@TedShifrin Yeah, absolutely, that is good advice.
The thing that impresses me most about this student is her resilience, she was in my precalc class, came in knowing really nothing (came from a bad school system), fought discouragement the whole way and ended up getting an A in the class. Medal of honor stuff, I really was impressed.
The trouble comes, @AlexG, with students who ask for a letter after not having made any effort to distinguish themselves or get to know one. I had a business major in my probability class who was very smart, ended up with an A-, asked me to write for about 15 places for Ph.D. in different sorts of business. I wrote, but I couldn't say much. I told him he should have been coming to office hours and working on the more challenging problems to impress me :)
That's a good letter, @AlexG, particularly if you can now say she's gone on to do well in subsequent courses.
@arkamis I feel your pain though. It takes me a bit of time to remember how to use the parallelogram law at times (which might not matter yet to you, but will when you get to hilbert spaces/inner product spaces)
For example, since students only have a limited number of letters for REUs or grad school, etc., I often incorporate comments from a few other people because there just aren't that many letters allowed :)
@TedShifrin Yeah, I suspect that may have been me for one of my grad school letters :p a lot of my office hours people ended up being physicists, and I didn't want all my letters to be from non-mathematicians. In retrospect, I think I shouldn't have cared.
The other thing you might do, @AlexG, is show your letter to your faculty mentor (or a faculty member you feel comfortable with) and ask for suggestions/feedback on how to write such letters.
@AlexG: Not gaming. Trying to have maximum impact in as few words/letters as possible.
No one ever suggested this to me. I've just been doing it for the last 15-20 years. :)
I wish I learned general topology first before learning about metric spaces..I feel like knowing metric spaces already is messing me up in my abstract learning of general topology
No, mr eyeglasses, better to have concrete examples before ridiculous abstraction. Most topology courses use metric spaces as examples to go on and build on.
I am bad with the terminology they use in real analysis with the weirestrass continuity and limits there, but I get limit points when they are phrased using neighbourhoods
@Committingtoachallenge My professor defines everything sequentially..sequential continuity, sequential compactness, sequential limit point, etc. ($\epsilon - \delta$ continuity is a theorem for us lol)
I am saying I can't remember the $\forall \epsilon \gt 0, \exists \delta \gt 0, |x-a|\lt \delta \implies \implies |f(x)-f(a)| \lt \epsilon$ or something
Yes, one uses sequences and convergent subsequences all over analysis. I do compactness that way in my multivariable course, because it's more elementary and concrete than other approaches for that level.
Some people choose to do things for sound pedagogical reasons, mr eyeglasses, and I see no reason to think this person didn't do so.
You could also just belligerently deny the existence of infinite sets, denounce the real numbers as a sham, and never become good at analysis. That's worked pretty well for me.
@Mike: LOL ... Where, then? .... I've forgotten the bordism stuff. Is $\Bbb RP^3$ an element of order two?
I've had lower back and neck/shoulder, @AlexG ... and it all sucks. I was almost immobilized for several months with lower back agony about 10 years ago. The chiropractor totally saved me.
I just watched the 2015 math panel breakthough prize in mathematics. It think it was terrible, really awkward and it got kind of dark at moments, I also didn't understand anything Kontsevich said, and the moderator wasn't versed in the art of speaking either.
@DiscipleofBarney Yeah, they got a lot of major figures, Kontsevitch, Tao, Donaldson, Lurie, Taylor and Milner and started to ask them philosophical questions.
Oh yea @TedShifrin Someone in my class mentioned that they watched your multivariable calculus videos and that you explain much better than his professor lol
@Mike This looks maddeningly hard. A klein bottle doesn't work either : you can use a disk instead of S^1 in your bundle. That gives you a compact 3-manifold with boundary the bottle.
@TheEmperorofIceCream Just my OCD themes worsening. Sometimes, I do certain things and then things get worse. I did not expect those things I did would worsen things of course, and now I blame myself for doing them, which makes me feel even worse.
@infinitesimalsimplicio yeah, I didn't realize it but I saw some of the music mods talking and there seems to be a lot of mod teaching that goes on when new mods are inducted. one of the guys in the Music SE said its like a cross between being a janitor and a referee :D
@Committingtoachallenge The commutator of $a,b$ is defined to be $ab-ba$, so it is just saying the bracket operations you equip to the space of matrices is taking commutators. They are zero if they commute.
Lie brackets can be defined abstractly, so they want the operation to be explicitly defined.
Are you considering $\mathbb{R}^n$ a vector space over $\mathbb{R}$? if that is the case then yes, otherwise not necessarily, for example as a vector space over $\mathbb{Q}$ a basis (if you accept the axiom of choice a basis does exist) will have cardinality of the continuum. @Howcan
@Vrouvrou One generally does not ping random people to answer math questions in this chat. You can leave the question there and those who will answer will answer.
@Vrouvrou If you are a grad student, I suggest you brush up on your undergrad studies. Your foundation is pretty weak which is why you have difficulty in later studies.
