Recent content by eliya

Everything in topology has a bunch of different definitions that are all equivalent, but still can be confusing, and sometimes using one definition and not another is actually helping in understanding a problem more clearly. But it's also interesting, and is a little bit like walking through an...

30 isn't that old to start or to finish. A lot of mathematicians ``made impact" beyond their 30's. Andrew Wiles, for instance, missed the Fields Medal by a few months. As a general rule though, don't think about making an impact. Every mathematician who's active and writing papers is changing...

Wowza. Six chapters of Rudin in six weeks? How many times do you meet every week? I'm not sure what you meant by ``thoughts?", I'll take it that you ask how to understand the material quickly. I don't think there's a tired and true method to expedite one's understanding other than practice in...

I don't go to any of these schools, but I live in Chicago and can second mathwonk's opinions about UChicago. It's in a bad area of Chicago, but their math program is terrific. It's safe to say that other than UChicago, none of the schools you listed are well known for math. If you want to...

Everyone failed to mention this, but you should take a class that instructs how to prove things. Or at the very least get a book about it. I also got Spivak when I started Calculus, and while the theorems were the same as what I studied in Calculus, I couldn't understand the proofs. I took a...

Your undergrad institution is more than a name. Lowly ranked schools are usually the schools with small grad programs and a slim selection of classes. If you didn't take as many classes as some other students, then the gradschools you're applying to might think you don't have as good a...

I took two classes at a community college the summer before my freshman year. My intention was to take classes there for two years and then transfer to a four year university. I transferred after the summer semester and I couldn't be any happier. The biggest benefit is that universities...

That doesn't make you a nerd. Unless your definition of a nerd is derived from 90's american teenage movies. Everyone can be regraded as nerd. People who are into football? They can be regarded as nerds too. Fantasy football is super "nerdy", especially if you go into all of the statistics...

mathwonk is correct, of course, but it's not just that. I sometimes feel like people think that mathematicians sit in a study and work on mind boggling problems to a candle light. People have this very romantic (not in the sense of falling in love) view of mathematicians, or scientists in...

I got 113/120 two years ago. I didn't study for it, but it did help that at the time I was in a job where I was required to speak and write in English 8 hours a day. What I noticed is that you shouldn't really read the passages they give you. Read the questions and look up the answer in the...

I'm not in grad school (I'm an undergrad like you are) but here's how I think you can deal with your problem: First, identify what's your problem in those classes. Are they proof based? Are the problems just hard? and if so, in what way? Do they require long, arduous calculations, or is the...

UIC have a few logicians, and they seem to hold a few logic and set theory seminars. I don't know how that compares to Stony Brook or the other schools on your list that in terms of logic and set theory.

While I like Abbott's discussions, I don't know if I'd recommend it. Some of his definitions are actually shown in other books to be theorems. I don't think it's necessarily a bad thing, I just found it confusing. Another book that people like to recommend is...

I think you can email the program and ask if they look at the subject GRE scores or not. If they don't then there's no need to report them. I can't see how reporting a low score will help you in any way. On the other hand, if you don't report it, they can immediately assume that you just did...

My so far short experience with analysis books is that just one book won't answer all your questions. In fact, no book will answer all of your questions or explain every little detail for you. What's going to happen is that all books will leave some gaps for you to fill in. Some of them will say...