Logic and Set theory(MAS 270)
Tuesday, Thursday: 14:30-16:00
Room: E6 3433
TA:
Instructor: Suhyoung Choi
Room: E64403
Mail: shchoixk at math kaist ac kr
Course Homepage: mathsci.kaist.ac.kr/~schoi/logic.html
See moodle.kaist.ac.kr for the moodle page. All the activity
will take place there.
You have to submit reports and so on there. This
homepage may not be updated at times
so please go to moodle.kaist.ac.kr.
We will introduce the logical structure of
mathematics. You will learn to prove mathematical statements. Also, the set
theory and transfinite numbers are introduced.
We will not go deeply into mathematical logic
or set theory but we will concentrate on learning to prove. We will try to be
elementary as possible.
The students will be required to give
presentations and will be graded.
Grade points: To be decided later in
September.
Text: Buy all of these. If
not available in Korea, order from www.amazon.com.
Nolt, Logic, Schaum Series (Logic)
Velleman, How to Prove it, Cambridge University Press (HTP)
Halmos, Naive Set theory, Springer (NS)
|
Week |
Date |
Lecture plan |
Homework |
|
1 |
Sept. 1,3 |
Logic. Chapter
1,2. Arguments |
|
|
2 |
Sept. 8,10 |
Logic. Chapter
3. Propositional Logic |
|
|
3 |
Sept.15,17 |
Logic. Chapter
4. Propositional Calculus |
|
|
4 |
Sept. 22,24 |
Logic. Chapter
5,6 Predicate Logic |
|
|
5 |
Sept. 29. Oct. 1 |
Logic. Chapter
7. Predicate Calculus |
|
|
6. |
Oct. 6,8 |
HTP. Chapter 2 |
|
|
7 |
Oct. 13,15 |
HTP. Chapter 3.
Proofs |
|
|
8 |
Oct. 20-26 |
Mid term period |
|
|
9 |
Oct. 27,29 |
HTP. Chapter 4.
Relations HTP. |
|
|
10 |
Nov. 3,5 |
Chapter 5.
Functions, Chapter 6. Induction |
|
|
11 |
Nov. 10,12 |
NS. Sections 1-5
Set theory |
|
|
12 |
Nov. 17,19 |
NS. Sections
6-10 Relations, functions |
|
|
13 |
Nov. 24, 26 |
NS. Sections
11-14 Peano Axioms, order |
|
|
14 |
Dec 1, 3 |
NS.
Sections 15-20 Axiom of Choice |
|
|
15 |
Dec 8.10. |
NS. Sections
21-25 Ordinals, Cardinals |
|
|
16 |
Dec. 15-21 |
Final exam period |
|