503: Metamathematics II
Time and Place: MWF 2-2:50pm,
Control Number: 22977
Office Phone: (312) 413-3150
Office Hours: MWF 1-2pm,
or by appointment.
Prerequisites: Math 502 (Metamathematics I); some elementary number theory.
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to download the class information handout.
The focus of this course will be incompleteness and undecidability in
mathematics. In particular, it will provide an introduction to two
landmarks of 20th-century mathematical logic: Gödel's
Incompleteness Theorems, and the undecidability of Hilbert's Tenth
Problem. (Hilbert had asked for an algorithm to decide whether a given
polynomial equation with integer coefficients has a solution in the
integers. Matiyasevich, based on work of Putnam, Davis, and Robinson,
proved that no such algorithm exists.) Time permitting, we will
contrast this with positive results such as the decidability of
For Hilbert's 10th Problem: Hilbert's 10th Problem by Yuri Matiyasevich, MIT Press, 1993.
texts that you might want to consult:
A good general reference for
R. Shoenfield, A K Peters, Ltd., 2000.
To get an idea about ongoing research on extensions of Hilbert's 10th Problem see Alexandra Shlapentokh's book manuscript Hilbert’s Tenth Problem: Diophantine Classes and Other Extensions to Global Fields, Cambridge University Press, to appear.
See also the Hilbert's 10th Problem web page.
There will be a problem set due
two weeks or so, to be handed in at the beginning of class. No late homework will be accepted.
Homework 1 (due February 13)
Homework 2 (due March 10)
Homework 3 (due April 28)
below for biographical information about some of the main actors involved the solution of Hilbert's 10th Problem:
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