Hi.. I didn't know what a flag means, so I flagged a math question that I shouldn't. How can I unflagging it. I wanted to post it as Wiki but I see this option in the browser but not in Android app.
trying this, and one challenge is (tan 60/cot 30)(24*2-36/3)*2-2^3 , I'm pretty sure that is 64, but either the thing is broken or I'm doing the math wrong.
tan 60 = cot 30, so that should be 1. (24*2-36/3)*2-2^3 should be 64.
In a game where two players alternatively pick and replace a number with one of it's divisors other than that number, how can I determine who will win?
@Cbjork the sequence of partial tetrations should converge to a fixed point, i.e. a value $\alpha$ for which $x^\alpha=\alpha$. But $1$ is not such a fixed point.
You can skim through a good deal of G&P because you've already had manifolds from a more sophisticated perspective. You need to understand transversality, intersection numbers, degree.
I'll give you the exercise one of my undergraduate mentors gave me when I was taking complex analysis and G&P at the same time. He asked me to prove that when you have complex submanifolds of a complex manifold, intersection numbers are always non-negative.
I would encourage you to get a bit of breadth, but I know that's less the European style. ... Like analysis stuff is pretty important in geometry, too.
@TedShifrin Easy enough. If $f$ is holomorphic, determinant of $Df$ is the sum of square of the partials of the real and imaginary parts of $f$, which is obviously always greater than $0$.
This is just a straightforward application of C-R equations.
My general advice has always been that it's more useful/helpful (in terms of getting into good graduate programs) to take Ph.D.-level graduate courses than to write an undergraduate thesis. But still some do both.
@TedShifrin I am a bit uncomfortable with the $(z, \bar{z})$ coordinates, but doing this by identifying $\Bbb C$ with $\Bbb R^2$, this approach is not really different my approach...
It generalizes better to manifolds and higher dimensions, @Balarka. I didn't say it was distinctly different. We talked before about how the C-R eqns say $\bar\partial f = 0$, so $f^*dw = f'(z)\,dz$ ($w=f(z)$).
I'm glad all the students I voluntarily did reading courses with appreciated the time I devoted to them, rather than having a "I am paying for more" attitude.
even if that's true for his current position, that doesn't detract from the fact that the "non generous" thing to do would be to say: Piss off students, I'm gonna go have real money now.
@0celo7 People have their own work to do. Research/conferences. Respect that he's spending some time on you whereas he could have done his own research in that amount of time.
