@TedShifrin Especially at Berkeley these last few years. A lot of my female friends told me some horror-tales. A lot of the male grad students abused their positions.
@Mathein I doubt we're doing that. Our Prof said we're doing the basics of rings/ideals, a bit on PID/factorization in polynomial rings, Noetherian rings, general modules, and then modules over a PID
Given a skew-hermitian matrix $\Phi = (\phi_i^j)$ of $(0,1)$ forms (satisfying an integrability condition), I want smooth functions $f_i^j$ so that $$\bar\partial f_i^j + \sum f_i^k\phi_k^j = 0.$$
@TedShifrin The only thing that ever grinds my gears with exams where ~70 is an A (or something like that) is when scores are posted without any explanation of what they mean.
@EricSilva: Part of the issue is whether (and I believe the answer is yes) there's an analog of Frobenius for $\bar\partial$. It should just follow from $\bar\partial^2 = 0$ analogous to $d^2=0$.
@Daminark A professor at Berkeley was infamous for failing people (Alexander Givental). His 104 (1st sem analysis à la Baby Rudin) had an average grade of a D most semesters. By contrast, other professors had an average of B- usually.
But I was notorious for teaching tougher classes than most of my colleagues. My grades weren't so far out of line, except for a few ridiculous faculty.
@Mathei: In first-year courses I gave real grades. In more advanced courses, most faculty gave automatic A's. I conceded that I'd give an automatic B if you attended all the classes, but you had to do some work to earn an A.
@EricSilva: I'd love to talk with you about this when you have some time. :)
So the courses tended to be just the equivalent of regular core courses, but taught for students in the program. The math classes I created were outliers ...
@MatheinBoulomenos classes in America are for the most part easier than in Europe is the vibe I get, even your standard classes are probably at least as good as our honors
but then we don't really have "grad" versions of the basics. We don't have "grad algebra", because we think of general abstract algebra as undergrad material. That means our undergrad algebra sequence has to prepare the people for algebraic number theory and algebraic geometry, for example
Actual grad schools are really rare in Germany. We always do a masters first and I think that corresponds to the first part of grad school. If you're accepted as PhD candidate, you start working with a group of researchers from the beginning
So Newlander-Nirenberg is integrability of almost-complex structures, without assuming real analyticity. @EricSilva. I'll look more at what you linked me.
Well, we shouldn't be doing politics here ... but there are a lot of white supermacist American (and European, too) citizens who voted for Trump only because of prejudice.
It's just that so many right-wingers in the US brag about the "American values" and how they are superior to the rest of the world's culture and morals.
@TedShifrin i am litterally taking all of the courses listed in your playlist this semester plus some number theory wish i finished them this summer :(
Funny thing: the sub-countries (don't know the official English term, they're like states in America) in which there were the most demonstrations of "patriotic Europeans against the islamization of the occident" were also the sub-countries were the fewest muslims in Germany live and where there are the fewest refugees
@TedShifrin just want to make sure I understand some notion of sheaves.
So here each of the $A(X)$ etc is just a group right and we are looking for to construct the group element c from those $b_i$ i.e glue them in some fashion
do you want to know something funny @Daminark speaking about financial math
So in my last year of undergrad I had economics right. I never attended a class because it was super boring. Then, I studied 2 days before the final and ended up getting 90 class avg was like 65
@BalarkaSen originally I was having second doubts about doing math but after these roasts I'm dedicating my life to proving a point wrt roasts. Not sure which point, but a point.
@TedShifrin nah if anything the roasts are my motivation for being the way I am. I'd actually learn calculus if not for... Okay I can't say that with a straight face but you get the idea
finite groups are great. Sometimes when people talk about Lie groups I say "I'm very interested in Lie groups, especially zero-dimensional compact ones"
I won't spell out the whole representation theory of $D_4$ here, but it's not difficult to see that there's only one faithful 2-dimensional representation
Okay, I want to understand this in step by step. By $D_4$ you mean symmetry group of the square, just to clarify notation? I agree then; the symmetries of the fundamental square (hyperbolic rotation/reflection) should be symmetries of the whole lattice.
I don't believe you. What if I take a unit hyperbolic square in $\Bbb H^2$ with center at the origin of the disk and look at the rotational and reflectional symmetries of it?
(I mean I do, I am just trying to sound aggressive :P)
it's really just some basics of representation theory. You can classify all homomorphisms $D_4 \to \operatorname{GL}_2(\Bbb R)$ up to conjugacy and then you see that some are not injective and the others are not contained in $\operatorname{SL}_2(\Bbb R)$
Hey @ted, quick question: Gotta run in a second, but I was wondering...is there an old website at Georgie or elsewhere that would have supplemental materials to your video lectures? I.e. Homework assignments, etc... from the textbook?
Hello! $C^n$, where $n\in\mathbb N$, is the set of continuous, $n$-times differentiable functions. However, while reading a publication, I saw $C^\beta$, where $\beta\in\left[1,2\right)$. What in the world does this mean?
I wouldn't know, but as an outsider... I remember one student's poster on lattice diagrams of $D_{\text{something}}$... and just thinking, what's the point?
A while back I was learning about finite groups in an algebra class. I mentioned to a friend that finite group theory might be an interesting area of research to pursue. She asked something along the lines of "Isn't finite group theory 'done?' I thought that ended with the classification theorems...
