About the course    The instructors    The text and other references    Students in the course    Outline
diary of the course Part 2 Part 1 
See the awardwinning YouTube video by Douglas Arnold and Jonathan Rogness: more than one million (1,000,000) views! 
Things to do 
Final letter grades were submitted to the Registrar's computer late
yesterday (Friday, December 21). Here is
information about grading. Here's one last esthetic comment.
This one or this one? The final exam grade of students who analyzed Aut(C^{*}) (problem 5) using a theorem related to the name of the character in this picture has been decreased.

Title (with PDF links) 
What is it?  Handed out or posted 

The final exam  The final as it was given (with the word "Preparation" deleted
from the title, though). Grades ranged from 20.5 to 58.9 out of
60. Since part of the purpose of the final was to prepare our
firstyear grad students for the written exams, I'll return the exams
to these students in their department mailboxes "soon". This has been done (1/4/2007). 
12/20/2007 
Final exam
information Updated 12/14/2007 
See these problems to help prepare for the final exam. Mr. Williams kindly informed me that the diagram drawn for problem 6 was mislabeled. This was unintentional, and this copy has been changed (i to –i and 1+i to 1–i). I regret the confusion. 
12/11/2007 
A result from the mid20^{th} century  This is a discussion of Hans Lewy's example of a very simple linear partial differential equation with no solution. It relies on some easy (!) complex variables facts.  12/11/2007 
MittagLeffler & Weierstrass  Some notes about constructing holomorphic and meromorphic functions with specified behavior (MittagLeffler and Weierstrass Factorization Theorems). We only had time to discuss some special cases, so here is a fairly direct and naive approach to these results, together with some neat corollaries.  12/11/2007 
Problem set 6  Please hand in solutions on Tuesday, December 4. The evidence mentioned in problem 6 is here: k=4 and k=41. The originator of question #6 is Dr. Vincent Vatter. His published analysis of the problem connected with this question used a result called Pringsheim's Theorem. This and a great deal more about the application of "simple" complex variable techniques to enumerative combinatorics is explained in a publication by Phillipe Flajolet with title Symbolic Enumerative Combinatorics and Complex Asymptotic Analysis. I think these are notes taken by Yvan Le Bourgne, who was then (bien sûr!) a grad student. Don't grad students do all the work? 
12/14/2007 
The midterm exam  The midterm as it was given. Grades ranged from 20 to 48 out of 50.  11/15/2007 
Problem set
5 and midterm exam information Updated 11/7/2007 Further updated 11/9/2007 
Please hand in solutions on Tuesday, November 13, and prepare for
an exam on the same day.
A change has been made (11/7/2007):
Further changes (11/9/2007): 
10/26/2007 & 11/7/2007 & 11/9/2007 
Problem set 4  Please hand in solutions on Tuesday, October 23.  10/14/2007 
Problem set 3  Please hand in solutions on Tuesday, October 9. Please see the currently posted version, with a change made in response to some student observations.  9/28/2007 
Problem set 2  Please hand in solutions on Friday, September 28. In order to avoid temporal contradications, I have changed to due date, following the suggestion of Mr. Amos. 
9/18/2007 
Problem set 1  Please hand in solutions on Friday, September 15.  9/9/2007 
Problem set 0  Please hand in solutions on Friday, September 7.  9/2/2007 
Information sheet  A sheet to be passed out on the first day of class.  9/1/2004 

Maintained by greenfie@math.rutgers.edu and last modified 9/2/2004.