Recent content by Anonymous217

I would give an answer, but I think Wikipedia does it best: http://en.wikipedia.org/wiki/Fractal_geometry

http://arxiv.org/list/math.CT/current I'd say that's pretty popular.

^ In particular (not sure about fractals), I haven't seen much work in foliations since the '70s, on Thurston and Haefliger's publications. I'm not too sure if there are any recent developments within the 2000's.

^ This is a very insightful post! I do worry that going to an REU at my stage might be going backwards in progress. That is, doing an REU in combinatorics or similar seems like a stepping stone into the type of grad-level research I'm already doing. Other REUs which offer pure-based subjects...

Thanks for the info. Is it really the case that research in one field might cause difficulties when applying to another? I'd imagine that any research would be good on applications (for REUs), regardless of the field. I'm aiming to do geometry/topology in graduate school (hence, the...

I'm talking about Math REUs. Thanks for the info though.

^I'll just ignore that post. Anyways, what's the competition like at (Math) REUs? Now that I know what makes a good application, I'm curious what the actual REU experience is like. For anyone who's been to one, how has your background fared compared to others? I've checked out a lot of past REU...

Perhaps a better correlation instead of using historical figures would be using IMO/Putnam winners. With this, it's easy to see that quite a few famous mathematicians have been past IMO medalists or Putnam fellows: Milnor, Shor, Elkies, Tao, Borcherds, Perelman, Ngo Bau Chau, Green, ... The list...

Foliations, Fractals? Haven't seen much work on foliations since Thurston and not much on fractals beyond recreation. No clue how obscure you mean though. There aren't really obscure fields that haven't been researched into anymore. Granted, if there was one, most mathematicians would jump at...

I'm applying regardless of a person's opinion, and you seem to completely misinterpret the main purpose of this topic: to see how I can improve my application, not to soothe my ego. And sure, you assert that I should just make my application as strong as possible regardless of opinion, but...

Topics like these give information on how to improve one's application. The main purpose of the topic is to learn the 'standard' criteria that makes a strong application, so I know how to better my own. I simply listed my own background as a reference, and I don't see what's necessarily wrong...

So I'm currently an undergrad at a top math university with ~3.6-7 GPA (probably all A's this semester). Here's my full coursework by the end of this year: Lower Division: Multivariable Calculus Linear Alg. & Diff. Eq. Discrete Math Upper Division: Linear Alg. Abstract Algebra Real Analysis...

I don't think that applies anywhere beyond undergraduate admissions.

Just to note, you're not proving the cartesian product, but the properties of cartesian products. Otherwise, you're claiming to prove a definition, which is logically impossible (?).

That's quite a bit of an exaggeration. I'd recommend reading Thurston's "On Proof and Progress in Mathematics" if you want more insight in perspective and intuitions within knowing mathematics (or fields thereof). Several of these meta-mathematics papers by famous mathematicians are practically...