Patrick Barrow
PhD candidate in Mathematics, UC Berkeley
Office: 1097 Evans
Email address: patrick (dot .) barrow (at @) gmail (dot .) com
Office Hours: Monday 10:15-12, Wednesday 3-5
MA185
This summer I will be the instructor for MA185, otherwise known as complex analysis. The textbook
is the most recent edition of Churchill & Brown's Complex Variables and Applications. Regardless of what
nonsense you might encounter within the online schedule of classes, we will meet Monday through
Thursday, from 8am to 10am, in 3102 Etcheverry.
MA185 Schedule
NOTE: Final exam review office hours will be held Wednesday, 8/13, from approximately 10:30 - 5:00, in 891 Evans.
Practice final, choose 4 problems to do for HW10, due Wed. 8/13
List of theorems, to appear on the exam
NOTE: I have been carrying around a folder full of uncollected HW's that has now reached
unreasonable proportions. If you have not gotten any of HW1-7 back, and you would like it back,
stop by my office.
7/31 - Midterm #2
8/4 - These last two weeks
will be a plethora of results that follow from our extensive classification of the nature of
holomorphic functions, their singularities, residues, etc. Specifically, today we finished the
behavior of functions near an isolated singularity (last section of Ch. 6), culminating in the
Casorati-Weirstrass theorem.
We
started using
complex integral techniques to derive real valued results (beginning of Ch. 7).
8/5 - Finish
Jordan's lemma.
Continue integral techniques, over
possibly more sophisticated contours ("indented paths"), and considering functions involving branch cuts, sines, cosines, etc.
8/6 - Conclude integral techniques. Start on the
argument principle and
Rouche's theorem.
8/7 - Rouche's theorem implies the
open mapping theorem.
Possibly continue on to the
Schwartz lemma, definitely throw out some ample hints for HW9.
8/11 - Use the Schwartz lemma to characterize the bijective analytic maps
from the open unit disk to itself, and then move on to some practice problems. Specifically,
we will review the behavior near a removable singularity, Rouche's theorem, and Morera's theorem.
8/12 - Practice problems involving the Schwartz lemma, Liouville's theorem, Rouche's theorem, and singularities.
8/13 - Review practice final.
8/14 - Final exam
MA185 archive
Research Interests
My two primary areas of interest are in noncommutative geometry, pioneered by Alain Connes, and in
chainlet geometry, pioneered by my advisor, Jenny Harrison. Vaguely speaking, I aspire to use these
"modern" theories to derive new "traditional" results.
Past Courses
Undergraduate Seminar in Advanced Linear Algebra Spring 2008
Student Noncommutative Geometry Fall 2007
MA110 Summer 2007
MA74 Spring 2007
MA74 Fall 2006
MA104 Summer 2006
Prelim Workshop Summer 2006
Some NCG Links
NCG resource site, under construction
NCG Blog
Alain Connes' website