課程名稱 |
代數二 ALGEBRA(Ⅱ) |
開課學期 |
98-2 |
授課對象 |
理學院 數學研究所 |
授課教師 |
陳榮凱 |
課號 |
MATH7106 |
課程識別碼 |
221 U3840 |
班次 |
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學分 |
3 |
全/半年 |
半年 |
必/選修 |
選修 |
上課時間 |
星期一3,4(10:20~12:10)星期四7,8(14:20~16:20) |
上課地點 |
新201新204 |
備註 |
研究所數學組基礎課。 總人數上限:50人 |
Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/982Algebra |
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 |
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 |
Field Theory:
Algebraic extensions.
Galois groups
Cyclotomic extension and cyclic extensions.
Radical extensions.
Transcendental extensions.
Cmooutative Ring Theory:
Integral extensions, Dimension theory, Dedekind Domain, Hilbert's Nullstellensatz.
Some further topics:
a few topics from the follwoing list: Lie groups and Lie algebra, homological algebra, algebraic groups
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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. |
課程要求 |
Grading scheme:
1. Homework 30%
2. Midterm 30%
3. Final Examination 40%
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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 |
1. Hungerford, Algebra, GTM 73 (Textbook)
2. Lang, Algebra, GTM 211
3. Herstein, Noncommutative rings
4. Atiyah, MacDonald, Introduction to commutative algebra
5. Artin, Algebra, Prentice Hall
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參考書目 |
1. Hungerford, Algebra, GTM 73 (Textbook)
2. Lang, Algebra, GTM 211
3. Herstein, Noncommutative rings
4. Atiyah, MacDonald, Introduction to commutative algebra
5. Artin, Algebra, Prentice Hall
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評量方式 (僅供參考) |
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週次 |
日期 |
單元主題 |
Week 1 |
2/22,2/25 |
Field Extensions |
Week 2 |
3/01,3/04 |
Algebraic Closed Fields and Algebraic Closure |
Week 3 |
3/08,3/11 |
Finite Dimensional Galois Extension |
Week 4 |
3/15,3/18 |
Algebraic Galois Extension and Normal Extension |
Week 5 |
3/22,3/25 |
Galois Group of a Polynomial, Cyclotomic Extension |
Week 6 |
3/29,4/01 |
No class this week! |
Week 7 |
4/05,4/08 |
Cyclotomic Extensions |
Week 8 |
4/12,4/15 |
Cyclic Extensions, Radical Extensions |
Week 9 |
4/19,4/22 |
Separable and Purely Inseparable Extensions |
Week 10 |
4/26,4/29 |
Transcendental Extensions |
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