Initially I asked this question on math stackexchange but it seems academia stackexchange is more appropriate place for this.

Note: a question similar to that I’m going to ask was discussed here, but answers to the questions I’m going to ask were not covered there.

Basically, I’d like to understand how significant is the gap between lower- and higher-ranked graduate schools in mathematics. I’ll be referring to the USN graduate schools ranking. Let me fix the notation straight away. By ‘higher-ranked schools’ (which I will also refer to as ‘top schools’) I will mean top 10 (or if you want top 20) and by ‘lower-ranked schools’ I will mean schools ranked 20-40 (all according to USN).

What I understood from the question I provided the link to above is that being amidst ‘top students’ at a higher ranked school is more beneficial than being amidst ‘average students’ at a lower-ranked school. Also, higher-ranked schools may be more diverse and provide more opportunities in meeting people from other top schools as well as in obtaining a job in the academia.

But I still have a couple of questions.

The first one is about the first two years of the study. Is, in general, the instruction level at lower-ranked schools worse than that in higher-ranked ones? Also, are graduate corses at ‘top schools’ more difficult to master and to pass? If so, does it imply that one needs a better preparation (i.e., a stronger mathematical background) to succeed in a top graduate program? Also, does it imply that the students enrolled in a top program will eventually have a better mathematical background that will make it easier for them to conduct research? If you have anything else to say about the coursework at top universities in comparison to that at lower-ranked universities, I would appreciate it.

Secondly, in the question I referred to above (or elsewhere), some people mentioned that exposure to new ideas in various branches of mathematics (which is one of the advantages of top programs) is a consequence of the size of the department and the ‘quality’ of faculty/post-docs/students. Whereas I do agree that students at top universities are more knowledgable and creative, I cannot see why the other assertions hold. Correct me if I am wrong but the the math department of say Stony Brook or Indiana (ranked 25 and 34, resp.) is not smaller than that of Chicago or Columbia (ranked 5 and 9, resp.). Furthermore, the vast majority of professors in all of the places mentioned are alumni of Harvard/Princeton/Berkeley/MIT/Chicago/Stanford (i.e., a top school in my terminology); post-docs also come from very prestigious places to all of the four mentioned universities. So what makes Chicago or Columbia ‘better’ than Stony Brook or Indiana? Just their name? (Of course Chicago may have more publications than Indiana but I don’t think that graduate students feel it.)

This question may not be well fitted here. But I will be grateful, if somebody can share something in this matter.

I recently have joined in a research group, where everything was excellent until 2 weeks of my joining. My supervisor was very friendly when I met him first time in a conference. He was very interested to conduct similar work as of mine in his lab. So he showed interest and insist me to make an application for a vacant position in his group. He was very very happy when I cleared all formalities (made application, shortlisted, performed well in the interview and received an offer letter). After joining, I felt that I got a very good group to enhance my research skills as all colleagues are very friendly and helping each other. But 2 weeks later, when I met my supervisor to discuss about my work, he suddenly gave me many difficult tasks, many are very new to me and out of my skills and told that every should be finished by another 2 weeks. He also told that, please do everything by yourself and never disturb to other colleagues. When I discussed with other colleagues about this, they told that he is very strict, not a good person and his intention is to dominate all. My question is how would I know about these things before joining his group? Now I can’t imagine how to continue work in this group.

I had the chance to talk to two professors last week regarding admission to the PhD program. After I was done, I was told that I would be invited for an on-site interview, if admitted.

After not receiving any feedback from the school, I emailed them and found out that I was not invited to the interviews on the campus. Now they’re just telling me to wait and I may be invited for another visit in the future.

This is a problem for me as I need to start looking for funds in another programs that I have been already admitted to (The one I am waiting on is my first choice).

What would be the best approach to handle this kind of situation?

Thanks.

How to deal with fellow students who put little effort on their part while solving assignments, and sometimes ask you to spoon-feed them solutions. Lot of times these students end up scoring more on the assignments on average, because I don’t generally feel inclined to get any sort of help on assignments, and am content with submitting my best solutions.

It is very difficult to avoid these students entirely cause grad classes are typically small and you don’t want to end up alienating them.

Does he know immediately (from some internet / intranet access) which students in his classes are undergraduates, masters students, PhD students, non-degree students? Does he typically have access to his students’ transcripts, thesis work (dates submitted / approved / topic), and knowledge of his students’ academic / research advisors?

I have background in math, cs and stat(BS and MS degrees). I may apply to grad school. What I like most is discrete mathematics/combinatorics and algorithms.

However, it seems to me that the work of most of the applied math researchers is just to write papers and the results of these papers are not applied anywhere(almost always) and by no one.

To what extent am I right and can you point out departments and institutions where this is not the case(i.e. the departments have strong relations to industry)? One such example is the IEOR department at Berkeley, IEOR in Columbia Univ. is similar. I guess that several EE departments could be other counterexamples.

Note: I know about some theoretical CS depts and programs, like the ACO programs in CMU and Gatech, but they look too theoretical, eventhough their curriculum looks great.

One of my labmates used to be the “star student”. Super smart and productive, really engaging to talk to etc. However, it seems like overnight, he’s become a totally different person. He’s stopped coming into lab for multiple days in a row, has stopped making any progress, and is starting to complain a lot. He seems very frustrated with our advisor and the lack of support, and bad-mouthes him every chance he gets now. I’m pretty sure our advisor has noticed, but is just ignoring this or even avoiding him. I’m afraid this student might be dropping out soon. This isn’t really affecting me so much, but I’m just wondering why someone would change so suddenly. As a new grad student, I hear a lot about the stress of grad school, and I’m concerned about whether this is a common occurrence? It wouldn’t stand out so much, but he was actually one of those “oh, he’s going to open his own lab one day” type person. What can I do to avoid a similar burn-out, and is there anything I can do as a colleague? Out of curiosity, is there anything the PI should do?

Let me briefly specify what I mean.

Let’s say that there is a famous working scholar in your field of interest. Is it a good idea to email him/her saying that you admire his/her work so much that you would love to if he/she would become your advisor?

It’s clear that you have to be enrolled at the institution where your advisor normally works. But you would only apply to that institution if he/she promised you to become your advisor. Is this a rather good or bad way of choosing a graduate school?