I don't understand well enough to put this in the context of what you are talking about. But...
A virtual displacement is when you change the coordinates of the particles by an infinitesimal distance. This is different from a normal displacement in that this displacement does not take place...
From data points of past applicants who have posted their profiles online, this is the case for UCLA and basically any other decent grad program. What are you trying to say?
If you're transferring now as a sophomore and haven't started doing research/gotten an REU for this next Summer, you've probably missed the Caltech train. Straight A's with no research experience won't get you even in UCLA's grad program.
I graduated in the bottom 50% of my high school class. Graduating university with a 4.0 now to a top 10 grad program.
That said, I wasn't a complete idiot in high school. My SAT was high enough to get me a full scholarship to a decent state school and I placed near top in a national science...
Don't think that just because an REU is at a good school that it is a good REU. The math REU at Duluth in Minnesota is incredibly competetive yet at an unknown school. On the other hand, I personally did the Cornell REU awhile back and the quality of people/research was significantly lower than...
When choosing a graduate program, how much weight should be given to its US News ranking?
I've been accepted to two schools which fall within the top 10 for general math, but for my particular subarea in math, one of them ranks about 15 spots ahead of the other. Do people actually care about...
Physics is sort of a bastardized version of mathematics. The proofs are there more to help you remember things, and not because they're actual proofs. What book did you use for QM? Maybe try an axiomatic text like Shankar?
Given \triangle u = f(x,y,z) on a given body with vanishing neumann boundary conditions. I'm asked to interpret it in terms of heat and diffusion.
Since heat/diffusion take the form u_t = k \triangle u, I am a little confused as I there is no time term here. I think the answer is that u...
Given an arbitrary system, show that when Newton's equations of motion are written out for the system as a whole and for the different subsystems, they will always have a unique solution.
Is that any better? Basically asking to show that when all the forces acting are known, that Newton's laws...
How would you show mathematically that Newton's laws, when taken as given, always yield a motion and that this motion is always unique (given initial positions/velocities) for arbitrary systems?
D_H gave a pretty good hint. I'll give you a little more.
First consider the problem AB=B. Given A you can easily find all such B using eigenthings.
You can transform AB=A into this form by taking the transpose of both sides.
Very good problem if you came up with it yourself.
This is a common subject I'm sure, but for reasons unknown this information is difficult to find.
I have written my statement of purpose, all that remains is to customize it to each institution that I am applying to. How did you handle this?
Did you talk about faculty you think would be...
If one wishes to look at where mathematics has influenced physics, there are an abundance of examples.
What are some examples of physics influencing mathematics? The development of calculus would be one certainly, but what about in the last century?