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Another Math Ph.D. applicant here. I'm interested in algebraic number theory. I applied to Berkeley, Stanford, Harvard, Princeton, MIT, Caltech, UCLA, and UCSD. Berkeley is the only one to have gotten back to me so far (an offer). Well, up until I got that offer I was very, very nervous...

Another possibility is the author has a disability that makes it difficult to write.

Oh I see your third question: how specific should you be about your interests. The answer, I believe, is "as specific as your interests are." If you already know you want to work on Galois representations in arithmetic algebraic geometry, then you should say so. If you know that you want to...

First, sorry to hear about your health problems. You mentioned that the surgery really has helped you: for that I am glad, and I hope you enjoy good health for many years to come. So I basically detected two questions in your post: how much should you write about your health problems, and...

1. Is taking a course just on Logic (or Set Theory) necessary? It is a good idea to learn axiomatic set theory if you're a math major. Whether you do it in a course or not is up to you. 2. Complex Analysis before, after or concurrent with Real Analysis? I don't think it matters unless the...

My applications to graduate school have been complete for a while, but now that fall semester is over it really feels like I'm waiting. AHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH! Anybody else going crazy?

Combinatorics likely isn't essential, but that also depends on what your goals are with your degree. If you're trying to gauge what an undergraduate "should" know: Does your program have degree requirements? These are likely a good gauge for "essential undergraduate material," though not...

All the things you've mentioned are essential. I recommend a first course in real analysis before topology, perhaps just because that is the way I did it. I think that topology is more abstract, and I argue that it is more canonical to see concrete cases before abstract cases. Honors...

clope023 : "I agree sleep is important but you don't need 8 hourse everyday if you catch my drift, lol" That varies from person to person. My point is, get as much as you need. (Not as much as you need to stay alive: as much as you need to be refreshed and operate at your best.) Getting...

Study things that interest you. You can only get to neverland if you find your happy thought. Have a positive attitude about your work. Exercise, eat well, and sleep. I'll say it again: sleep. It's a common practice amongst college students to stay up late and get up early to "get...

Do they round down? They say your raw score is C - I/4 where C is number of correct answers and I is number of incorrect answers. Somebody told me that on other tests, ETS tends to round down. I.e., they might use something like: C - ceiling(I/4) Does anybody know?

Tensor with the field of education.

Excellent. Thank you!

I have something like A \rightarrow B \rightarrow C I'd like to put function name's about the \rightarrow's, to replace the notation \phi : A \rightarrow B, \psi : B \rightarrow C. Is this possible? Thanks!

Might check out Berkeley's "Logic and Methodology of Science" degree. http://logic.berkeley.edu/

I'd say at least an undergraduate class on set theory or logic is probably a good idea. In fact, to get the B.A. at my school, this is a requirement. Rather on topic: A professor of mine said that knowing the compactness and incompleteness theorems of logic is something that most...

Looks like Caltech moved up a few spots. i.e., lucky pull from the hat :P

I emailed you, but I'll also respond with my thoughts on 260 here. First, 261A is probably a bit much, as I've not done any differential topology or geometry, and 214 is a prerequisite. (I'm not afraid to work hard, but I am afraid of blatantly being owned.) For 260, which sounds rather...

Thank you for those links ircdan. I'm going to try to simultaneous strategies as I research programs: building a list up from one with only a few schools and adding ones that are compelling, and a second list that starts long and that I remove schools from that are not compelling. I'll...

So I have another question: One thing I really enjoyed thinking about was the idea of a topological group, even though I barely got to spend any time on that topic. It's something I'd definitely like to spend some more time on in graduate school, and possibly even go into some area of research...

Yes, I see what you mean. I read the question sort of like the unique representation of vectors as coordinates of a basis.

That's interesting. How do you define the intersection then, in ZF? The resources that I've learned from define the intersection of a set to be the set given by the comprehension axiom. Are you specifically defining the empty intersection to be the class of all sets?

EDIT: I guess I assumed you were talking about ZFC... What theory are you talking about in particular? OLD: Well, if you define the intersection to be "the set of all things in all A_i", then intersection may not be well-defined (i.e., you're defining something that really can't exist). In...

I'm a little worried about the uniqueness comment, mathwonk. Aren't space filling curves necessarily not injective? EDIT: I guess these sets have the same cardinality. But a bijective map therebetween is necessarily discontinuous.

So I hope you'll forgive more questions: What would be some examples of the "decent" programs? Like UCSD, or farther down the list?

Yeah, Leon, thanks for your advice on improving my probabilities overall. That is obviously important. The thing with my situation now, and really the nature of my questions, I don't know how many schools I should be applying to (it's not free after all). I don't know how many top schools I...

Well, I did read what they wrote. Neither they nor you have answered my pointless question, whose vacuousness fills the title of this thread. Do you have any reason to say that my question is pointless?

Is it highly unlikely for somebody like me to be accepted to the likes of Stanford or Caltech?

It is still a considerable ways off from the time I'll be applying, but I'm trying to get an idea of what grad programs are realistic for me. My primary disadvantage is that I started at community college, and my first course there was a high-school level course (intermediate algebra). I...

I believe the theoretical answer to the difference is that a BA is supposed to reflect a broader but less deep education, whereas a BS is supposed to reflect a deeper but less broad education. That is what my advisor here at Berkeley told me. The reason I say theoretical is that in practice...

I followed this link and it is very easy and the documents come out looking really decent. I may eventually grab open office, but for now, this app will do the trick. Thanks all.

Homework Statement How do I create a PDF document with math symbols in it without spending a lot of money. Homework Equations The limit of my spending tends to zero. The Attempt at a Solution Should I just get acrobat and use the program I already own (rapid-pi) which helps to...

I have a feeling you'll see me around.

Ended up going with Berkeley. Thanks for your input!

What if one was accepted to both? Choosing a university is a serious task and I want to make the best decision. What criteria would you judge by as best to prepare for graduate school in pure math?

I am in the exact same situation... I am a transfer student going in as a junior and I have the choice between UCLA and Berkeley. From what I have seen, Berkeley is more prestigious, but UCLA is closer to home (making it a more convenient option). I do not care about my undergraduate alma...