Summer 2013 -- Foundations of Mathematics

Summer 2013 `C' Term-- Foundations of Mathematics - MHF 5206-01/MAA 4934

Meets MTWRF 2:00-3:20 102 LOV
Instructor Dr Steve Bellenot (bellenot at math.fsu.edu) 850.644.7405
OFFICE HOURS TBA

The class ad
The course Syllabus.
The schedule of due dates.
The on-line gradebook

Resources

Short addtional material: complete ordered fields, omega_1 and another model of the natural numbers, both currently in draft form.
Euclid's Elements on-line
Free on-line non-standard calculus book by Keisler
Free on-line Foundations of non-standard analysis book by Keisler

Textbook:

	   Title: Basic Set Theory
     Authors: A. Shen and N.  K. Vereshchagin
Edition/date: 1st/ 2002
   Publisher: AMS (American Math Society)
        ISBN: 0-8218-2731-6
    Comments: Student Math Library Volume 17

About twenty dollars at Amazon

Textbook: TBA, here is the text from last time (Springer recently raised the price and changed the isbn to 0-387-28722-5 there are still some of the old isbn numbers at the cheaper price: Or maybe I'm confusing a hardcover with a softcover.
```
       Title: Notes on Set Theory
      Author: Moschovakis, Yiannis
Edition/date: 2nd  (2006 or Dec 2005)
   Publisher: Springer
        ISBN: 0-387-28723-X
    Comments: Part of the Undergraduate Texts in Math series, Softcover.
```
Springer Link to the textbook. A different isbn for a higher price. Other places charge less for the book with the isbn above.
On-line textbooks. I've not used any of these
- Roitman's Introduction to Modern Set Theory
- Dixon's PMA603: Set Theory Notes
- Huntington's The Continuum and other types of serial order with introduction to Cantor's transfinite numbers
- Goldblatt's Topoi, the categorial analysis of logic develops the foundations of mathematics from category theory. Assumes you know the set theortical version of foundations and the basics of algebra, topology and analysis.
- Carus's The foundations of mathematics 1908 but it is about geometry!
- Abranmsky and Jung's Domain Theory a computer science viewpoint of mathematical foundations.
Other books: These are the books I learned set theory out of back in the 60's and 70's
- Halmos' Naive Set Theory is now reprinted by Springer.
- Kelley's General Topology is now reprinted by Springer. It has an excellent appendix on set theory from the viewpoint of classes.
- Paul Cohen's Set theory and the continuum hypothesis. Used prices are much higher than the price I paid in the 70's.
- There is one more, also out of print that was used in the Foundations class I thought in 70's. We used it for at least 30 years. Here it is: Hayden and Kennison's Zermelo-Frankel Set Theory
Software
- The free matlab clone scilab and the local examples directory and the