SEP-Algebra
Here you can find the notes for each session. The students are supposed to read the notes previous to the class. During the meetings the qualifying problems listed at the end of the notes will be discussed.
First Week: Linear Algebra.
Second Week: Group Theory.
One recurrent problem in the Algebra qualifying, is to show that a group G
of certain order is not simple. The files below show how to do that for almost
any number less than 1001 for which there is such a group. The number not appearing
in the tables is 720 . Although there are no simple groups of such order, I
don't know a proof of this fact that uses only the standard material cover in
Math-741.
Third Week: Fields and Galois Theory.
Fourth
Week: Theory of Modules and Non Commutative rings.
Fifth
Week: Commutative Algebra.
Algebra Qualifying Exams:
These are my solutions to some of the algebra qualifying without solution in the math webpage.