拓扑学(H)（2021春季学期）


中国科学技术大学数学科学学院

[课程公告] [课程信息] [课程安排，讲义以及习题]

课程公告

o (05/28) 期末考试时间：7月5日14:30-16:30 @ 2210. 内容涵盖 Lecture 1 - Lecture 29. .

o (07/07) Done.

课程信息

o 授课老师：   王作勤 (wangzuoq at ustc dot edu dot cn)

o 上课时间：   星期一上午 9:45am – 12:10pm; 星期四下午 14:00am – 15:35am　

o 上课地点：   五教 5205

o 办公室：   管研楼1601

o 助教：   Wenbo Li (patlee at mail dot ustc dot edu dot cn)

o 答疑时间：   周日晚上， 19:30-21:30

o 答疑地点：   5305

o 参考教材：   James Munkres，拓扑学（第二版）

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课程安排，讲义以及习题

o 课程安排可能会随着课程的进行而略有变动。

o 课程的讲义将在每堂课后上传。

o 作业在每周一课前交。

序号 日期 内容 讲义 作业
  Lecture 1     03/08     Introduction     Lect 1     PSet 1, part 1   : Due March 15.
  Lecture 2     03/11     Metrics spaces     Lect 2     PSet 1, part 2   : Due March 15.
  Lecture 3     03/15     Topology: definitions and examples     Lect 3     PSet 2, part 1   : Due March 22.
  Lecture 4     03/18     Convergence and continuity in topological spaces     Lect 4     PSet 2, part 2   : Due March 22.
  Lecture 5     03/22     Bases and sub-bases, induced and co-induced topology     Lect 5     PSet 3, part 1   : Due March 29.
  Lecture 6     03/25     The quotient topology     Lect 6     PSet 3, part 2   : Due March 29.
  Lecture 7     03/29     Limit points, interior and boundary     Lect 7     PSet 4, part 1   : Due April 08.
  Lecture 8     04/01     Compactness     Lect 8     PSet 4, part 2   : Due April 08.
  Lecture 9     04/08     Compactness in metric space     Lect 9     PSet 5, part 1   : Due April 12.
  Lecture 10     04/12     Compactness of product space, Tychonoff theorem     Lect 10     PSet 6, part 1   : Due April 19.
  Lecture 11     04/15     The Stone-Weierstrass theorem     Lect 11     PSet 6, part 2   : Due April 19.
  Lecture 12     04/19     The Arzela-Ascoli theorem     Lect 12     PSet 7, part 1   : Due April 26.
  Lecture 13     04/22     The axioms of countability; metrizability     Lect 13     PSet 7, part 2   : Due April 26.
  Lecture 14     04/26     Separation axioms; Urysohn lemma     Lect 14     PSet 8, part 1   : Due May 10.
  Lecture 15     04/29     Tietze extension theorem; partition of unity     Lect 15     PSet 8, part 2   : Due May 10.
  Lecture 16     05/06     Connectedness     Lect 16     PSet 9, part 1   : Due May 17.
  Lecture 17     05/08     Path connectedness，components     Lect 17     PSet 9, part 2   : Due May 17.
      05/10     Midterm: Cover Lecture 1-Lecture 15  
  Lecture 18     05/13     Homotopy and path homotopy     Lect 18     PSet 9, part 3   : Due May 17.
  Lecture 19     05/17     The fundamental group     Lect 19     PSet 10, part 1   : Due May 24.
  Lecture 20     05/20     The fundamental group of the circle     Lect 20     PSet 10, part 2   : Due May 24.
  Lecture 21     05/24     Covering spaces     Lect 21     PSet 11, part 1   : Due May 31.
  Lecture 22     05/27     The classification of covering spaces     Lect 22     PSet 11, part 2   : Due May 31.
  Lecture 23     05/31    Van Kampen theorem     Lect 23     PSet 12, part 1   : Due June 07.
  Lecture 24     06/03     Applications of the fundamental groups     Lect 24     PSet 12, part 2   : Due June 07.
  Lecture 25     06/07    Brouwer's fixed point theorem; Brouwer's invariance of domain theorem     Lect 25     PSet 13, part 1   : Due June 17.
  Lecture 26     06/10     Jordan curve theorem     Lect 26     PSet 13, part 2   : Due June 17.
  Lecture 27     06/17     Classification of curves     Lect 27     PSet 14, part 1   : Due June 24.
  Lecture 28     06/21     Topology of compact surfaces     Lect 28     PSet 14, part 2   : Due June 24.
  Lecture 29     06/24     Classification of compact surfaces; Poincare-Hopf Theorem     Lect 29  
      07/05     Final Exam Cover Lec. 1 - Lec. 29  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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