Recent content by modnarandom

How is the Implicit Function Theorem listed here (http://ocw.mit.edu/courses/mathematics/18-965-geometry-of-manifolds-fall-2004/lecture-notes/lecture4.pdf) a generalization of the usual one seen in multivariable calculus (see https://en.wikipedia.org/wiki/Implicit_function_theorem)? I've also...

Ok, thanks! But doesn't your first post assume that you're considering the limit as n goes to infinity? Or is the definition something else? I guess I'm not sure how this definition follows from o being a function continuous at 0.

Oops! I forgot to mention that I initially interpreted o(||x - x'||) to be the kind of little o you mentioned. It's just that I don't know how it makes sense in the context of the definition of a derivative of a map between vector spaces.

I'm trying to understand the definition of maps between vector spaces (in normed vector spaces) listed in the following link: http://ocw.mit.edu/courses/mathematics/18-965-geometry-of-manifolds-fall-2004/lecture-notes/lecture3.pdf On the surface, this seems similar to what I expected from the...

What are your thoughts on the fact that most math PhD program applications do not contain interviews? Consider the following link: https://quomodocumque.wordpress.com/2011/11/21/are-math-departments-better-at-recruitment-than-elite-financial-firms/ One of the comments expresses concerns about...

It's great that you have a lot of these things out of the way already! But I'd like to repeat other people's comments about how well do you actually know the material in classes you've taken. I've found that a lot of lower-level classes are computationally focused and don't actually require a...

What is a reasonable analytical writing GRE score for a science/math/engineering programs? I had something like a 4.5/6.0 which seems kind of mediocre. I talked to some professors about why the general GRE is required, but they said that it was mainly aimed towards testing international...

What do you consider to be missing definitions in Rudin? I think the comment above was specifically about missing steps in proofs.

Hi there! I feel like I'm in a similar situation with regards to having a hard time with everything. I'm a math major and I'm also at a pretty competitive university. Since I have much less background than a lot of my peers, I end up taking forever to pick up things and have a lot of difficulty...

I haven't had a phone interview before, but it looks like SMALL used to do them in the past (see https://www.physicsforums.com/showthread.php?t=576725). Maybe you could look at that thread or ask people who applied there before?

Do grad school admissions for math typically involve interviews? I can't find this on the official websites, but it seems like some do from a few friends I talked to. If so, what are they like? Does it mainly involve talking about what sort of research you are interested in doing?

Thanks for the response! Yes, I definitely expect it to be intense. Maybe I should have phrased it as "before starting to do research". One of my reasons for considering it is that I want to better understand what areas of math I'm interested in studying later and look at how things are studied...

I think someone might have mentioned it earlier, but what did people who did Part III in Cambridge think about it? Why did you go there? Who would benefit from it?

I don't think so, but to be honest I'm not sure. I originally intended to study something that was much more "useful" and then ended up doing something else since I enjoyed that lot more. While I thought that the first topic was more "useful" for society, I really didn't enjoy studying it. I'm...

What do people who studied theoretical math (or some other theoretical subject) think about whether their work had applications in the real world? I study the subject since I really enjoy it, but I can't think of a good reason about why my work could be "useful" and how I can use it to help...