MATH 320 Set Theory (Spring 2004)

2003 - 04 Spring

MATH 320: Set Theory

...self-evidence ... must not be confused with ... provability. --- Ernst Zermelo

Announcements:
- Final exam is take-home and it is due on 11 June 2004, 17:30. (Questions are available as a .dvi file and a .pdf file. If you can not open these files, then you can obtain a hard-copy from my office.)
- How do mathematicians choose? - A seminar by the students of the course
- Hints to the first midterm questions:
  1. a. True.
  b. False.
  2. a. This is in the book.
  b. Take the set of integers with the usual successor function (+1) and consider f(0)=0 and f(x)=x+1.
  3. a. Use the Axiom of Infinity to prove there exists at least one such set. Take the intersection of all such sets.
  b. Let A be a subset of w (omega) containing the empty-set and x' whenever x is in A. By definition, w=A.
  4. a. Apply induction on the set given in the hint.
  b. Using (a), show that there is an order-preserving bijection between A and w.
  c. Take the reverse order on w.
  5. Define a map from w into the set of functions from w\{0} into w taking m to f_m, where f₀=id and f_m+1=n^f_m(n).
  Bonus. In naive set theory, all classes are assumed to be sets.
- The Winter issue of Matematik D�nyas� is out now and it contains a good introduction to axiomatic set theory and construction of natural numbers.
- Please check this page for future announcements.
Lectures:
Monday 15:40-17:30 (M-106) Wednesday 12:40-13:30 (M-106)
Main Text. Notes on Set Theory by David Pierce

Reference Books: You can use any book on set theory that discusses Peano Axioms, Cardinals, Ordinals, Axiom of Choice, Well-Ordering Principle, Continuum Hypothesis.

Office Hours:

TBA

Exams:

I am planning to make the midterm exams during the class time.

Exam 1: (Written Exam)
Date and Time: 19 April 2004 Monday, 15:40
Place: M - 106
Contents: Sections 0 - 12 (inclusive)

Exam 2: (Presentation)
Date and Time: 12 May 2004 Wednesday, 13:40
Place: Arf Hall (M - 13)
Contents: Axiom of Choice and related topics

Final: (Take-Home Exam)
Date: due on 11 June 2004 Friday, 17:30
Place: M - 242 (My office)
Contents: Everything we covered.

Make-up: (Written Exam)
Date and Time: 9 June 2004 Wednesday, 9:30
Place: M - 242
Contents: Same as the Final contents.

Grading:

Those who miss two exams will receive NA. Those who miss one exam may take the make-up exam which will be given after the final. Those who took all three exams, attended 75% of the lectures and received an FD may take the make-up exam to increase their letter to DD. Please note that those who passed the course can not take the make-up to increase their letters.

Exam 1 - 30 points
Exam 2 - 30 points
Final - 40 points

Last updated on 4 June 2004.