Recent content by diligence

The question I always ask myself is this: what would I do if I applied to every graduate school for math in the country but only got admitted to the school with the absolute worst ranking? Would I still decide to accept the admittance and pursue math? I think asking yourself questions such as...

I'm not an expert by any means since I'm just a senior undergrad taking grad courses and doing research, nor do I have much experience outside of PDE. But it certainly seems that PDE fits the mold for the type of problems that you describe. There are seemingly endless projects to work on, that...

No offense, but I think this is probably the worst advice you could possibly give to someone who wants to learn proofs and hopefully move on to high-level mathematics. Cheating? That's beyond ridiculous! It's about doing whatever it takes to understand the material, beyond that is...

It's not about your abilities. Rather, it's about your level of interest.

What should you do? Start with shutting the **** up, then move on to counting your blessings ;)

This is false. A buddy of mine just got into Berkeley with a quite low GRE score and a GPA in the 3.5-3.75 range. His letters of recommendation and statement of purpose were key. I also know another student who got admitted to Princeton. Surely he had a better profile than my friend who...

Summer: research in partial differential equations Fall: Geometry of curves and surfaces (intro diff geom) linear algebra (graduate) film analysis Spanish for high beginners (maybe French instead) History and culture of native north americans

Can i just use compactness and be done? (EDIT no i think that's wrong)

Homework Statement Let F be the set of all analytic functions f that map the open unit disc D(0,1) into the set U = \left\{w=u+iv : -2 < u < 2 \right\} such that f(0)=0. Determine whether or not F is a normal family. Homework Equations DEF'N: A normal family on a domain (i.e. open and...

Honestly, I think those are the type of thingsyou just need to figure out what works best for you. I don't see any general trends in my classes, some use pens, some use pencils, some use notepads, some use notebooks...I use blank paper and binders. The only thing I would recommend is either...

This is the pure truth right here. Just because some person is an expert on a topic (any topic) doesn't make he or she an expert on what it takes to become an expert (i think that makes sense). True, he has an IDEA of ONE way to become an expert (his way), but there are many paths to any single...

Textbooks are collections of the most important theorems since the birth of modern mathematics. It's taken ALL OF HUMANITY HUNDREDS OF YEARS to compile these results, yet you expect to be able to prove them all on your own in the amount of time you spend on your studies (i.e. much less than a...

Ah yes that makes sense, thanks. Apparently i need to be more careful. There's still something I'm a bit unclear about though. If one says that a function is never zero, does that imply there exists an ε > 0 such that |f| > ε everywhere?

I can't seem to wrap my head around this concept, I'm hoping you can help me out. Suppose you have a continuous function defined on some compact subset of the plane, say {0 <= x <= 1, 0 <= y <= 1}. I guess the function could be either real or complex valued, but let's just say it's real so we...

What do you think are the chances the drugs were in fact his? I honestly think they're basically slim-to-none, though it seems he's certainly guilty of lacking common sense no matter how the outcome plays out. Other articles report he claims to have traveled to South America to meet a model he...