I looked for the thing they were quoting Lee's book on, but wow, it's a one-word citation of gauge theory,.
"...just to get to the point where one can even think about studying specialized applications of manifold theory such as comparison theory, gauge theory, symplectic topology, or Ricci flow"
@AndrewThompson I once was working on a project over the summer, sent in a calculation. Realized it was wrong, sent in another. Did this three more times before sending an email saying "That's all garbage. I'm going to stop sending emails. See you on Monday."
Hahah. Had my algtop and cohomology exams right before christmas. (Two courses, however cohomology is half the credit.) Did alright in algtop, got my ass kicked in cohomology. Nice sensor gave the same grade for both.
I like the algebraic feel of it (co)homology, more so than what one sees in undergrad courses in commutative algebra. (Which might be why I'm studying homological algebra now.)
This is the kind of thinking that ruins you a lot in general. I'm not good at that. Really? How do you know that? Why don't you try to work extremely hard for years, 12-16 hours a day and see then who you really are and what you can actually do?
I teach my kids to never use this type of thinking.
@Danu I only identified a way of thinking, but maybe you just joked and think differently.
Sure, the idea is that after much work we change our opinions about ourselves.
I remember that during some of the interviews I had I was asked to identify negative traits, define, say, 3 (I don't know why they don't ask for 2 or 4, or 5) of them.
But the thing is that one cannot give such an answer. What one may consider a negative trait, it can be a positive one in certain circumstances. Then, I don't like to think I'm the whole life like a statue, but I permanently make improvements.
What's the idea then? Today I had the interview, right? In one week I'm far more better than I was one week ago. The idea is to see the potential of a human being.
Anyway.
BE EPIC IN EVERYTHING (and to put an end to the small talk)
okaly. what i'd point out first is that, while you've stated the boundary conditions in Cartesian coordinates, these aren't necessarily the most useful for this situation
now, there's two routes to take. one where you make an intelligent guess, and one where you derive it by hand. probably for now i'd suggest the second approach.
well, does that form work?
i.e. can it satisfy the boundary conditions?
if it's not obvious, you should plug in some values and see. so, for example, you can check $g(1,0)$ and $g(-1,0)$---both should equal 3.
correct. Cartesian coordinates aren't so helpful there, because both $x$ and $y$ change under rotations about the origin even though the domain doesn't.
