Logic and Set theory(MAS 270)

 

M, W, F 11:00-11:50 

Room: E11 311 (From 09/05/2011)

TA: 배다슬 (E6-1 4417) bds0822-at-kaist.ac.kr, 임현재 (E6-1 3417 phone: 2762) attack1234-at-kaist.ac.kr

Instructor: Suhyoung Choi

Room: E6-1 4403

Mail: shchoixk at math kaist ac kr

Course Homepage: mathsci.kaist.ac.kr/~schoi/logic2012F.html

 

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.


Grade points: Attendance 10%, Quiz 50%, Report 20%, Presentation 20%

 

Course schedules:

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

Week

Date

 Lecture plan

 

 1

Sept. 3, 5,7

 Introduction, Logic.
notes 1,

Chapter 1,2. Arguments , Logic. Chapter 8 Fallacies, notes 2,

 

 2

Sept. 10,12,14

Chapter 3 Propositional Logic

notes 3, 

  12, 14 lecturer

 3

Sept.17, 19, 21

Chapter 3. Propositional Logic notes 4,

Chapter 4. Propositional Calculus notes 5, notes 6 

 

 4

Sept. 24, 26, 28

 Chapter 5,6 Predicate Logic notes 7-8

 lecturer

 5

Oct. 5

Chapter 5,6 Predicate Logic notes 7-8 

 Oct. 1, 3 holidays

 6.

Oct. 8,10,12

Chapter 7. Predicate Calculus, notes 9-10,

HTP. Chapter 2 notes 11-12

 

 7

Oct. 15,17,19

 HTP. Chapter 3. Proofs, notes 13

  lecturer

 8


 

  Midterm period, Oct 22-26

 9

Oct. 29, 31, Nov 2


HTP. Chapter 3. Proofs  notes 14,
HTP. Chapter 4. Relations notes 15,

 

 10

Nov.5,7,9

 HTP. Chapter 4. Relations  notes 16
  HTP. Chapter 5. Functions notes 17

 

 11

Nov. 12,14,16

  Chapter 6. Induction  notes 18

  NS. Sections 1-5  Set theory notes 19 

 

 12

Nov. 19, 21, 23

NS. Sections 6-11 Relations, Functions, Numbers notes 20,  NS. Sections 12-25,  notes 21

 

 13

Nov. 26, 28, 30

 NS. Sections 12-25,  notes 21

  Presentations

 

 14

 Dec 3,5,7

  Presentations

 

 15

Dec 10,12,14

 Presentations

 

  16

Dec. 17, 19, 21

  Presentations

 Final exam period, Dec.15-21

 
 

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



Open courseware

 MIT Logic I

MIT Logic II