Logic and Set theory(MAS 270)

 

M, W 10:30-11:45 

Room: 산경 Industrial Engineering Management Building E2-2504 (This is a special room with many whiteboards for Edu. 3.0)
TA: 정홍택(E6-4423 htjung1905 at gmail), 강성경(E6-3425 sungkyung38 at kaist),
       박종호(E2-4213 togomi2 at kaist), 김호진(E6-3427 khj920214 at kaist)


Instructor: Suhyoung Choi

Mail: shchoixk at math kaist ac kr

Course Homepage: mathsci.kaist.ac.kr/~schoi/logic2014F.html

 

This is an EDUCATION 3.0 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 Monday class and ones with an even id number will attend the Wednesday class.
(The team will be divided on the first day by the last digit of the student ID number. After the 3rd week, we will regroup if necessary)
•    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 4-5 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 four 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.

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,

  2. Logic: Chapters 5,6,7

  3. HTP: Chapters 2,3.

  4. HTP: Chapters 4,5,6

  5. NS: Chapters 1-11

  6. Presentations: You will be given topics.


Texts:


Nolt,  Rohatyn, Varzi, Logic, Schaum Series (Logic)
Velleman, How to Prove it, Cambridge University Press (HTP)
Halmos, Naive Set theory, Springer (NS)

(Buy all of these. If not available in Korea, order from www.amazon.com. )


Grades and so on:

See KLMS at edu3.kaist.ac.kr for the moodle page. You must join MAS270 in KLMS. All of the activity will take place there except
that the lectures notes will be posted here. 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 and reports will be done individually.

There will be exercise sessions probably in two sections from the third 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)

 

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. 1, 3

 Introduction, Logic. (Lec 0)

 

 2

Sept. 8, 10 

No classes (National Holidays 7-10 Chuseok)

 

 3

Sept.15, 17

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

 

 4

Sept. 22, 24

Chapter 3. Propositional Logic (Lec 3, 4)

 

 5

Sept. 29, Oct. 1

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

 

 6.

Oct. 6, 8

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

 

 7

Oct. 13, 15

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

 8

Oct. 20, 22

 

  Midterm period, Oct 20-24

 9

Oct. 27, 29

HTP. Chapter 2 (Lec 11, 12)

Group presentation topic assignments 

 10

Nov. 3, 5

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

 Group presentation topic assignments

 11

Nov. 10, 12

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

 

 12

Nov. 17, 19

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

 Nov. 18-19th (KAIST enterance exam day)

 13

Nov. 24, 26

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

NS. Sections 12-25 (Lec 21)   

 

 14

 Dec 1, 3

 Presentations

 

 15

Dec 8, 10

 Presentations

 

  16

Dec. 15, 17

  Presentations (3 hour once)

 Final exam period, Dec.15-19

 
 

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: 


Topic 1: Peano axioms (NS Section 12), Arithmetic (NS Section 13)
Topic 2: Order (NS Section 14), The axiom of choice (NS Section 15)
Topic 3: Zorn's lemma (NS Section 16), Well ordering (NS Section 17)
Topic 4: Transfinite  recursion (NS Section 18),
Topic 5: Ordinal numbers (NS Section 19)
Topic 6: Sets of ordinal numbers (NS Section 20),
Topic 7: Ordinal arithmetic (NS Section 21)
Topic 8: The Schroeder-Bernstein theorem (NS Section 22), Countable sets (NS Section 23)
Topic 9: Cardinal arithmetic (NS Section 24)
Topic 10: Cardinal numbers (NS Section 25)
Topic 11: Category theory: Refer to wikipedia or plato.stanford.edu.
Topic 12: Gödel's theorems (incompleteness): Refer to wikipedia or plato.stanford.edu



Open courseware

 MIT Logic I

MIT Logic II