Math 200C ~ Graduate Algebra
Suggested Timeline if you are just starting to study! (a rough guide)
Week 1 (Apr 11-17) go through your own notes from class to make sure
you understand everything in them - ask Prof. Small or Kat for help if
you find holes in proofs that you cannot fill in yourself
Week 2 (Apr 18-24) review groups (topics lists are below if you don't
like making them yourself) and take a practice test of some sort!
Week 3 (Apr 25-May 1) review rings (again topic list below) and take a
practice qual!
Week 4 (May 2-8) review modules (topic list below) and take a practice
test of some sort!
Week 5 (May 9-15) review fields (topic list below) and take a practice
qual!
Week 6? (May 16-22) if time allows go back through the noncommutative
material Small has been going through this quarter ~ he says it won't
be on the qual, but I don't believe him ~ he asked us to prove
something on our qual that used idempotents heavily even though he said
we wouldn't have to know that material
Week 7? (May 23-29) if you still have time take another practice qual
or two, or three
Resources:
My notes from 200 A/B/C with Lance
Small for the '07-'08 school year. These are not guaranteed to be
entirely accurate or complete or coherent, as I wrote them to help ME
study for the qual.
These are from Larissa Horn and Amanda Beeson who ran qual prep summers
of 2007 and 2008:
Linear Algebra: Topics
Group Theory: Topics, Timed
Problems
More problems on Linear
Algebra and Groups, and some on just groups
Ring Theory: Topics, Timed
Problems,
Modules: Topics, Timed
Problems, Timed Problems
More problems on Modules
and Rings, and more Rings, and more Modules
Fields and Galois Theory: Topics, Timed Problems
More Fields and Galois problems,
and even more
Sample Qual Questions
Practice Qual 1
Practice Qual 2
Practice Qual 3
Practice Qual 4
Practice Qual 5
Practice Qual 6
Notice that this material was originally designed for the course when
it was slightly different (with a larger emphasis on Linear Algebra),
and not taught by Professor Small, but was still very useful for
students doing qual prep in the 2008 summer after taking the course
from Prof. Small (I've put up both files where they seemed different
enough to both potentially be useful, and only the one with more
material in other cases). You'll notice that very little actually
changed from one year to the next.