Hi mathematicians. I admire you've taken the math field for your studies. I would like to know how you mathematicians think out of the box when it comes to solve math problems? Any books? Any tricks?
Okay so I saw a Riemann surface once, defined as "gluing copies of the complex plane together along branch cuts so that you can make a smooth choice of branch" (yeah it was in the old physics stuff)
Yup, that's the correct definition, Demonark, but understanding the former is worthwhile. However, it is thinking of explicit branched coverings of $\Bbb CP^1$.
It's probability at the college level. It's typically an upper-division course that requires multivariable calculus. But there's a lot more stuff in such a course.
You're doing the same stuff as before, best I can recall. It's still probability.
The idea is that you want to cut off the negative real numbers so you can integrate around a loop, but you lose all the info about it being multivalued. Now, I can see why that gives you a helicoid
I forget the statement. Every compact analytic (aka can be locally cut out by analytic functions) submanifold of CP^n is also algebraic (aka can be locally cut out by algebraic functions)?
I think two, because if you go to it along positive numbers (principal root) you're approaching infinity, if you do it along negative numbers you're picking up i
Okay, uh, I'm sorry if you go blind reading this but I'm gonna say one point over infinity, because sqrt(1/z) when you go to infinity goes to 0, and at that point you're single-valued. 1/z is also single-valued so...
(Also sorry I'm taking forever to respond, I'm still grappling with this)
Demonark: So you need to think of parametrizations at $\infinity$ in domain and range. You need a conjugation. But you understand what's going on, methinks.
@Semiclassical so tutorial was literal BS, we didn't do the quiz but spent an hour doing the "practice problems" I ended up just reading the text book and then the prof from the first section of the class showed up. I sent him an email asking about required readings and he never answered.
Assume $ Sup(S) + Sup(T) > Sup(S+T) $ where S and T are bounded subsets of the reals does my assumption that $ \exists \alpha \in \mathbb{R} $ s.t $ Sup(S) + Sup(T)- \alpha \geq Sup(S+T) $
it does, some of my collegues also comment it looks like a butterfly
As for the context, this is a potential energy surface profile as I rotate the base of some boron containing rhodium complex, I strongly suspecting there's a minima at around 175 degrees (the horizontal axis) but the SCF energies is so screwed that nothing can be determined from it
What is certain, is that there are at least two minima located somewhere at 75 and 300
Currently figuring how to fix it. But at least, it is a chemistry problem, and no longer a computer one
In the context of chemistry, having a potential energy surface profile tells you alot of how different isomers are related energetically, which is why when nearly 90% of the potential energy surface is blank is not very illuminating
and later on when moving on to transition states, it tells you the reaction profile such as how fast it is and how thermodynamically favourable it is
I think it is safe to say that regardless of what discipline, being able to plot a graph is always useful
