Spring 2008 Topology

Lecture will be given in English! at least 90% of the time.

(I will enforce this and give C or below to 20% of the students from this semester.)

(I guess that more and more top companies ask for their top executives to be fluent in English.
The communication would be done instantaneously without any “translation services”.
With extremely fast technology and business developments, no one has leisure to go back home
and translate the today’s proceedings. Nowadays, we are closer to the U.S. than France was
to England in 19th century. With world getting smaller and smaller, I would think that
Koreans would be working with many peoples in world. The rapidly developing 3rd world
with their population growing extremely fast, their demand for goods and intellectual properties
would be growing exponentially in the next 20 years.)


Time: MWF 15:00-16:00
ROOM: 3435

Exams: Wednesday 15:00-17:00 (2 hours)

Instructors: Suhyoung Choi Building E6-1 No. 4403
schoi at math dot kaist dot ac dot kr Phone: 2732

Assistant: (1) Gye-Seon Lee: Building E6-1 No. 4423
smileabacus at kaist dot ac dot kr Phone: 2772
(2) Dhrubajit Choudhury: Building E6-1 No. 4423
druba.choudhury at kaist do ac do kr Phone 2772

Important notice: Those people who do not take the midterm or final exam will be given F.
Those students who do not take more than 30% of the quizzes will be given F. 

Grade distributions: A:35%, B:45%, C or below 20%. (I will include the people who drop the course.)

 

 

You are expected to have prepared for the lecture by reading ahead and solving
some of the problems.

If you have questions about lectures, please ask your classmates and the lecture assistants and then finally myself.
Also, the web site to ask questions is at mathsci.kaist.ac.kr. Help desks in the 1st floor also available in the evening.
With 60-70 students in the classes and the fact that KAIST asks professors to do a lot of research, it is unfortunate but
practical that the professors cannot be contacted directly for help.

 

****Important Lecture policy

 

 

Course book:  Topology, 2nd Edition by James Munkres Prentice Hall

References: Topology, James Dugundji WCB
                  Basic Topology, M.A. Armstrong Springer Verlag

 

Grades: Midterm(150pts) Final(150pts) Quiz (100pts) Class participation (50pts)
Total 450pts

Exams will be given according to the KAIST schedule. There are old exams at math.kaist.ac.kr/~schoi/teaching.html.

Quizzes: There will be a quiz almost every week. There will be one or two problems to solve
given 20 minutes. The quiz problems are very similar or identical with the homework problems.
One should prepare for them by groups of students working on homework problems together.
The homework problems are not to be turned in.

Class participation score:
In order to earn class participation scores, you need to ask questions and/or answer
the questions that the instructor poses to you. The instructors will give points from 1-10
each time and they will be normalized. Those people who do not ask questions or not
able to answer class questions or not come to the classes will be given 0 points naturally.
An advice here is that you need to think much to be able to pose a question. I don’t really
recommend questions such as what is the purpose of these stuffs and why are we learning
these abstract concepts which are useless by the way and so on. The students who feel this way
can go to many other departments at KAIST which are very concrete. Also, these questions are
too general and vague and are out of the scope of the course. Points will be given to the questions
pertinent to the materials that we are learning.

The teaching homepage: http://math.kaist.ac.kr/~schoi/teaching.html

Course homepage: http://math.kaist.ac.kr/~schoi/Topology2008I.htm

 

Chapter 1: Set theory and logic: Review

Chapter 2: Topological spaces and continuous functions

Chapter 3: Connectedness and Compactness

Chapter 4: Countability and Separations

Chapter 5: The Tychonoff theorem

Chapter 7: Complete metric spaces and function spaces

Chapter 8: Baire spaces and dimension theory (48 only)

Midterm: Sections 1-25

Final: Sections 26-48

 

Monday

 

Wednesday

 

Friday

 

2/11

 1-4

2/13

 5-7

2/15

 9-11

2/18

 12, 13

2/20

 13

2/22

 14

2/25

 15

2/27

 16

2/29

 17

3/3

 17, 18

3/5

 18

3/7

 19

3/10

 20

3/12

 20

3/14

 21

3/17

 22

3/19

 22

3/21

 23

3/24

 24

3/26

 25

3/28

 26

3/31

Midterm

4/2

Midterm

4/4

Midterm

4/7

 26

4/9

 26,27

4/11

 27

4/14

 28

4/16

 29

4/18

 30

4/21

 30

4/23

 30,31

4/25

 31,32

4/28

 33

4/30

 33,34

5/2

 34, 37

5/5

 holiday

5/7

 43

5/9

 44,45

5/12

 holiday

5/14

 45

5/16

 46

5/19

 46

5/21

47,48

5/23

 48

5/26

Final

5/28

Final

5/30

Final

 

 

 

 

 

 

 

 Lecture note for mathematical logic odd pages and even pages

Lecture notes 1.(Sections.1-22)

Lecture notes 2. (Sections 22-27)

Lecture notes 3 (Sections 28-36)

Lecture notes 4 (Sections 37-48)

Homework sets: Do not turn in your works but you should know how to solve these problems.
For quizzes, the teaching assistants will make problems similar to these. The best way is
to study the problems that were taught on that day.

 

S.1: p.14: 2,3,5,  S.2:p.20: 2, S.3:p.29:11,12, S.4:p.34:1,3, p.35:6,7,9, S.7:p.51:4,5,
S.10: p.66: 1, p.67: 2, 3,6, S.11:2,3, p.72:5

S.13:p.83: 3, 4,

S.16:p.92:3,4,8,9.

S.17:p.100: 2,3, p. 101: 6, 9, 13, 14, p.102: 19, S.18:p.111: 1,3,4,

S.19:p.118: 1,4,6,9, S.20:p.126: 2, p.127: 4,6,

S.21:p.133:3, p.134:5,7,9. p.135: 12. S.22:p.144:2, p.145:3,

S.23:p.152:2,3,10, S.24:p.157:1, p.158:5,7,8, S.25:p.162:1,6, p.163:8.

S.26:p.170:1, p.171:3,4,6,7, S.27:p.177:2, p.178:6

S.28:p.181:3,6,7, S.29:p.186:1,4,7,8, S.30:p.194:2,4,5,14.

S.31:p.199: 1,2,5,7, S.32:p.205: 1,2,3.

S.33:p.212: 2,3, p.213:4,5,7, S.34:p.218:3,6,7,

S.37:p.235:2 S.43:p.270:2,3,4, p.271:8, S.45:p.280:1,2,4,5.(13th and 14th week)

S.46:p288:1,6, p.289:9, S.47:p.292:1, S.48:p.298:1, p.299:2,3