拓扑学(H)（2019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 (05/07) Final Exam: 06/27, 14:30-16:30 @ 5203

o (06/25) 答疑 06/26, 19:00-21:00 @ 5206 (Time Changed!)

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 5505

o 办公室：   管研楼1601

o 助教：   Yulin Gong (gylustc at mail dot ustc dot edu dot cn)

o 答疑时间：   周日晚上 7:00pm - 8:30pm

o 答疑地点：   5405

o 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     02/25     Introduction； Metric Spaces: Definition and Examples     Lect 1     PSet 1, part 1   : Due March 4.
  Lecture 2     02/28     Metrics Spaces: Continuity; Open Sets     Lect 2     PSet 1, part 2   : Due March 4.
  Lecture 3     03/04     Topology: Definitions; Examples; Convergence and Continuity     Lect 3     PSet 2, part 1   : Due March 11.
  Lecture 4     03/07     Topology: Bases and Subbases; More Examples     Lect 4     PSet 2, part 2   : Due March 11.
  Lecture 5     03/11     Closed Subsets and Limit Points     Lect 5     PSet 3, part 1   : Due March 18.
  Lecture 6     03/14     Connectedness     Lect 6     PSet 3, part 2   : Due March 18.
  Lecture 7     03/18     Compactness: Definitions and basic properties     Lect 7     PSet 4, part 1   : Due March 25.
  Lecture 8     03/21     Compactness: Tychonoff Theorem and its applications     Lect 8     PSet 4, part 2   : Due March 25.
  Lecture 9     03/25     Compactness in Metric Spaces     Lect 9     PSet 5, part 1   : Due April 1.
  Lecture 10     03/28     Axioms of Countability; Urysohn's Metrizability Theorem     Lect 10     PSet 5, part 2   : Due April 1.
  Lecture 11     04/01     Separation Axioms; Urysohn's Lemma     Lect 11     PSet 6, part 1   : Due April 8.
  Lecture 12     04/04     Tietze Extention Theorem     Lect 12     PSet 6, part 2   : Due April 8.
  Lecture 13     04/08     Paracompactness, Partition of Unity     Lect 13     PSet 7, part 1   : Due April 15.
  Lecture 14     04/11     Stone-Weierstrass Theoerem     Lect 14     PSet 7, part 2   : Due April 15.
  Lecture 15     04/15     Arzelá-Ascoli theorem     Lect 15     PSet 8, part 1   : Due April 29.
      04/18     Problem Session  
  Lecture 16     04/22     The space of closed subsets in a metric space     Lect 16     PSet 8, part 2   : Due April 29.
      04/25     Midterm Cover Lec. 1 - Lec. 14  
  Lecture 17     04/28     Homotopy between maps     Lect 17     PSet 9, part 1   : Due May 06.
  Lecture 18     04/29     The Fundamental Group：Definition     Lect 18     PSet 9, part 2   : Due May 06.
  Lecture 19     05/06     More on Fundamental Groups: Homotopy Groups, Homotopy Invariance     Lect 19     PSet 10, part 1   : Due May 13.
  Lecture 20     05/09     The Fundametnal Group of the Circle     Lect 20     PSet 10, part 2   : Due May 13.
  Lecture 21     05/13     Covering Spaces     Lect 21     PSet 11, part 1   : Due May 20.
  Lecture 22     05/16     Van Kampen Theorem     Lect 22     PSet 11, part 2   : Due May 20.
  Lecture 23     05/20     Applications of the Fundamental Groups     Lect 23     PSet 12, part 1   : Due May 27.
  Lecture 24     05/23     Brouwer's Fixed Point Theorem     Lect 24     PSet 12, part 2   : Due May 27.
  Lecture 25     05/27     Invariance of Domain, Topological Manifolds     Lect 25     PSet 13, part 1   : Due June 03.
  Lecture 26     05/30     The Jordan Curve Theorem     Lect 26     PSet 13, part 2   : Due June 03.
  Lecture 27     06/03     Topology of compact surfaces     Lect 27     PSet 14, part 1   : Due June 10.
  Lecture 28     06/06     Classification of compact surfaces     Lect 28     PSet 14, part 2   : Due June 10.
      06/10     Problem Session  
  Lecture 29     06/13     Review     Lect 29  
      06/27     Final Cover Lec. 1 - Lec. 29  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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