@BalarkaSen Let G be a topological group, let K be a compact subset of G, and let U be an open subset of G such that K ⊆ U. Then, there is an open set V containing the identity such that KV ⊆ U.
is it true that given $X$ hausdorff, $K \subseteq X$ compact, and open $U_1,U_2$ covering $K$, then we can find compact $K_1,K_2$ with union $K$, and $K_i \subseteq U_i$ ?
Let $M_n(\mathbb R)$ be the space of $n\times n$ matrices with real entries. Consider $M_n(\mathbb R)$ as a Lie algebra with the usual Lie bracket. Let $A,B\in M_n(\mathbb R)$ such that $B[A,B]=[A,B]B$. Prove that $[A,\exp(B)]=\exp(B)[A,B]$
@Chris'ssis Many users on MSE have been there once, looked at something and not really participated much. The people on chat are on site more frequently.
@evinda @JasperLoy The book used in my course is called "schritte plus", there are 6 volumes (two for A1, two for A2 and 2 for B1), I also bought a copy of "Hammer's german grammar and usage", it is by far the best reference on german grammar
@Jasper: Somehow I don't think of that as the point of a linear algebra class. It's a nice application at the end, but there's so much more to consider ...
Well, recommending books that are good for you is not necessarily a good thing for other readers ... You need to assess the level/interest/strength of the student/reader, as well.
@Balarka: They're slow for you, but they go 3 to 4 times faster than I would go in our usual linear algebra class. The multivariable class is our best students on campus.
so let's do $D=p-q$, @JC574. Then you'd have a meromorphic function with one zero and one pole, so it would give a holomorphic one-to-one mapping to $\Bbb P^1$. So the curve would have to have genus $0$.
But if $g>0$, you can't make it work, right?
yes, @Balarka, I stress geometry in (almost) everything I teach :P
@TedShifrin I never appreciated much geometry in my undergrad classes because it was mostly absent. But I finally began to when I saw material elsewhere.
That's also consistent with Riemann-Roch, I do believe.
@Jasper: I keep trying to get my differential geometry students to draw a picture and use what they know about a circle and basic trigonometry, rather than writing out a page of calculus computation (which takes way too long, anyhow). I have been doing it dozens of times in class, but they just don't work on understanding it themselves.
@TedShifrin I'm beginning to dislike non-mathematicians for their lack of rigor. I was told on Econ SE that $$\frac{dy}{dx} = - \frac{\partial U(x,y} / \partial x}{\partial U(x,y)/\partial y}$$ is how economists write this thing called marginal utility of substitution. But to me, that looks like a single variable expression on the left and a multivariable one on the right.
I taught a course called topological analysis, @Jasper, which I made up ... I did Munkres for 1 quarter and then put in a bunch of analysis for the second quarter.
no it's fine :) i'm just glad to have all the help you've given, and someone to talk to about this. I don't have any classmates taking this course really
