Hey everyone? Can anyone give a list of important topics in complex analysis one should have a good grasp of before starting to read about algebraic curves and Riemann surfaces? In particular, are $H^p$ spaces important?
Most good books on Riemann surfaces are self-contained, other than assuming a first course in complex analysis. If it wants to use those, it will likely talk about them.
Ah great I want to start reading from Rick Miranda's "algebraic curves and riemann surfaces" this summer but i wasn't sure about the prerequisites. Thanks!
@AlecTeal Proper equipment is pretty much required for good astrophotos. I don't use my largest scope right now because I don't have a mount that is sufficient.
@SaalHardali Be careful with modular functions. At least if you are the Sherlock Holmes type, habitually searching the darkness for the few identities that might be clues to your solution. In the modular realm, identities are the rule, not the exception. Blinding lights! These might burn out your brain. Wear sunglasses. (Take my userpic as a warning.)
The reason why it's not happening is not just because of the relative stability of I- and Cl-, but because (HCl and I-) is more stable than (HI+Cl-). If HI wwas highly unstable for instance, the reaction couldn't occur either.
Now i'll get back to the main question
A sn2 requires a nucleophile. I,Cl, Br are all nucleophiles and can take part in sn2 s. However, it's easier energy-wise to have an Sn2 with I than with Br, with Br than with Cl. That is because I is more polarisable.
Ok I'd like to make sure of one thing : what did you mean when you said 'Why can I replace br and cl in sn2 reactions?' ? are you asking why a sn2 which uses Br can also be done using Cl, or why Br-+(...)Cl -> (...)Br +Cl- occurs ?
the logic in polar aprotic solvent sis that a better base is better nucleophile so Cl->I- however in polar protic solvents its the opposite because cl engages in hydrogen bonding with solvent , decreasing its effectivity
@robjohn here is an amusing question I created today
$$\Re\left \{1-\frac{1}{1!}-\frac{i(i-1)}{2!}+ \frac{(i-1)(i-2)}{3!}+ \frac{i(i-1)(i-2)(i-3)}{4!}- \cdots \right \}$$ it's meant for fun. Thinking to add it to my book too.
@Chris'ssis I have to go to the vets. That is interesting. I will look when I get back. I've been dealing with MSE crap this morning. Sorry for being absent.
@Hippalectryon Before going, I wanna say that as regards my last creations it is possible that even Euler and Ramanujan working together to be in trouble with them.
@Chris'ssis Okay, this is where I'm going to draw the line. You're vastly underestimating the great minds of the past, and going around comparing yourself to them will get you nowhere. I know this is rich coming from me, but I think you need to learn to show some more humility.
If this comment leads to me being suspended from the chat for a bit, then so be it. I just said what I felt should've been said.
@teadawg1337 I love Ramanujan and Euler, I don't compare to them in that comment although I have no problem to say that I wanna become like Ramanujan or far beyond, but for the fact that my last creations use a certain technique (pretty complicated) I also developed, it seems hard even for a very good mathematician to easily get an answer there in my opinion. I cannot show humility anymore, there is no need for that.
@teadawg1337 I understand your comment. No problem.
@Chris'ssis it looks like something that can be solved with taylor series to me , is it so? i only know a tiny bit of real variable calculus so forgive me if i'm speaking nonsense
@Chris'ssis To me, you seem to be coming off as arrogant. In my opinion, showing some humility (maybe even feigning humility) will get you farther than acting like you're better than everyone else.
Maybe it's just because I'm in a super crappy mood today, I dunno.
@Chris'ssis Did you research to make sure that it is a method that you in fact developed, and hasn't been done before? That's what I do, and I generally end up walking away with a lesser opinion of myself. Perhaps I don't have the resilience to pursue a career in maths, I dunno.
All I know is that I'm in no position to give advice
I'm starting to get to that point where the material is becoming more and more scarce, and I guess that implies a higher probability of uniqueness in my work
And one of them, one of our grad students, had the nerve to waltz up to me at 5 PM yesterday, @teadawg, and innocently ask "What did I miss?" I told him it wasn't my problem.
I still remember a calculus student from my first year teaching here who missed one class out of 50 in integral calculus, apologized to me and told me that in the next quarter's class he would miss not a single one and he would get a higher grade. He was right.
@Jasper: If someone gets an A and doesn't need my help, I don't care either, although I do like to have class participation. But usually the ones who miss are doing poorly.
I'm paranoid of missing classes because I feel like at any given class, the professor might say something super important or something (besides the lecture)
I think lectures for me are more of an assurance from an authority figure on the topic that what I learned from the textbook is correct because I'm always scared of misunderstanding something I read and learning the material completely incorrectly, but an affirmation from a professor who knows the topic puts me more at ease
@Hippa: Sometimes they do look in the general area of your face ...
I've had several students with Asperger's, @teadawg. One in particular is extremely smart and extremely stubborn, has taken 6 classes from me, and gotten grades from C- to A- ... but all should have been B or better. Sigh.
He just refuses to read problems carefully and to give himself enough time to do a good job, insists on his creative approaches even when they fail :(
But he did ask me a really good question in probability (about the law of large numbers). I had to go off and think for about an hour to answer it and explain it.
Someone recently targeted me with downvotes, @Jasper, and it's happened once before. Occasionally I deserve them, and I have removed a few answers that were just bad.
I prefer to air grievances and not stay angry, but I have a colleague who hasn't spoken to me in over 10 years. And it's basically because he believes I did something I in fact did not do.
But I figure that if I have friends from more than 50 years ago, I can't be that horrible :P
I think I was here when that happened, @Hippa. He doesn't like your assumptions any more than you like Chris'ssis's assumptions that you're twice as old.
I don't usually care if people think I did something that I didn't, but it gets really annoying when other people that significantly impact your life begin to believe it and it messes up your life
I remember when I first saw Ted Shifrin in this chat, I thought he was a celebrity because my friend had shown me his differential geometry textbook the year before and he told me it was a famous textbook
Well, he surely approved/encouraged it, mr eyeglasses.
On the other hand, such projects rarely turn out the way one expected ... And if she's writing sentences like that, I can see it would be embarrassing.
@JasperLoy There is no such a thing. It was only your appeciation about that I think. Well, one needs some practice for a bit of progress. That's true for all.
I want to find the solution of the following initial value problem:
$$u_{tt}(x, t)-u_{xt}(x, t)=f(x, t), x \in \mathbb{R}, t>0 \\ u(x, 0)=0, x \in \mathbb{R} \\ u_t(x, 0)=0, x \in \mathbb{R}$$
using Green's theorem but I got stuck...
$$$$
I found the following example in my notes:
$$u_{tt...
Hello @DanielFischer!!! I want to write an algorithm that gets as input two strings s1, s2 and determines if the one is a subsequence of the other. So if we have for example abcdk and ak, is ak a subsequence of abcdk?
@DanielFischer I found this: A subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.
Can the integral $$\int_0^1 w_{xt}^2 dx$$ be written as an exact differential?? Can it be written in the form $$\int_0^1 \left (\frac{d}{dt} ... \right ) dx$$ ??
Can the integral $$\int_0^1 w_{xt}^2 dx$$ be written as an exact differential?? Can it be written in the form $$\int_0^1 \left (\frac{d}{dt} ... \right ) dx$$ ??
I want to find the solution of the following initial value problem:
$$u_{tt}(x, t)-u_{xt}(x, t)=f(x, t), x \in \mathbb{R}, t>0 \\ u(x, 0)=0, x \in \mathbb{R} \\ u_t(x, 0)=0, x \in \mathbb{R}$$
using Green's theorem but I got stuck...
$$$$
I found the following example in my notes:
$$u_{tt...
