|About the course|||||The instructors|||||The text and other references|||||Students in the course|||||Outline
diary of the course|
See the award-winning YouTube video|
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|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.
(with PDF links)
|What is it?||Handed out|
|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
first-year 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).
|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.
|A result from the mid-20th 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|
|Mittag-Leffler & Weierstrass||Some notes about constructing holomorphic and meromorphic functions with specified behavior (Mittag-Leffler 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?
|The midterm exam||The midterm as it was given. Grades ranged from 20 to 48 out of 50.||11/15/2007|
5 and midterm exam information
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):
|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.
|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 email@example.com and last modified 9/2/2004.