SEMINAR

HOW DO MATHEMATICIANS CHOOSE

by the Students of the Math Department

12 May 2004
13:40
Arf Hall (M-13)

Contributors

(To view the slides, please click on the topics below. They are all .pdf files, unless otherwise stated.)

1. Can Başkent
- History and Philosophy of the Axiom of Choice (.html file)
2. Tolga Karayayla
- Axiom of Choice implies Zorn's Lemma
3. Anıl Gezer
- Zorn's Lemma implies Well Ordering Principle and Well Ordering Principle implies Axiom of Choice (.doc file)
4. Can Deha Karıksız
- Every vector space has a basis
5. İlksen Acunalp
- Hahn-Banach Theorem
6. Arda Doğan
- Tychonoff's Theorem
7. Aykut Arslan
- Banach-Tarski Paradox
8. Ali Altuğ
- Handout (.doc file)
9. Sait Karalar
- Poster (.jpg file)

Some Equivalent Statements of the Axiom of Choice

1. Axiom of Choice: Every non-empty set has a choice function.
2. Zorn's Lemma: Every non-empty partially ordered set in which every chain has an upper bound has a maximal element.
3. Well Ordering Principle: Every non-empty set has a well ordering.

References

K. Ciesielski, Set Theory for the Working Mathematician, Cambridge University Press, 1997.
M. Eisenberg, Axiomatic Theory of Sets and Classes, Holt, Rinehart and Winston, 1971.
T. Terzioğlu, Fonksiyonel Analiz Yöntemleri, Matematik Vakfı, 1998.
S. Wagon, The Banach-Tarski Paradox, Cambridge University Press, 1985.
Matematik Dünyası (Fonksiyonlar Özel Sayısı), Kış 2003.

MIDDLE EAST TECHNICAL UNIVERSITY Department of Mathematics