Logic and Set theory(MAS 270)

 

Tuesday, Thursday: 14:30-16:00

Room: E11 301

TA: Choi, Kanghyun (e-mail: k_choi at kaist dot ac dot kr) Room E6-4423

Ha, Jae-Soon (e-mail: hjs83 at kaist dot ac dot kr) Room E6-4423

TA website: http://mathsci.kaist.ac.kr/~manifold/

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.

 

Teaching policy!!!!!

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)

 

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

  1. Logic: Chapters 1,2,3,4,

  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. 1,3

 Introduction, Logic. Chapter 1,2. Arguments
notes 1, notes 2

 

 2

Sept. 8,10

 Logic. Chapter 3. Propositional Logic

notes 3, notes 4

 Preview (1) due Sept. 10

 3

Sept.15,17

 Logic. Chapter 4. Propositional Calculus

notes 5, notes 6

 

 4

Sept. 22,24

 Logic. Chapter 5,6 Predicate Logic

notes 7-8

 Review (1) due Sept. 22.
Preview (2) due Sept. 22.

 5

Sept. 29. Oct. 1

 Logic. Chapter 7. Predicate Calculus
notes 9, notes 9-10

 

 6.

Oct. 6,8

 HTP. Chapter 2

notes 11, notes 11-12

 Review (2) due Oct 6.
Preview (3) due Oct. 6

 7

Oct. 13,15

 HTP. Chapter 3.  Proofs

notes 13, notes 14

 

 8

Oct. 20-26

 Mid term period

 

 9

Oct. 27,29

 HTP. Chapter 4. Relations

notes 15, notes 16

 Review (3) due Oct. 27
Preview (4) due Oct. 27

 10

Nov. 3,5

 HTP. Chapter 5. Functions, Chapter 6. Induction

 

 11

Nov. 10,12

 NS. Sections 1-5  Set theory

 Review (4) due Nov. 10.
Preview (5) due Nov. 10

 12

Nov. 17,19

 NS. Sections 6-11 Relations, Functions, Numbers

 Presentation due

 13

Nov. 24, 26

 Presentations

 Review (5) due Nov. 24.
(The final one)

 14

Dec 1, 3

  Presentations

 

 15

Dec 8.10.

 Presentations

 

  16

Dec. 15-21

  Final exam period

 

 

 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.