Logic and Set theory(MAS 270)

 

Tuesday, Thursday: 10:30-12:00

Room: E11 401

TA: 최 강현 (kchoi1982 at kaist.ac.kr) Room E6-4423, 최락용 (proudasia at gmail.com) Room E6-3425

Instructor: Suhyoung Choi

Room: E6-4403

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 of 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: Attendance 10%, Quiz 50%, Report 20%, Presentation 20%

 

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)

 

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.

 

Week

Date

 Lecture plan

 Homework

 1

Sept. 1

 Introduction, Logic.
notes 1, 

 

 2

Sept. 6,8

Chapter 1,2. Arguments , Logic. Chapter 8 Fallacies,
Chapter 3 Propositional Logic

notes 2, notes 3, 

 

 3

Sept.15

 Chapter 3. Propositional Logic

notes 4, 

 

 4

Sept. 20,22

Chapter 4. Propositional Calculus

notes 5, notes 6 

 

 5

Sept. 27,29

Chapter 5,6 Predicate Logic notes 7-8 

 

 6.

Oct. 4, 6

Chapter 7. Predicate Calculus, notes 9-10

HTP. Chapter 2 notes 11-12
 

 

 7

Oct. 11,13

 HTP. Chapter 3. Proofs notes 13

 

 8

Oct. 18

 HTP. Chapter 3. Proofs  notes 14

  Midterm period, Oct 20-26

 9

Oct. 27

 HTP. Chapter 4. Relations notes 15

 

 10

Nov.1,3

 HTP. Chapter 4. Relations notes 15, notes 16
  HTP. Chapter 5. Functions notes 17

 

 11

Nov. 8, 10

  Chapter 6. Induction  notes 18

  NS. Sections 1-5  Set theory notes 19 

 

 12

Nov. 15,17

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

 

 13

Nov. 22,24

 NS. Sections 12-25,  notes 21

  Presentations

 

 14

Nov.29, Dec 1

  Presentations

 

 15

Dec 6, 8

 Presentations

 

  16

Dec. 13

  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.

Presentation topics include:

Topic 1. Peano Axioms and arithmetics, Section 12, 13 in NS.

Topic 2. Order, The axiom of choice, Sections 14, 15, in NS.

Topic 3. Zorn's lemma, Well-ordering, Sections 16, 17 in NS.

Topic 4. Transfinite recursion, Ordinal numbers,Sections 18, 19 in NS.

Topic 5. The sets of ordinal numbers, The ordinal arithmetic, Sections 20, 21 in NS

Topic 6. The Schroeder-Bernstein Theorem, Countable sets, Sections 22, 23 in NS

Topic 7. Cardinal arithmetic, Cardinal numbers, Sections 24, 25 in NS

Topic 8. Category theory: Refer to wikipedia or plato.stanford.edu.

Topic 9. Gödel's theorems (incompleteness): Refer to wikipedia or plato.stanford.edu

Topic 10. Logic and artificial intelligence: Refer to wikipedia or plato.stanford.edu.


Open courseware

 MIT Logic I

MIT Logic II