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課程名稱 |
近世代數一
Modern Algebra (Ⅰ) |
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開課學期 |
110-1 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
陳榮凱 |
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課號 |
MATH5001 |
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課程識別碼 |
221 U6140 |
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班次 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
必修 |
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上課時間 |
星期三6,7(13:20~15:10)星期五6,7(13:20~15:10) |
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上課地點 |
天數102天數102 |
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備註 |
總人數上限：30人 |
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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 |
Algebra provides common and powerful language in describing symmetry in all areas of science. This course provides an opportunity to learn the basics of algebra, both commutative and non-commutative, especially to those who did not have them in their undergraduate study and would like to know them as tools or as research topics toward their graduate study. |
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課程目標 |
We will focus on ring theory, module theory and commutative algebra in this semester. The theory of fields, group representation, and Galois theory will be cover in the second semester.
1. Ring Theory
2. Module Theory
3. Commutative Rings and Algebraic Geometry
4. Basic Homological Algebra |
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課程要求 |
待補 |
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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 |
待補 |
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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 2 |
9/21,9/24 |
Rings and Ideals, Homomorphism and Localization |
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Week 3 |
9/28,10/01 |
Factorization in a Ring |
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Week 4 |
10/05,10/08 |
Basics of Modules |
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Week 5 |
10/12,10/15 |
Exact Sequences of Modules, Projective and Injective Modules |
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Week 6 |
10/19,10/22 |
Hom and Tensor Products |
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Week 7 |
10/26,10/29 |
Modules over PID |
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Week 8 |
11/02,11/05 |
Chain Conditions |
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Week 9 |
11/09,11/12 |
Midterm (2021/11/10 Wed.) |
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Week 10 |
11/16,11/19 |
Noetherian Rings and Artinian Rings |
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Week 11 |
11/23,11/26 |
Integral Extensions |
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Week 12 |
11/30,12/03 |
Discrete Valuation Rings and Dedekind Domains |
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Week 13 |
12/07,12/10 |
Spectrum of a Ring and Hilbert's Nullstellensatz |
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Week 14 |
12/14,12/17 |
Complexes and Cohomologies, Homotopic Equivalence and Quasi-isomorphisms |
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Week 15 |
12/21,12/24 |
Injective Resolutions of Complexes |
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Week 16 |
12/28,12/31 |
Functors and Derived Functors |
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Week 17 |
1/04,1/07 |
Final Exam (2022/1/5 Wed.) |
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