Logic and set theory (MAS 270)

Monday, Wednesday 10:30-11:45 (Zoom meeting time)

Room:   E6 No. 3434  (If we need offline meetings, we will use this room)
TA: to be announced


Instructor: Suhyoung Choi

Mail: shchoixk at kaist ac kr

Course Homepage: mathsci.kaist.ac.kr/~schoi/logic2021F.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. We will use OneNote for lecture notes and distribute the links to you.
(Download OneNote from kftp.kaist.ac.kr)
• You will listen to
video lectures each week and read corresponding parts of the books. (See the course schedule pdf file.)

How the course will run:

1.     We will have a Zoom meeting at each class time (Monday, Wednesday 10:30-11:45). The Zoom meeting will be divided into the online quiz section and the discussion section. The meetings will be recorded often. 

2.     The students with even student Id numbers will attend the Monday meetings and ones with odd Id numbers will attend the Wednesday meetings. The team will be divided on the first week by the last digits of the student ID numbers. After the 3rd week, we will regroup if necessary. However, if the number of students are small we may have only one meeting per week.

3.     We take an online quizz for 15 minutes using the KLMS online quiz system. The exam will be proctored by Zoom. 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.) (We will have various policies for Zoom proctoring later for various IT set-ups you have.)

4.     Then we do Zoom group discussions for 40 minutes by dividing the class into breakout rooms. We will be solving and presenting the solution to group problems in teams of 3-5 students helped by TAs. One person from the team will present in Zoom. Teams are to be organized by us and posted in the KLMS. The answers will be graded by TAs. The grades will be for the teams. (The discussion problems will be posted and assigned one or two days earlier. You can work on these ahead of classes.)

5.     In the final 20 minutes, the groups will present their solutions by Zoom. Microsoft OneNote will be used here. We will make OneNote notebooks for each group.

6.     In the last two or three weeks, we will have presentations on materials not covered by lectures by teams. Your team will be given two to three weeks to prepare. The team scores are given.

7.     IT requirements: We suggest you to have something like ipads or galaxy tablets to help writing. The group can share their notes between the members since it is realtime updatable. During the quiz, you cannot use OneNote. (There will be peer grading. This is experimental. We will give precise policy later. The points will go to the class contribution scores. Of course we will only consider the grades you gave and not actually be bound by these.)

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, 3rd edition, Cambridge University Press (HTP) (Section 4.5 of the 2nd edition will be covered. A scan is provided.  )
Halmos, Naive Set theory, Springer (NS)

(Some of these might be downloadable from the KAIST main library. Buy all of these. If not available in Korea, order from www.amazon.com. I recommend Kindle versions.)

You cannot make copies in large numbers with the classmates. This can only be done individually. Please respect the copyright laws.

Grades and so on:

You must join MAS270 in KLMS. All of the activity will take place there and in the Zoom. You have to submit reports and homeworks 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. Teams will be assigned topics to present then.

Evaluation will be done as follows: A, B, C, D,
E, F, I, S, U. You can choose S/U as your grading system much later in the semester, which you have to let us know. Also, A+ will be given to only very exceptional work surpassing expectations. A0 is given to the perfect work for reports and so on. We will have a claim session twice during the semester. The grading is done by subjective judgements of the TAs and the instructors following the long tradition of the universities of the world. Since we will be running online courses, the quizzes and the presentations will be online. The quiz will be submitted to the KLMS system by clicking your solutions. We will also give group problems ahead of classes by one or two days. Your group can discuss and solve and plan presentations ahead of the classes. (We will experiment with "peer grading" for group presentations. This is strictly experimental. These are counted in class contribution scores)

Any cheating during exams using IT devices are against the KAIST ethical policies. You are subject to submitting your IT records. You will need to show your entire PC screens and your entire desk from your cell phones when we are doing the Zoom proctoring. These will be recorded. You can consult your textbooks above and your notes during the quiz and the group work. However, you cannot do internet searches during the exams or the group work. By taking these courses, you are subject to these ethical rules which are very many and are in the university ethics. Note that you will need to agree to a contract with me about all these ethical issues. If you don't agree to these policies, I advise you to drop the course.

Grades Distributions: Attendance 5%, Class contribution 5%, Quiz 50%, Solving Discussion Problems 20%, Final Team Presentation 20% (no midterm, no final exam) (One can miss up to two classes without any penalities. After that, the grades will be normalized with some penalties.)

Course schedules:

See also the course schedule pdf file.

Week

Date

Lecture plan (The video file to see on KLMS)

1

Aug. 30, Sept. 1

Introduction (Lec. 0)

Online mock quiz

2

Sept. 6, 8

Chapter 1,2. Argument, Chapter 8 Fallacies (Lec. 1, 2)

quiz starts

3

Sept.13, 15

Chapter 3. Propositional Logic (Lec. 3, 4)

4

Sept. 20, 22 

Holiday, no classes  

5

Sept. 27, 29

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

6

Oct. (4).  6 

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

Combined class (The 4th may be a holiday)

7

Oct. (11), 13

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

Combined class (The 11th may be a holiday), Group presentation topic assignments

8

Oct. 18, 20

Midterm period

9

Oct. 25, 27

HTP. Chapter 3. Proofs (Lec. 11, 12)

Group presentation topic assignments

10

Nov. 1, 3

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

11

Nov. 8, 10 

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

12

Nov. 15, 17

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

13

Nov. 22, 24

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

14

Nov. 29, (Dec 1)

Zoom presentations meetings

Attend both   Monday and Wednesday classes. (Dec. 1st is a KAIST entrance exam day) 

15

Dec 6, 8

Zoom presentations meetings

Attend both Monday and Wednesday classes.

16

Dec 13, 15

Attend the Zoom presentation meeting on the exam time.

Final exam period