Let's compile a list of theorems we think every mathematician ought to know!
I'll start:
Stoke's Theorem: If M is a smooth n-dimensional manifold, and \omega is a compactly supported (n-1) form on M, then \int_{M} d\omega = \int_{\partial M} \omega
After reading about the
http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser" [Broken] experiment,
I thought of two interesting questions.
Here I have taken http://en.wikipedia.org/wiki/File:Kim_EtAl_Quantum_Eraser.svg" [Broken] and simplified it:
In the normal delayed choice quantum...
I go to NYU, and to remain in the honors program I am required to study abroad at least one semester (fall, spring, or summer). My university has study abroad "satellite campuses" where it's incredibly easy to study abroad. The problem is that the course offerings at these satellites are...
Is there such a thing as "non-action"?
I'm sure you've all heard this hypothetical scenario:
A train is barreling towards a junction where (unless you intervene) it will go down one path and kill two people who are tied down. However, there is a switch you can toggle that will send the train...
I've been thinking about this. Suppose you have an n-point set P in Rm which has the property that for any two points x, y in P, ||x - y|| < 2. If we fix n, what can we say about the smallest set S in Rm that contains P, allowing for both translations and orthogonal transformations of S?
If...
I am a current freshman at NYU, and I want to make it into Princeton's graduate program in math.
My Reasons for Wanting to Do This
I'll be frank: this is a very immature goal for me to have. Aspiring for the "top" graduate program reeks of a misplaced notion of achievement. Love of math is...