PCMI 2008: Introduction to Algebraic Geometry

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.

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