here's what i learned from reading math for the past 5 hours straight...

* how to prove dickson's lemma (which says monomial ideals are finitely generated)
* how to prove the hilbert basis theorem (which says ideals (monomial or not) in k[x1,...,xn] are finitely generated)
* what a grobner basis is, as well as minimal and reduced grobner bases and that reduced grobner bases are unique
* the S-polynomial criterion
* buchberger's algorithm
* how to use grobner bases to solve systems of equations, to test for membership in an ideal, and how to implicitize an ideal
* how to improve buchberger's algorithm with a few tricks with syzygies

don't you wish this was your afternoon too?

my brain hurts... time for mindless TV and eventually dinner ;-)

later dudes