by B.Good » Tue May 31, 2011 6:42 am UTC
Capefeather, the only advice I can give you is that analysis and topology are not the only branches of mathematics, one of my favorite professors of all time did poorly in analysis as well and I'd say he's doing very well for himself (his field of study was algebra, commutative algebra to be specific.) However, if you wish to do some work in geometry, it will be almost required to have some knowledge of analysis because from what I know, a lot of modern geometry is done in the context of manifolds which requires some knowledge of analysis. Someone tell me if I'm full of it, but I think what I said earlier is the case. If you plan on going to graduate school, you may have to take an analysis qualifying exam at some point depending on where you go, however at that point, you will have taken more than a few analysis courses so it probably wouldn't be too difficult for any graduate student who puts a reasonable amount of work into it. Also, there are a LOT more branches of physics than General Relativity. As far as I know, General Relativity isn't as ingrained into the general physics curriculum as analysis is, as far as I know, so don't let that bring you down.
It's natural to get knocked on your ass as both a physics and math student, god knows in my (as of now) short stint as a math student at least almost minoring in physics it has happened to me. Keep your chin up and keep swinging, even though I know this is hard at times. Even if you find yourself not liking either physics or mathematics at the end of your undergraduate career, you will have qualifications that will allow you to have almost any job you could ever want.