|Come again?||:||Call me N|
|What?||:||MATH 215A, Commutative algebra|
|When?||:||MWF 12:00-12:50 P.M|
|Office and hours?||:||MS 6310 and by appointment (give me at least 24 hours notice!)|
|Do you also check email at odd hours?||:||Yes. My id is nbhaskh AT math DOT ucla DOT edu (But please send short emails and not essays)|
There are several severely good books which one could use for this course. We'll mainly follow Atiyah-Macdonald's "Introduction to commutative algebra". You might also like to read from Eisenbud's "Commutative algebra with a view toward algebraic geometry" and the more elementary "Undergraduate commutative algebra" of Miles Reid from time to time.
We'll also learn (or review, as the case may be) some homological algebra - flat modules, projective and injective modules, Ext and Tor, and dimension theory. Apart from the usual suspects of "Introduction to Homological Algebra" (one by Weibel and another by Rotman), you might also like to check out "Rings and Homology" by James P. Jans and "Injective modules" by Sharpe and Vamos.But keep in mind, too many books spoil the broth!
"This brings us to the topic of prerequisites. It is a subject on which instructors frequently lie, claiming that whoever can count up to ten and recognize a few greek letters will immensely profit by attending their courses1" - Inta Bertuccioni.
A little more than that is required for this course (though recognizing greek letters will be an immensely useful skill to possess). Undergraduate algebra is essential (fields, rings, and modules). You should know also the classification of finitely generated modules over a PID, and the fact that polynomial rings over a field are unique factorization domains. Galois theory is not required.However, if you still feel inadequately prepared for any part of the course, feel free to talk to me during office hours so that we can work around the possible gaps.