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 Ba�kent
- History and Philosophy of the Axiom of Choice (.html file)
2. Tolga Karayayla
- Axiom of Choice implies Zorn's Lemma
3. An�l Gezer
- Zorn's Lemma implies Well Ordering Principle and Well Ordering Principle implies Axiom of Choice (.doc file)
4. Can Deha Kar�ks�z
- Every vector space has a basis
5. �lksen Acunalp
- Hahn-Banach Theorem
6. Arda Do�an
- Tychonoff's Theorem
7. Aykut Arslan
- Banach-Tarski Paradox
8. Ali Altu�
- 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. Terzio�lu, Fonksiyonel Analiz Y�ntemleri, Matematik Vakf�, 1998.
S. Wagon, The Banach-Tarski Paradox, Cambridge University Press, 1985.
Matematik D�nyas� (Fonksiyonlar �zel Say�s�), K�� 2003.

MIDDLE EAST TECHNICAL UNIVERSITY Department of Mathematics