Fall 2024 Combinatorial Topology (MAS 430. 25.430)

Time: M, W 10:30-11:45

Lecture room: E2-1225

Instructor: Suhyoung Choi 4403(office) 
Office Hours:
schoi at math dot kaist dot ac dot kr Phone: 2732

Prerequisite: MAS 331 Topology
Course book:  Topology, J. Munkres, Secondary: A basic course in Algebraic topology, W.S. Massey, Tertiary: Basic Topology, M.A. Armstrong, Springer)

Topics: Fundamental groups, Surface theory, Covering space theory

This is an EDU4.0 course. Lectures are given by videos at the KLMS. The class time will be devoted to discussions. You need to study the material and watch the videos for the week before coming to classes. Problems or discussion material will be given before the week. We will have two classes per week. At each class, we will have group discussions and presentations of the solutions of assigned problems. Usually, we will only have discussions on Monday and we will have presentations on Wednesday. Then the presentation file must be submitted in the KLMS. The oral presentation will be peer graded. However, the final grades of the presentations will be done by us using the final file and the inputs from the students.

Grading: Final (150 pts.),  Midterm (150 pts.), Presentation (written part 50 pts. and oral part 50 pts), Class contribution (25 pts.), Attendance (25 pts.) Total 450pts

There will be presentations of your group discussions. These are 50% of the presentation grades.  There will be peer grading which will be counted for class contributions. The midterm and the final will be off-line exams.  

Course schedules:

Week

Date

 Lecture plan

 

 1

Sept. 2, 4

 Introduction

 

 2

Sept. 9, 11  

S. 51; S. 52, Fundamental groups

 

 3

Sept. 16, 18

Holidays

 

 4

Sept. 23, 25

 S.53, S.54, Covering spaces

 

 5

Sept. 30, Oct. 1

S. 55, S.56, S.57, Retractions and fixed points

 

 6.

Oct. 7, 9(holiday)

S. 58; S. 59, S. 60,  Homotopy types

 

 7

Oct. 14, 16

S. 61, S.62; S. 63,  Separation theorems

 

 8

Oct. 21, 23

 

  Midterm period  

 9

Oct. 28, 30

S. 64, S. 65, S. 66, Winding numbers

 

 10

Nov. 4, 6

S. 67, S. 68, S. 69, Seifert van-Kampen theorem

 

 11

Nov. 11, 13

S. 70, S. 71; S. 72, S.73 Seifert van-Kampen theorem

 

 12

Nov. 18, 20 

S. 74, S. 75; S. 76, S. 77, S. 78, Classification of surfaces

 

 13

Nov.25,27

S. 79, S. 80, Classification of covering spaces

 

 14

Dec.2, 4

  S. 81; S. 82, Classification of covering spaces

 There might be a KAIST entrance exam day in this week.

 15

Dec. 11, 13

  S.83, S.84, S.85 Application to graph theory


 

  16

Dec. 18, 20

 

 Final exam period