Depends a lots on what you are interested in. For high energy theory, in particular, you will need to know a fair amount of group theory, while analysis is less helpful in comparison.
Well, find me the http://en.wikipedia.org/wiki/Anomalous_magnetic_dipole_moment" of the electron, I dare you, with just addition of numbers. The anomalous magnetic dipole moment of the electron is a number, and it has been experimentally verified to an incredible precision.
You sound...
From what I noticed from sitting in class: specific concepts from abstract algebra is not extensively used, but you should at least know the basics (i.e. what is a group, subgroup, field, some knowledge about matrix groups, etc.). After all lie groups are still groups :)
Depending on the level...
I did that myself. The worst you would get a reply on the line of "we cannot consider anyone earlier". I got that one, as well as one very nice reply that tells me that I'm a strong candidate (followed by an official offer few days later). It certainly doesn't hurt to ask. (although I did feel...
I heard rumors about the selection process, namely, your application is forwarded to prospective mentors only if your application happens to contain certain keywords the mentors specified (maybe C++? ROOT? quantum mechanics?). Otherwise your application would never see the light of the day no...
Yes I was there for a summer, but not through the official CERN program. All I can say it's awesome.
I did travel over the weekends, but be aware that traveling in Switzerland is _expensive_! The people you meet will also be awesome, though you might end up going to a lots of meetings -...
1) It depends. Being a sophomore is perhaps a slight disadvantage as supposed to being a junior, but not by too much (again it depends on the places and the projects and whether you show that you know a decent amount of physics). REU admission is somewhat random because of the limited spots, so...
I know 2 people who have doctorates in two completely different field (I think they started one degree after the other was finished), and 1 who is currently pursuing some sort of dual-doctorate at this moment.
So yes, it is not impossible, but very, very, very rare. The logistics, however...
[Professor] Slater asked, 'Why do you think you should go to graduate school at MIT?'
'Because MIT is the best school for science in the country.'
'You think that?'
'Yeah.'
'That's why you should go to some other school. You should find out how the rest of the world is.'
--...
Not really. I did once got an A- instead of an A that I expected based on how well I know the materials (in fact I knew well enough to get an A+ in the second semester of the same course). Other than that, I almost always get what I expected, and in a few occasions was pleasantly surprised with...
Or take analysis and topology at the same time. It's a bit intense, but it will surely reinforce your command of the materials that are common to both.
It's not a myth. A grade below B means you probably should NOT be taking the class to start with, and below B grade is almost like failing in grad standard. There is little reason why a prof would give out non-A and non-B's in grad classes since grade matters much less in grad school than in...