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課程名稱 |
代數二
Algebra (Ⅱ) |
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開課學期 |
100-2 |
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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 |
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。先修知識:代數導論。
總人數上限：30人
外系人數限制：5人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1002algebra2 |
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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 theorem; character theory; theorems of Burnside and Hall. |
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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 |
建議先修:Undergraduate algebra, including Sylow theorems and group actions, Galois theory, and Algebra 1. |
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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 |
N. Jacobson: Basic Algebra II, 2010
N. Jacobson: Basic Algebra I, 2009
S. Lang, Algebra, GTM Springer, revised 3rd ed. 2002.
M. Artin, Algebra, 2nd ed. 2011, Prentice Hall.
A. Cox, J. Little, and O'shea: Ideals, Varieties, and Algorithms, 2nd. ed. Springer. |
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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. |
Mid-Term |
25% |
6 hours open book test |
2. |
Homeworks |
25% |
To be graded by the assistant |
3. |
Oral Presentations |
25% |
Individual projects |
4. |
Final |
25% |
6 hours open book test |
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