Most college students in the US don't really want to learn, @Julian. Sad, but true. They're there to join fraternities and sororities. Not so true with the students who are the first in their family to go to school.
@DanielFischer: I solved the problem I mentioned to you. It relied explicitly on the chosen form of the parametrix. It's seems likely that if I had chosen a different one, it wouldn't have worked.
@ABeautifulMind: sure, the Tripos provides an exceptional undergraduate mathematics education. I don't know that that's evidence that the U.S. college education system isn't also strong.
And my friends in Europe tell me it's been diluted there, too, @Balarka. Everyone wants to copy the US. ... Of course, this doesn't apply to people like @Hippa.
Indeed we are, @Julian. I have excellent students who thrive on being challenged and learning, too, @Julian, but it's a minority. You just need to seek out teachers in good classes.
@teadawg: the high school I went to was just fine as well. I didn't say all high schools were bad, only that high school education in the U.S. seems to be /generally/ less well regarded than our college education system.
@DanielF: One can see that for a suitably chosen bump function $\chi$, if $P(D)$ is our differential operator, $$\frac{1-\chi(\xi)}{P(\xi)} \in \mathcal S'(\Bbb R^n).$$ The Fourier transform of this is our parametrix.
@AlexWertheim The problem is that the GPA system is standardized, and students attending less rigorous schools will appear to be better students than those being challenged academically
@TedShifrin: Oh, I didn't tell you the other great value of teaching complex analysis; upper divs have only one section a week, and it's on Thursday. Since I'm in LA, that means Tuesday is beach day.
@teadawg: sure, I can agree with that. I went to college with many very bright friends, but many of them had very easy high school experiences. I went to a high school where I was challenged often. The transition to college level work was much easier for me than it was for them. It catches up eventually.
@ted Today, I suddenly stopped struggling against my mental problems. I suddenly felt as if all the shit in my life just had to happen. It's a strange feeling.
(if i'm remembering the stuff i learned about that, this one-form really should have a second-order PF operator. but mathematica isn't coming up with one.)
I was waiting for the bus some days ago. My eyes sometimes water from the wind, and I kid you not, a tear froze to my eyelashes. Apparently, it was -13 that morning.
one of the things i learned from my time in grad school is that i really really don't care for this attitude of "you should be here b/c you love what you're doing. hence, if you're not working 24/7, then you don't really love it."
@ABeautifulMind There are different forms of accomplishment-brilliance is but one. You can do something requiring sustained effort, or discover implications of brilliant discoveries, or re-cast old ideas in modern language, for a couple examples
which in part had to do with me no longer understanding why i was in grad school, but the issues of anxiety / depression have played a big part in all of it
@Ilya, since it's mostly the same people here all the time and none of us knows that stuff, you shouldn't find it surprising that none of us knows that stuff.
one is that mental health issues are more visible than they used to be. so even if the base-rate were held fixed, i think it'd appear more prevalant nowadays
Well, it's still more advanced than I'd typically recommend, @Julian, but I won't fight you. But I'm waiting for you to get back to me on that topology question.
just getting more and more worn down by the process, failing to make progress on necessary goals, and having to struggle with cycles of anxiety/depression
@ABeautifulMind PTSD should get somewhat better with time. The OCD and depression might only respond to medication. It's really sort of touch-and-go with those, as everyone's brain chemistry appears to be "fine-tuned" to them, particularly.
@Ted: Hrm. I certainly don't know it all, far from it. But I would say I'm comfortable on most of D&F, save some of the sophisticate commutative algebra that comes later, and a bit of the module theory in the middle.
@Mike: well, perhaps I shouldn't have said sophisticated. Sophisticated for me, perhaps. I was thinking about some of the material on Grobner bases in chapter 9, and then the later material in chapters 15-18.
I don't really know of the relevance of Grobner bases... I guess they exist. I think they're one way to prove the Nullstellensatz, but not the way I'd do it.
