Recent content by deRham

I think if you had a strong knowledge of both PDE and differential geometry (certainly subjects which are linked, but by the latter I understand emphasizing properties of the global objects, whereas PDE emphasizes actually understanding the differential equations), it would be possible to read...

I'm afraid someone will tell me "there have been 6000 threads on this topic" and start getting cranky ... I personally think this topic can't have particularly easy answers if it's still so hotly debated, so I'd be interested at least to be pointed to what some opine to be good discussions of it.

As an outsider to this discussion, I'm wondering if someone can tell me why string theory does have so much activity. Perhaps it is experimentally unfounded, though I would hope that there are people who found the mathematics of an established, successful (experimentally, and theoretically...

I don't have such an extreme example, but honestly it isn't uncommon to see someone in later 20s entering graduate school. Now, it is true that programs can and will ask what you were doing in the time in between, and at times will rule you out in favor of an applicant perceived (though not...

Probably the reason it's hard to make a distinction is that applied mathematics is usually studying "the mathematics of X" where X is some discipline that uses mathematics. And thus, mathematical physics might fit this description, yet the already theoretical nature of theoretical physics might...

Unfortunately, there is somewhat an element of truth (not about your intelligence, but to the philosophy behind the concern) ... for whatever reason, physics is generally a more difficult major to survive than English. This isn't to say that it's necessarily harder to make it in academia (I just...

For what it's worth, I think this is good advice (despite being a non-specialist in physics). There are always physics books that explain the mathematics better than some of the others, and I think differential equations is the sort of subject that, if you're not exactly a specialist in it...

You might be right, simply because the letter writers have a little extra pull, but quite honestly, students from all sorts of schools get accepted to the top schools, and I've heard a school like Berkeley is a little more willing to take students from "random" schools than, say, some of the...

I second theorem's advice that course selection has little to do with rank (just look at Princeton!). Usually, large departments have more courses to offer, but at some point, this breaks down - look at Caltech, a tiny program, as compared to programs 3 times as big. It offers a pretty good load...

@Zz - the question of the thread brings up a number of things, so while I share your sentiment that there's a large amount of information swimming around in unorganized form, the question of whether to switch from one discipline to another involves addressing misunderstandings or insights about...

Sure, it wasn't only textbooks, but my impression was he was talking about things meant to introduce a topic (at whatever level). You yourself mentioned that some books or sources or people seemed to convey things better, and I wonder if to some degree, this just means there need to be various...

Yes, king vitamin is right. Letters really help your application. They are essential for any competitive program. That said, doing a good job at everything you do is one of the few things you have serious control over. Assuming you do try to do a mini thesis with a professor, that's a good...

Maybe we are speaking of different parts of the establishment - is the article not more a criticism of how textbooks introduce mathematics while obscuring a lot of what goes behind the definitions? I of course think there is more to mathematics than solving problems - it is also understanding...

I don't think he was claiming it is lacking (and had a different point of view entirely), but I could be mistaken. I don't think this is lacking, like you say.

What homeomorphic might mean is the difference between being able to string through a linear algebra proof using familiar methods, and actually having a good idea of why you can and should expect that sort of result to hold, how it relates to the body of the theory, etc. It's a level that goes...