable extensions (II) |
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第3週 |
3/07,3/10 |
Introduction to infinite Galois theory/Projective limit & 助教習題課 |
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第4週 |
3/14,3/17 |
Krull topology and the fundamental theorem/Hilbert theorem 90 & 助教習題課 |
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第5週 |
3/21,3/24 |
Galois resolvent/Hilbert's theorem for the existence of polynomials with S_n as Galois groups & 助教習題課 |
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第6週 |
3/28,3/31 |
Preliminary for modules/free modules & 助教習題課 |
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第7週 |
4/04,4/07 |
春假/tensor product |
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第8週 |
4/11,4/14 |
Exact sequences and projective modules/injective modules |
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第9週 |
4/18,4/21 |
Categories and functors & 助教習題課/期中考 |
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第10週 |
4/25,4/28 |
Flat modules/tensor algebras |
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第11週 |
5/02,5/05 |
Symmetric and exterior algebras(I)/Symmetric and exterior algebras(II) & 助教習題課 |
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第12週 |
5/09,5/12 |
Matrices over PID/modules over PID |
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第13週 |
5/16,5/19 |
Generalities on linear representations/Semisimple rings & 助教習題課 |
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第14週 |
5/23,5/26 |
Wedderburn's structure theorem/Character theory(I) |
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第15週 |
5/30,6/02 |
Character theory(II)/Burnside's theorem & 助教習題課 |
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第16週 |
6/06,6/09 |
端午節/Induced characters (I) |
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第17週 |
6/13,6/16 |
Induced characters (II)/Applications & 助教習題課 |
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