stuff i more or less know now that i didn't know 24 hours ago

* why the hilbert function of a monomial ideal is eventually a polynomial
* radical monomial ideals have square free generators
* prime monomial ideals are generated by variables
* irreducible monomial ideals are generated by powers of variables
* as associated prime to ideal I, is a prime ideal P for which P=(I:f) for some f
* a primary monomial ideal is an ideal with only one associated prime
* you can always find an irredundant minimal primary decomposition for a monomial ideal, by finding an irreducible decomposition, intersecting all the components that have the same radical, then throwing out redundant components. moreover, the associated primes of the ideal are exactly the associated primes of each of the primary components
* altogether you can tell if a monomial ideal is primary because it is if and only if for each variable that shows up in a minimal generator of the ideal, some power of that variable should also be a generator of the ideal (which is more along the lines of the general ab, b^n definition of primary than the associated prime condition)

seriously, people, my blog is going to be exceedingly boring for the next 17 days, modulo the super bowl. i wake up saying math proofs out loud... when i'm not actively studying new ones, i'm reciting what i've learned in the past few days out loud (as eric says, i'm leaking math)... i'm generally not in a frame of mind to talk to anyone about not math until i'm about ready to go to sleep, which is fairly late, so all my social interactions have to do with math...

here's an analogy for you:
check this picture out -- the chinese soldier jumping rope is math, the dog being forced to jump along is me.

woohoo for qual studying.