Name: David Nadler
Committee: Christodoulou, Kochen (C), MacPherson
Topics: Algebraic Topology, Differential Geometry
Date: May 6, 1997
Duration: Two and a half hours or so
Kochen and I chatted a couple of minutes before MacPherson and Christodoulou
arrived. Kochen mentioned that he had been a grad student at Princeton and
had taken this exam when "men were men" and the exam was far more fearsome.
I was not sure if this was a good or a bad sign... The others arrived, they
sent me out of the room for a minute to get themselves organized, then called
me back in and we got underway with Christodoulou somewhat sinisterly
announcing, "We will begin with real variables..."
Real Analysis (Christodoulou):
What is a necessary and sufficient condition for a function to be Riemann
integrable?
Is it possible that the characteristic function of an open set is not
Riemann integrable?
What is a necessary and sufficient condition for a function to be the
indefinite integral of its derivative?
If a function is continuous and of bounded variation is it absolutely
continuous?
Suppose you have a sequence of functions f_n of bounded variation on a
compact interval [a,b] (normalized so that f_n(a)=0 for all n) such that
their total variations are uniformly bounded, i.e. there exists a constant
c>0, independent of n, such that Tf_n(b)