Algebra Review
If you will be attending the PCMI undergraduate Introduction to Algebraic
Geometry course, please see the algebra
review sheet linked here. If you have not had a course in abstract algebra
or if your algebra is rusty, please do the exercises before the session begins. I have gathered some
relevant Wikipedia pages below, but you may want find a beginning text.
Contemporary Abstract Algebra by Gallian and Abstract Algebra by
Dummit and Foote are standards.
The part of abstract algebra you need to know
is ring theory. A topic that will be useful for us but is sometimes not taught
in a standard algebra course is exact sequences, especially short exact
sequences.
As part of the course, I will eventually ask you to do some computer work using
the computer algebra system CoCoA. You can find a link below. The program is
free, and it is easy to install. You may want to look at the online tutorial. I have
also included links to a couple other (free) computer algebra systems.
PCMI homepage
course homepage