Author Archives: hoxide

2019-秋季 线性代数 MA270

课程信息

  • 时间: 星期一 第3节–第4节(10:00 AM – 11:40AM)、星期四(双周)) 第1节–第2节(8:00AM – 9:40AM)
  • 地点: 下院114 (1-16周)
  • 课本: 上海交通大学数学系,线性代数(第三版),科学出版社,2014
  • MOOC(慕课)地址

分数比例

平时:20%,大作业: 10% 期末:70%

大作业

就线性代数中有意思的定理,例题或相关应用写一份学习报告. 报告长度控制在2面A4纸以内.
12月22日23:59前请将大作业发至邮箱: hoxide@sjtu.edu.cn
邮件标题格式: 2019线性代数大作业-xxxxxxxxx-姓名 (xxxxxxxxx为学号)

答疑时间

课件(ppt)

作业:

  • 作业1, 9月23日交: p41 习题一: 1.2, 1.3, 1.5, 3, 4, 7
  • 作业2, 9月30日交: 习题一: 8.1, 11.1, 12.1, 12.4, 12.5, 12.6, 13.1, 13.3, 19.2, 20.4
  • 作业3, 10月14日交: 习题一: 14.1, 14.3, 14.5, 15, 16, 17
  • 作业4, 10月21日交: 习题二: 6, 7.1, 7.3, 8, 9, 10, 13, 15, 17, 27, 32, 33
  • 作业5, 10月28日交: 习题二: 21.2, 21.7,22.1,22.3, 22.4, 26, 28
  • 作业6, 11月11日交: 习题二: 47, 48, 49, 51.1, 51.3, 51.5, 52, 53, 54 习题三: 1, 3, 4, 6.1, 6.2, 7.1, 8 思考题(不用交) 9
  • 作业7, 11月18日交: 习题三: 17, 19.2, 20.2, 22, 23, 24.1,24.3, 24.5, 25, 26, 27.1, 27.2, 28.2, 33, 35
  • 作业8, 12月02日交: 习题四: 3.1, 3.2, 3.3, 4.1, 4.3, 4.5, 6.1, 6.2, 6.3, 7, 9, 12, 13.2, 17
  • 作业9, 12月09日交: 习题四: 18, 19, 22, 23.1, 24 思考题: 25
  • 作业10, 12月16日交: 习题五: 1.3, 1.4, 1.6, 2, 6, 7, 11, 12, 17.2, 20, 22

2019 春季 代数拓扑

课程信息

习题

  • 3月13日交,选做2题: Chapter 0: 4, 11, 13, 15, 23, 26
  • 3月27日交,选做2题:
    Section 1.1: 14, 15, 16 (f);
    Section 1.2: 6, 7, 8, 14, 19,20, 21;
    Section 1.3: 8, 9, 18, 26, 28, 32

    • 4月17日交, 选做3题:
      Section 2.1: 4, 9, 28, 29, 31
    • 5月29日交, 选做3题:
      Section 3.1: 5, 7, 8, 9
      Section 3.2: 2, 9, 10, 11, 15

期中题目

以下三组题中选做一组, 5月8日交

Section 1.2: 20, Section 2.1: 20, 21, Section 2.2: 26
Section 1.2: 21, Section 2.1: 17 (a), Section 2.2: 36
Section 1.3: 28, Section 2.1: 17 (b), Section 2.2: 40, 42

2019-春季 大学医科数学(A类)[MA093]

课程信息

  • 时间: 星期三 第3节–第4节(10:00 AM – 11:40AM)、星期五 第1节–第2节(8:00AM – 9:40AM)
  • 地点: 东上院201 (1-16周)
  • 课本: 李铮、咸进国(主编),高等数学(生农医药版),上海交通大学出版社,2017

分数比例

平时:10, 期中:30,期末:60

期中考试

  • 时间: 2019-04-24 (第9周星期三) 13:10-15:10
  • 地点: 东中院3-104/105

课件(ppt)

附件

一些Cocalc笔记本:
* Sage演示
* 例 5.1.5 的函数图像

习题

  • 3月8号交, 习题5: 1.2, 2.3, 3.2, 4.2, 5.3, 6, 7.3, 7.4
  • 3月15号交, 习题5: 10, 12.2, 13, 16, 18, 19.1, 20.3, 21
  • 3月22号交, 习题5: 23, 24.1, 25, 26
  • 3月29号交, 习题5: 27.1, 29.2 ,30.3, 31.2, 31.3, 33
  • 4月3号交, 习题6: 1, 5, 7, 8
  • 4月19号交, 习题6: 12, 14, 17, 19, 20, 22, 23, 24, 25
  • 4月26号交, 习题6: 29, 30, 32, 34, 36, 39
  • 5月5号, 不交作业
  • 5月10号,习题6: 40, 44, 45, 46, 47
  • 5月17号交,习题6: 48, 49, 50,习题7: 1.(2), 2.(1),(2)(4)
  • 5月24号交, 习题7: 3.(2), 4, 9,10, 11,12
  • 5月31号交, 习题7: 13, 14.(2), 15.(1), 18, 19
  • 6月12号交(第16周 周三) , 习题7: 23, 24.(2), 25.(4), 26, 27.(2)

2018-春季 大学医科数学(A类)[MA093]

课程信息

  • 时间: 星期一 第1节–第2节(8:00AM-9:40AM)、星期三 第3节–第4节(10:00AM-11:40AM)
  • 地点: 中院413 (1-16周)
  • 课本: 李铮、咸进国(主编),高等数学(生农医药版),上海交通大学出版社,2017

课件(ppt)

附件

一些Cocalc笔记本:
* Sage演示

习题

  • 3月7号交, 习题5: 1.2, 3.2, 4.2, 6, 7.4, 10, 18, 20.3, 21.
  • 3月14号交, 习题5: 25, 26, 27.1, 29,30.
  • 3月21号交, 习题5: 31, 33
  • 3月28号交, 习题6: 1, 5, 7, 8
  • 4月4号交, 习题6: 9, 10, 12, 13, 16
  • 4月11号交, 习题6: 17, 18, 19, 20, 22, 23, 24, 25
  • 4月18号交, 习题6: 26, 27, 28, 29, 30, 32, 36
  • 4月25号, 不交作业
  • 5月2号交, 习题6: 33, 34, 39, 40
  • 5月9号, 不交作业
  • 5月16号交, 习题6: 44, 45, 46, 47
  • 5月23号交, 习题6: 48, 49, 50
  • 5月30号交, 习题7: 1.(2), 2.(1),(2)(4), 3.(2), 4
  • 6月6号交, 习题7: 10, 12, 14.(2), 15.(1), 18, 19
  • 6月13号交, 习题7: 23, 24.(2), 25.(4), 26, 27.(2)

2018-Spring Representations of Finite group and affine Hecke algebra

For 2018 Spring semester, from 28 Feb 2018 to the end of the semester.
Time: Wednesday afternoon 13:00-15:30, Week 1-17.
Venue: School of Mathematics SJTU, Room-1106.

We plan to read the following two papers.
1. Pierre Deligne and George Lusztig, Representations of Reductive Groups Over Finite Fields
2. David Kazhdan, George Lusztig, Proof of the Deligne-Langlands conjecture for Hecke algebras

The tasks are divied as the following:

Speackers Deligne-Lusztig’s paper
Ma Jiajun Introduction, Section 1-2
Chen Miaofen Section 3-4
TBA Section 5
TBA Section 6-7
TBA Section 8-9
TBA Section 10-11
Speackers Kazhdan-Lusztig’s paper
TBA TBA

2017-Fall Minimal length elements

For 2017 Fall semester, from 11-Sep 2017 to 21-Nov 2017, the time and venue are as the following:
Time: Wednesday afternoon 13:00-15:00.
Venue: School of Mathematics SJTU, Room-1106.

Time/speaker VenueTitle/Abstract
Sep 13, 2017,
13:00-15:00
Room-1106Introduction on conjugacy classes of finite coxeter groups.
Ma Jia-JunWe will discuss the geometric interpretation of the length function of finite Coxeter groups.
Sep 20, 2017, 13:00-15:00/Ma Jia-JunRoom-1106Geometric interpretation of the length function. (cont.)
Sep 27, 2017, 14:00-15:00/Ma Jia-JunRoom-1106Proof of the main theorem on minimal length elements (for finite Coxeter group)
Oct 4, 2017Cancelled due to the national day holiday.
Oct 11, 2017Cancelled due to an event of the department.
Oct 18, 13:00-15:00/Zhang GuanglianRoom-1106Elliptic elements in Weyl groups
Oct 25, 13:00-15:00/Zhang GuanglianRoom-1106Good elements in Weyl groups
Nov 1, 13:00-15:00/Qin FanRoom-1106Introduction to affine Weyl groups.
Nov 8, 13:00-15:00/Qin FanRoom-1106minimal length element in affine groups.
Nov 15, 13:00-15:00/Qin FanRoom-1106minimal length element in affine groups (cont.)
Nov 22Cancelled
Nov 29 13:00-15:00/Chen MiaofenRoom-1106Straight conjugacy class
Dec 6 13:00-15:00/Chen MiaofenRoom-1106Straight conjugacy class and its relation to other topics.
Dec 13: 13:00-15:00/ Ma Jia-JunRoom-1106Classification of nice elements.
Dec 20 10:00-12:00/
Ma Jia-Jun
Room-1106Cocenter of an affine Hecke algebra.

2017-Spring Springer theory

For 2017 Spring semester, from 21-Mar 2017 to 27-June 2017, the time and venue are as the following:
Time: Tuesday noon 12:00-13:30. (the time slot is updated) 
Venue: School of Mathematics SJTU, Room-1106.

TimeVenueTitle/Abstract
Mar 21, 2017,
18:30-20:00
Room-1106Introduction to Springer theory
This is the first talk of my proposed seminar on Weyl group, Springer theory, Hecke algebra and related topics. As an orientation, I will first explain the content of Springer correspondence. Then I will briefly review the basic idea of the constructions of the Springer correspondence. In the end, I will discuss some relationships of the Springer theory with other fields, such as combinatorics and representation theory of reductive groups. If time permits, I will also discuss the generalized Springer correspondence.
Mar 28, 2017Canceled
April 4, 2017Canceled due to Qingming Festival
April 11, 2017,
12:00-13:30
Room-1106A proof of Springer correspondence by Chriss-Ginzburg, (I)
I will present a proof of the Springer correspondence following Chriss-Ginzburg's book "Representation Theory and Complex Geometry" in the next two or three talks. In this talk, I plan to discuss the geometry of the flag variety and the Steinberg variety.
April 18, 2017,
12:00-13:30
Room-1106
Continue the discussion on Ghriss-Ginzburg's book.
April 25, 2017,
12:00-13:30
Room-1106
Continue the discussion on Ghriss-Ginzburg's book.
May 2 , 2017,
12:00-13:30
Canceled
May 9 , 2017,
12:00-13:30
Room-1106Discussion on Ghriss-Ginzburg's book: Borel-Moore homology
May 16 , 2017,
12:00-13:30
Room-1106Discussion on Ghriss-Ginzburg's book: Borel-Moore homology
May 23 , 2017,
12:00-13:30
Room-1106Discussion on Ghriss-Ginzburg's book.
May 30 , 2017,
12:00-13:30
Canceled due to Duanwu Festival(Dragon Boat Festival)
Jun 6 , 2017,
12:00-13:30
Discussion on Ghriss-Ginzburg's book.
Jun 13 , 2017,
12:00-13:30
Discussion on Ghriss-Ginzburg's book.
Jun 20 , 2017,
12:00-13:30
Discussion on Ghriss-Ginzburg's book. Finished Chapter 3

2018 春季 代数拓扑

课程信息

习题

  • 3月13日交,选做2题: Chapter 0: 4, 11, 13, 15, 23,26
  • 3月27日交,选做2题:
    Section 1.1: 14, 15;
    Section 1.2: 6, 7, 8, 14, 19,20, 21;
    Section 1.3: 8, 9, 18, 26, 28, 32
  • 4月24日交, 选做2题:
    Section 2.1: 4, 9, 28
  • 5月22日交, 选做2题:
    Section 3.1: 5, 7, 8, 9

期中考试

以下三组题中选做一组, 5月15日交
1. Section 1.1: 6, Section 2.1: 20, 21, Section 2.2: 26
2. Section 1.1: 17, Section 2.1: 17 (a), Section 2.2: 38, 39
3. Section 1.1: 20, Section 2.1: 17 (b), Section 2.2: 40, 42

* 思考题(题不用交):

  • Chapter 2
    Section 2.1: 11,12,13,15,16,22,31
    Section 2.2: 7, 8, 12, 15, 20, 21, 22, 23, 36
  • Chapter 3
    Section 3.2: 11, 15
    Section 3.3: 8, 9, 10, 11, 20, 22, 25

2017 秋季 代数数论

主要内容,简要介绍类域论的知识。

上课时间:第1周到第8周,周一11-12节和周三9-10节。 地点: 上院306

课本:

参考书:

  1. [S] Serre, A course in Arithmetic
  2. [SL]Serre, Local Fields
  3. [SD] Swinnerton-Dyer, A Brief Guide to Algebraic Number Theory
  4. [N] Neukirch, Algebraic Number Theory
  5. Weil, Basic Number Theory
  6. [AM] Atiyah and MacDonald, Introduction to Commutative Algebra
  7. [CF] Algebraic Number Theory, Proceedings of an Instructional Conference Organized by the London Mathematical Society
  8. [M] J.S. Milne, Class Field Theory
  9. [A] Michael Artin on noncommutative ring theory
  10. [FD] Farb and Dennis, Noncommutative Algebra, Chapter 4: The Brauer Group

思考题:

  • 第二章, 问题 4,12,习题 2.2
  • 第三章, 问题 3,习题 3.4

期末报告备选问题:

  1. Gamma函数与Sin函数的乘积公式. Erica Chan, The Sine Product Formula and the Gamma Function
  2. 复数域上的椭圆曲线 J.S. Milne, Elliptic Curves; Silverman, The Arithmetic of Elliptic Curves, An online lecture note
  3. Galois理论的回顾, Trace和Norm [K] 附录, [N] Section I.2
  4. 分圆域(Galois群,整数环,理想的分解等) [K] 相关章节, [N] Section I.10 [SD] Section 13
  5. 整闭整环及其扩张. [AM] Chapter 5, [N] Section I.2
  6. 局部化,局部环. [N] Section I.11
  7. Noether环,Artin环及例子 [AM] Chapter 6-8
  8. Dedekind环的定义,基本性质及例子. [N] Section I.3 [AM] Chapter 9 [CF] Section I.2
  9. 共轭差积与判别式 (Difference and Discriminant) [N] III.2 [K] 6.3(b)
  10. 理想及分式理想的分解 [N] Section I.3 [AM] Chapter 4, Chapter 9 [CF] Section I.2
  11. 逆向极限, pro-finite group及在Galois理论中的应用. [CF] Section V.1
  12. 完备局部域, Hensel引理及p-aidc域的乘法群结构. [S] Chapter 2 [N] Proposition II.5.7
  13. 不变测度及命题6.81,6.82的证明. [K] 6.4(g)节 [SD] 附录
  14. Pontrjagin对偶, 例子,及命题6.79的证明. [K] 6.4(h)节.
  15. 中心单代数及Brauer群的定义 [A] [M] Chapter 4 [SL] X.5, [FD]
  16. Brauer群的例子(有限域,局部域及inv映射) [A] [M] Chapter 4, [SL] X.5 XII, [FD]
  17. 关于素数分布的定理 [K] 第七章相关部分
  18. L-函数的函数方程 [K] 第七章相关部分
  19. 类域论在函数域情况下的结果. [K] 课本相关内容 [N] Section I.14

期末报告   地点:数学楼1106,2017年12月17日
题目及时间:

序号 报告时间 姓名 题目
1 09:00 — 09:30 岳宸阳  Gamma函数与Sin函数的乘积公式
2 09:30 — 10:00 阚晓鹏 复数域上的椭圆曲线 J.S. Milne, Elliptic Curves; Silverman, The Arithmetic of Elliptic Curves
3 10:00 — 10:30 梁乐 Galois理论的回顾, Trace和Norm [K] 附录, [N] Section I.2
4 10:30 — 11:00 肖凌 分圆域(Galois群,整数环,理想的分解等) [K] 相关章节, [N] Section I.10 [SD] Section 13
5 11:00 — 11:30 侯家齐 整闭整环及其扩张. [AM] Chapter 5, [N] Section I.2
6 11:30 — 12:00 钟宇涛 Noether环,Artin环及例子 [AM] Chapter 6-8
7 13:00 — 13:30 吴怡婕 Dedekind环的定义,基本性质及例子. [N] Section I.3 [AM] Chapter 9 [CF] Section I.2
8 13:30 — 14:00 吴斌香 共轭差积与判别式 (Difference and Discriminant) [N] III.2 [K] 6.3(b)
9 14:00 — 14:30 许逸凡 理想及分式理想的分解 [N] Section I.3 [AM] Chapter 4, Chapter 9 [CF] Section I.2
10 14:30 — 15:00 张正鑫 逆向极限, pro-finite group及在Galois理论中的应用. [CF] Section V.1
11 15:00 — 15:30 万仁星 完备局部域, Hensel引理及p-aidc域的乘法群结构. [S] Chapter 2 [N] Proposition II.5.7
12 15:30 — 16:00 张亚智 不变测度及命题6.81,6.82的证明. [K] 6.4(g)节 [SD] 附录
13 16:00 — 16:30 陈雨阳 Pontrjagin对偶, 例子,及命题6.79的证明. [K] 6.4(h)节.
14 16:30 — 17:00 盛晗晗 中心单代数及Brauer群的定义 [A] [M] Chapter 4 [SL] X.5,  [FD]
15 17:00 — 17:30 沈博健 Brauer群的例子(有限域,局部域及inv映射) [A] [M] Chapter 4 [SL] X.5 XII, [FD]
16 17:30 — 18:00 郑振洲 关于素数分布的定理 [K] 第七章相关部分