11320MATH559000 同調代數 Homological Algebra
- 任課教師: 廖軒毅 (Hsuan-Yi Liao)
- Email: hyliao@math.nthu.edu.tw
- Office: GEN III 綜三 607
- 上課時間(Time): Thursday 13:20 - 14:10, 14:20 - 15:10, 15:20 - 16:10
- 上課教室(Room): GEN III 綜三 631
- Office hour: Tuesday 13:10-14:10 or by appointment
- 課程講義(Lecture notes): 講義連結
- 參考書目(References):
- Cartan and Eilenberg; Homological algebra.
- Gelfand and Manin; Methods of Homological Algebra.
- Manetti; Lie Methods in Deformation Theory.
- Rotman; An Introduction to Homological Algebra.
- Weibel; An Introduction to Homological Algebra.
- 本課程主要會介紹並討論 (co)chain complex 相關的代數問題
- 問題意見箱
- 本課程無涉及AI使用
成績考核 (Evaluation)
1 open-book exam (50分) + 1 presentation (50分)
- 考試:
- Time: 13:30-16:00 (150 minutes), 5/1(四)
- Room: GEN III 綜三 631
- 可以用書或筆記
- 不可以用電子產品
- 學生於期中、期末考試不得請假。但因公、急病、分娩、近親喪亡、臨時發生不可抗力或不可歸責於當事人之因素，應檢附相關證明文件經任課教師同意。 詳情請見國立清華大學學生請假辦法第四條。
- 報告:
- 口頭報告預計在最後幾週，上課時間進行。
- 主題需先跟我登記，不能跟別的同學重複(先登記優先，需於5/21前登記完成)，跟同調代數有關即可。
- 口頭報告預計綠影，用youtube留言方式讓同學間互相討論(留言最後一行寫學號)，適當留言會提高成績。
- 另外需於 eLearn 繳交口頭報告時用到的投影片或筆記。
- 主題登記連結
- 目前登記結果
- 額外加分：
- 成績會在eLearn上公布
| 總分 |
90~∞ |
80~89 |
70~79 |
60~69 |
1~59 |
0 |
| 成績 |
A+ |
A |
B |
C |
D |
X |
相關連結 (Links)
教學進度 (Schedule)
下表隨時間更新。
- Week1(2/20): tensor product of modules, (co)chain complexes of modules (board-week1)
- Week2(2/27): homologies, chain homotopies, exact sequences (board-week2)
- Week3(3/6): constructions of chain complexes (board-week3)
- Week4(3/13): chain complexes in an abelian category, double complexes (board-week4)
- Week5(3/20): projective resolutions (board-week5)
- Week6( 3/27): injective resolutions (board-week6)
- Week7: 4/3 is a holiday
- Week8(4/10): derived functors (board-week8)
- Week9(4/17): derived functors, adjoint functors, acyclicity lemmas for double complexes (board-week9)
- Week10(4/24): Tor and Ext (board-week10)
- Week11(5/1): exam
- Week12(5/8): Ext, derived categories (board-week12)
- Week13(5/15): derived categories, distinguished triangles (board-week13)
- Week14(5/22): derived functors and derived categories (board-week14)
- Week15(5/29): presentation
- Week16(6/5): presentation (board-week16)
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