Guideline for course project

Requirement:

  • It is strongly suggested that you look out for and use more than one resources for your selected topic, and organize them in your own way. Entirely taking ones article is against copy right and moral integrity. Please include your references as the examples below:

    References

    1. Keith Devlin, 1992. The Joy of Sets, 2nd ed. Springer-Verlag.
    2. Michael Potter, 2004. Set Theory and Its Philosophy. Oxford Univ. Press.
    3. Patrick Suppes, 1972. Axiomatic Set Theory. Dover Publications.
    4. George Tourlakis, 2003. Lectures in Logic and Set Theory, Vol. 2. Cambridge Univ. Press.

  • Pictures and charts are encouraged.
  • The project is due on the last lecture.
  • Students are encouraged to talk to me to discuss your topics (during office hours preferred).
  • en.wikipedia.org and the Stanford Encyclopedia of Philosophy are good places to start with.

Suggested topics:

Biographies:

Gottfried W. Leibniz Georg Cantor Giuseppe Peano Gottlob Frege David Hilbert
Bertrand Russell Henri Poincaré Ernst Zermelo Thoralf Skolem Kurt Gödel
Alan Turing Alfred Tarski John von Newmann Nicolas Bourbaki Willard V.D. Quine
Alonzo Church Stephen C. Kleene Julia Robinson Abraham Robinson Azriel Levy
Paul Erdős Paul Cohen Gerald E. Sacks Saharon Shelah W. Hugh Woodin
Stevo Tordorčević ...... ...... ...... ......

Please focus on their contributions to logics.

Other topics:

  1. Logic
  2. Paradox
  3. First-order logic
  4. Foundations of mathematics
  5. Mathematical logic
  6. Set theory
  7. Model theory
  8. Recursion theory (aka. Computability theory)
  9. Proof theory
  10. Peano arithmetics
  11. Axiomatic system
  12. Mathematical induction
  13. logic problems in Hilbert's 23 problems
  14. Continuum Hypothesis
  15. Russell's Paradox
  16. Russell's Type theory
  17. Church's Thesis
  18. Gödel's completeness theorem
  19. Compactness theorem
  20. Axiomatic set theory (ZF, ZFC system)
  21. Gödel's Incompleteness Theorem
  22. Gödel's constructible universe, L
  23. Axiom of Choice
  24. Tarski-Banach paradox
  25. nonstandard number theory (models of PA)
  26. Robinson's nonstandard analysis
  27. Turing machine
  28. Halting problem
  29. Forcing (in set theory, in recursion theory)
  30. Large cardinals
  31. Infinitary combinatorics
  32. Goodstein's Theorem
  33. Ramsey's Theorem
  34. P versus NP problem
  35. Polish notation and Reverse Polish notation
  36. Skolem's paradox
  37. and ......