Did the normal SAT three times. First time I did good on math, okay on writing, not bad but suboptimal on reading. Second time math got better and the others didn't. Third time I figured out the trick for reading and then it became good
Oh on a nicer side note: today in AG we proved that given 5 points in $\mathbb{P}^2$, there is a conic going through them. On this pset we're gonna prove that if no 4 of them are colinear, then this is unique, and if no 3 are colinear, then the conic is non-degenerate
@Daminark fun fact - you might ask the same question counting the number of higher degree curves (e.g. degree $d$ rational curves) passing through $3d-1$ points in $\mathbb{P}^2$. Turns out the answer for this was first predicted by string theory and proved later by mathematicians.
another fun fact is that it turns out that the answer is a recurrence relation with the initial data being the input that there exists a unique line passing through 2 points
Yeah, given the 5 points $p_i = [x_i:y_i:z_i]$, you can consider $v_i = (x_i^2,x_iy_i,x_iz_i,y_i^2,y_iz_i,z_i^2) \in \mathbb{A}^6$, and note that $\mathbb{P}^5$ is the parameter space of conics. Then $p_i$ is in the solution space of a conic $[a:b:c:d:e:f]$ iff $(a,b,c,d,e,f) \in v_i^{\perp}$, then the idea is that intersecting 5 hyperplanes in $\mathbb{A}^6$ will give you something of dimension at least 1
@Eric: What's annoying is getting requests in by dribs and drabs over periods of weeks. The closest you can get to getting all the letter requests to your profs during one or two days, the better.
And yeah I imagine. Probably gonna be a lot of work, especially since the process is apparently different for each place (e.g. one might ask for an email, another might ask to scan/sign/upload, another might ask 5 questions, etc, which was part of why one of my recommenders said not to apply top 6, since it'd be taking time for a likely throwaway app)
Demonark: Plus typically you have to fill in a bunch of questions and check-boxes. I sometimes slightly modified my letters of rec depending on the school.
Most places now have forms to fill in on the web and you can upload a .pdf, but there are occasional schools (like UGA!!!) that require you to paste in text on their web forms, which always annoyed me (as I had to strip out all my LaTeX commands).
Maybe UGA finally got their act together. I dunno.
Yeah, Peter said to apply top 6 except Princeton ("I wouldn't send my worst enemy there"), have UCLA/Michigan as sorta mid-level, and Cornell as a safety. I think he's probably a bit more confident than me
Marianna said the classic "Take a bunch of rankings and take the intersection of their top 50 schools, that'll give 40-45, and apply away"
@TedShifrin: It doesn't follow directly. However, index is invariant under a lot of stuff. I would try to argue by deforming an existing metric to a flat one near the boundary. But this is surely subtle. I expect say Melrose has figured this out.
And I appreciate your reading it. It was a good exercise for me and a couple hours on a plane.
@dalbouvet: Speaking of small worlds. I got into a Lyft last time I went to the airport. The guy picked up two more people, who were flying to Charleston, SC. I commented that I had lived near there. "Where," she asked. I said, "Athens, GA." "Oh, I went to UGA," she said.
"I was a prof there," I said. ... To make a long story short, one of her closest friends was one of my favorite students (in 3 or 4 classes), and I had not gone to his wedding (to which I was invited), but she had. Small world indeed.
TeXing things, as far as I can tell. It seems to have a lot of features, but (possibly thanks to the piecemeal way I've learned TeX) I don't really find much use for them.
@EricSilva That's a feature I've never had occasion to take much advantage of (except for once or twice, working on algebra homework at my old school).
At the risk of sounding self-aggrandizing, I don't really know any other people at my school who I could do math stuff with---they're all either applied math or just not far enough along in the program.
@dalbouvet I know there were some packages Overleaf supports that I was surprised to see that it supports (stuff like alternate fonts, or tikz-cd, or things of that nature) but I don't know if there's any master list of packages it uses anywhere.
(Maybe I shouldn't be surprised that it supports tikz-cd)
I used to use Palatino for letters when I used a word processor. I liked Lucida, typeset my algebra book in it (that's what Hatcher used, too, and people in here bitch about it all the time), but then decided I didn't really like it. So now I use Spivak's Times Roman font package and I love that, actually.
But Palatino doesn't have a math font to go with it, so that sucks for math.
Yeah, basically. It was the first on the test, the easiest as always - got all the other questions right; and sat there all cocky for 20 mins thinking 'man, it's a myth I'm not allowed to leave.'
