Mathematics PhD program at the University of Washington, Seattle, has a requirement: Preliminary Exams. There are five of them:
A PhD student is required to pass two exams after the first year and a third exam after the second year.
Each exam contains 8 problems. It has the following scale of grades:
High Pass - Pass - Low Pass - High Fail - Fail - Low Fail
4 completely correct solutions make a clear Pass.
I have passed four of these exams in Autumn 2010, just before my first year.
Date Topic Result 09/13/2010 Algebra Pass 09/14/2010 Real Analysis High Pass 09/15/2010 Complex Analysis Not Submitted (Fail) 09/16/2010 Manifolds High Pass 09/17/2010 Linear Analysis High Pass The Department of Mathematics gave me two awards: Academic Excellence Award and a two-year McKibben & Merner Fellowship. See Graduate Student Awards