Math Department, University of Washington, Seattle
Seminar meets M 2:30-4:30, C-36 PDL
Moderator:
Prof. Judith M. Arms,
arms@math.washington.edu
Office: C-338 PDL, (206)543-9458, messages at (206)543-1150
Office hours: M 12:30, Th 2:30, and by appointment.
Assignment for August 6.
Topic: The Frobenius Theorem and foliations.
Problems to be presented on August 6:
2001#5, 2004#2, 2005#7, and 2006#7; if time, also 2001#6 and 2002#7*.
*2002#7 may be done in different ways, could have been assigned earlier.
Individual presentation assignments: I've assigned each of you 3 of
the first four problems (2001#5, 2004#2, 2005#7, and 2006#7), but ideally
prepare all four of these thoroughly. In addition each of you is assigned
one of the two "if time" problems.
Ashesh: 2001#6, 2004#2, 2005#7, and 2006#7.
Eina: 2002#7, 2004#2, 2005#7, and 2006#7.
Matthew B.: 2001#5 & #6, 2004#2, and 2005#7.
Matt K.: 2001#5, 2002#7, 2004#2, and 2005#7.
Michael: 2001#5, 2002#7, 2004#2, and 2005#7.
Wayne: 2001#6, 2004#2, 2005#7, and 2006#7.
Assignment for August 13. Do the 2000 prelim as a practice exam. That is, allow yourself four hours to work on it. Bring questions to discuss in seminar on the 13th. (Jack Lee will be subbing for me that day.)
Problems we've skipped on the 2002-2006 prelims:
Ones you should certainly work: 2002#6, 2003#6, 2004#5, and 2006#2.
"Stamina builders:" These seemed to be very difficult for students
to do under test conditions, but will reinforce your skills:
2002#4 & #8, 2004#8.
Interest was expressed in more problems using the gradient and similar manipulations. In the first edition of [ISM], Problems 17-10 and 17-11 are more "flow of a vector field defined from grad f" problems, not sure where they are in the second edition. Then there are a bunch of integration problems that use similar skills: 1997#3, and problems in the 1st (resp., draft 2nd) ed. of [ISM], 14-7, 14-8, and 14-15 (resp., 19-7, 19-8, 19-15). Also you might review the discussion of the divergence (1st ed, Ch. 18 "Applications to Geometry"; 2nd ed., Prop.19.24).
I will be out of town August 9-22. When I return, I would be happy to evaluate up one or two written solutions for prelim problems from each of you. I will aim to return your solution to you with comments within a week. You may get better comments if several of you turn in the same problem (and I can compare solutions), so you might consider collaborating on problem choice.
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Most recently updated on July 30, 2007.