Logic and the Set theory (MAS 270)

 

Monday, Wednesday 2:30-3:45 

Room: 산경 Industrial Engineering Management Building E2-1225
TA: to be announced


Instructor: Suhyoung Choi

Mail: shchoixk at math kaist ac kr

Course Homepage: mathsci.kaist.ac.kr/~schoi/logic2019F.html

 

This is an EDUCATION 4.0 course. (For more details, see CELT.)

•    The lectures will be given by videos posted in klms.kaist.ac.kr each week. One is automatically subscribed to this course in klms.kaist.ac.kr.
•    Lecture notes will be also posted in klms.kaist.ac.kr.
•    You will listen to about 2 lectures each week and read corresponding parts of the books.

The class: This is for quiz and exercise sessions:
•    The students with an odd student id number will attend the Tuesday classes and ones with an even id number will attend the Thursday classes.
(The team will be divided on the first week by the last digit of the student ID number. After the 3rd week, we will regroup if necessary. However, if the number of students are small we may have only one class per week.)
•    The quiz is given in the beginning for 15 minutes. It will cover the lecture material for the week and also the material in the previous week. (2 parts.)
•    Then we will have a Q&A time for the video lecture materials.
•    After quiz, we will be solving problems in teams of 5-6 students helped by TAs. (Teams to be organized by us and posted on klms.) One person from the team will solve the problems on the whiteboards and present the solutions. The answers will be graded by TAs. The grades will be for the teams.
•    In the last three weeks, we will have presentations on materials not covered by lectures by teams. Your team will be given 2-3 weeks to prepare. The team scores are given. The team scores will be graded by myself.


Course summary:

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 the set theory but we will concentrate on learning to prove. We will try to be elementary as possible. (The set theory is taught by myself in the beginning but you will have to present some later parts that you actively learn by teams.)

There will be six parts to this course. The first five parts are given by the instructor:

  1. Logic: Chapters 1,8,2,3,4, (Logic)

  2. Logic: Chapters 5,6,7 (Logic)

  3. HTP: Chapters 2,3. (Proof)

  4. HTP: Chapters 4,5,6 (Proof)

  5. NS: Chapters 1-25 (Set theory)

  6. Presentations: You will be given topics.


Texts:

Nolt,  Rohatyn, Varzi, Schaum's outline of Logic, 2nd edition, Schaum Series (Logic)
Velleman, How to Prove it, 2nd edition, Cambridge University Press (HTP)
Halmos, Naive Set theory, Springer (NS)

(There are many reprints from companies other than Springer. Buy all of these. If not available in Korea, order from www.amazon.com. )

 

Grades and so on:

You must join MAS270 in KLMS. All of the activity will take place there. You have to submit reports and homework and so on there. 

The midterm and the final will be replaced by quizzes, reports and group presentations. The students will be required to give presentations and
will be graded. Each presentation group will consists of several students. We will divide into teams after the midterm and your teams will
be assigned topics to present then.

Quizzes will be done individually.

There will be exercise sessions probably in two sections from the second week on. We will have quizzes and problem sessions
where the students will solve problems and exchange ideas with TAs.


Grades Distributions: Attendance 10%, Quiz 50%, Solving Problems 20%, Team Presentation 20% (no midterm, final exams) (One can miss up to two classes without any penalities. After that, the grades will be normalized with some penalties.)

 

Course schedules:

 (The lecture notes will be updated many times in the semester.)

Week

Date

 Lecture plan (video file to see on KLMS)

 

 1

Sept. 2,4

 Introduction, Logic. (Lec 0)

 

 2

Sept. 9, 11

Chapter 1,2. Arguments , Logic. Chapter 8 Fallacies (Lec 1, 2)

 

 3

Sept.16, 18

Chapter 3. Propositional Logic (Lec 3, 4)

 

 4

Sept. 23, 25

Chapter 4. Propositional Calculus (Lec. 5,6)

 
5

Sept. 30,
Oct. 2

 Chapter 5,6 Predicate Logic  (Lec 7, 8)  

 7

Oct. 7

Chapter 7. Predicate Calculus, (Lec 9, 10)

 Hangeul nal (There will be only one class this week)

 8

Oct. 14, 16

HTP. Chapter 2 (Lec 11, 12)

 Group presentation topic assignments 

 9

Oct. 21, 23

 

Midterm period 

 10

Oct. 28, 30

HTP. Chapter 3. Proofs (Lec 13, 14)

Group presentation topic assignments

 11

Nov. 4, 6

HTP. Chapter 4. Relations (Lec 15, 16)

 

 12

Nov. 11, 13

HTP. Chapter 5. Functions (Lec 17)
Chapter 6. Induction (Lec 18)
NS. Sections 1-5  Set theory (Lec 19)

 

 13

Nov. 18, 20

NS. Sections 6-11 Relations, Functions, Numbers (Lec 20), NS. Sections 12-25 (Lec 21)   

 

 14

Nov. 25

Presentations

 Nov. 27, 28, KAIST entrance exams (There will be only one class this week)

 15

 Dec 2, 4

 Presentations

 
16 Dec 9, 11 Presentations  

 17

Dec 16, 18

Presentations

Final exam period

 
 
Presentations:

The presentations must include: History and motivation, the outline of the theory, the theory itself, applications, the current status and uses,
the problems and limitations and controversies. Your principal source should be the book by Halmos. Each team will be given 25 minutes to present the material.

Presentation topics will be given later.