Recent content by InbredDummy

"Usual metric" So I had to solve a problem proving that the antipodal mapping on the sphere is an isometry. However, someone told me that the antipodal mapping is an isometry on the "usual metric" on the sphere, and in particular, the antipodal mapping is not an isometry for any metric on the...

EDIT: I got it! I finally got it!

Thank you so much! I love the \phantom{} command!

Hey I was hoping someone could help me on this LaTeX problem. So usually when we have tensors, we have to be careful in how they are spaced and ordered. However in LaTeX it just lines it up and does not give me the order that I want. Can anyone help me with this?

Homework Statement Prove that S^n and P^n(R) are locally isometric. Homework Equations So I proved that the antipodal mapping A(p) = -p is an isometry. And I proved that the projection map from S^n to P^n(R) is a local diffeomorphism. I'm just not sure what the Riemannian metric on...

How do I obtain the Levi-Civita connection from the concept of parallel transport? So Do Carmo asks to prove that for vector fields X, Y on M, and for c(t) an integral curve of X, i.e. c(t_0) = p and X(c(t)) = dc/dt, the covariant derivative of Y along X is the derivative of the parallel...

Not many schools have a strong dynamics department or have a desire to hire such a researcher to be honest. You can count on your hand the number of schools that have more than 7 faculty members who specifically study dynamics. It might be tough, but do what you love.

Cornell has a really good Applied Mathematics department, alongwith University of Maryland. Stony Brook has a much more pure dynamical systems department; not really focusing on the applications and really more on just the pure theory.

first of all, what is your current education level? if you are in high school, it is very silly to think you'll know what you'll do for the rest of your life. I'm an undergrad math senior, i have taken grad courses in math, i have done research in math and i have tutored math; i still am not...

I'm almost in your exact same situation. I finished out my math major last year, none of the classes I'm taking right now are mandatory except for my topology course. I think I'm going to stick it out this semester. I hate quitting on things. If I do terribly this semester and bomb the GRE's...

I'm currently entering my senior year. Anyway, I really think math is taking it's toll on me. I get very stressed out from mathematics and I truly think that one of the only reasons I don't quit math is because I have put so much time and effort into it. One of my main problems with math is...

i did want to add: it is certainly not impossible just because it isn't the norm. it can't hurt to send out emails to universities you might be interested in taking an RA position in.

I can't believe the NRC rankings come out in December 2007, precisely when all my grad applications are due for PhD admissions!

Possibly, yes. Think about all those kids who place in the Intel Science Fair. This years winner (or the most recent Intel's winner) did research in string topology under a university professor. So yes it is definitely possible. Some suggestions: 1) Try looking for a research professor at a...

In order to be an RA you need to be a resident of the school to begin with. I have never heard of someone who does not attend the school being an RA.