Courses Benefits: taking graduate courses as an undergrad/contacting professors

[Bourbaki1123]

This is a two parter, feel free to respond to one, two or no parts:

1)I'll be taking a grad level sequence in mathematical logic and possibly another in analysis with measure theory. I also have taken a couple independent studies in algebraic geometry ( my university does not normally offer them).

I was curious about how much benefit achieving A's in graduate level courses can improve your chances of being accepted to a good grad school. Intuitively, it seems like it should at least demonstrate that I can handle the coursework required, so that won't be a problem. I would also hope that it would show some dedication to a particular area or to a couple of them (specifically my interest lies in logic and algebraic geometry, specifically applying topos theory and category theory to logic and computer science, unfortunately that is a little tangential to what I have on paper). I doubt it would convince anyone that I can handle creative research (I'm working on getting some more of that in), but will it give me a significant leg up?

Note: I am not basing whether I will take these courses on anyone's advice, I am/will/ have already taken them. I just want to see a few opinions regarding how they will affect my chances for getting into a, say, top 40 school.

2) If there is a professor who's research seems interesting to me (even if I don't have a full understanding, but at least have the gist of it), and I would like to possibly have him advise me for my PhD, should I just send him an email? Should I try to be fluent with his some of his research first or is that overkill (it may be a possibility for some of the people who I am interested in)? Is it enough just to be interested in his subarea but not be totally familiar with his very focused work?

 

[story645]

I was curious about how much benefit achieving A's in graduate level courses can improve your chances of being accepted to a good grad school. Intuitively, it seems like it should at least demonstrate that I can handle the coursework required, so that won't be a problem.

Unless you're school is also top 40, (and even then), I doubt they'll give your grad course any more weight than an undergrad course 'cause there's no real way to evaluate. You need to do well to show that you're not in over your head or biting off more than you can chew, but I think any real advantage is going to be that it shows passion and dedication to your topic by taking courses to improve your knowledge in it.

2) If there is a professor who's research seems interesting to me (even if I don't have a full understanding, but at least have the gist of it), and I would like to possibly have him advise me for my PhD, should I just send him an email?

You don't usually get your adviser 'til your second or third year into a phd program, unless he's the one who recommended you for the program in the first place (or other special circumstances), so you may want to hold off unless you want to do an REU with this person, but I doubt it'll hurt you.

Should I try to be fluent with his some of his research first or is that overkill (it may be a possibility for some of the people who I am interested in)? Is it enough just to be interested in his subarea but not be totally familiar with his very focused work?

I figure it's good manners to be somewhat familiar with a professors recent work if he's a total stranger and you want to bug him for a favor. Seriously abstracts only take about 15/20 minutes to read. Practically speaking, his grants could also be geared towards his focus, so that could be the area he's most actively looking to hire research students for.

 

[Bourbaki1123]

Unless you're school is also top 40, (and even then), I doubt they'll give your grad course any more weight than an undergrad course 'cause there's no real way to evaluate. You need to do well to show that you're not in over your head or biting off more than you can chew, but I think any real advantage is going to be that it shows passion and dedication to your topic by taking courses to improve your knowledge in it.

Fair enough. I suppose it doesn't hurt to be able to be able to present some detailed and focused areas of interest when you are applying either?

You don't usually get your adviser 'til your second or third year into a phd program, unless he's the one who recommended you for the program in the first place (or other special circumstances), so you may want to hold off unless you want to do an REU with this person, but I doubt it'll hurt you.

I'm not really looking to put in requests for an adviser, but rather to get to know researchers who's interests are not far away from mine. This is more of an effort to make connections.

I figure it's good manners to be somewhat familiar with a professors recent work if he's a total stranger and you want to bug him for a favor. Seriously abstracts only take about 15/20 minutes to read. Practically speaking, his grants could also be geared towards his focus, so that could be the area he's most actively looking to hire research students for.

I am actually talking about being up to date with the professor's research (reading full articles). There is one professor who's work interests me and I happen to know just enough algebra/computer science/category theory to read one or two articles in order to be able to look at his publications with a good degree of understanding. For most of the professors I am looking at this is not necessarily the case, although I have put in a lot of time into looking at faculty with research that interests me and I spend a lot of time learning about my areas of interest on my own.

My main concern is developing connections at schools that have researchers who interest me. I am not so concerned that they just be at some top 40 school; if the school were ranked poorly and it had a great researcher in a very narrow area that interested me I would choose it over a school with a stronger rank without such a researcher. What is really important to me is making sure I can do research that I truly find to be fascinating and that has some room to grow (i.e. it isn't going to fizzle out right away, which is very hard if not impossible to predict).

 

[story645]

I suppose it doesn't hurt to be able to be able to present some detailed and focused areas of interest when you are applying either?

It's required for just about every fellowship application and should be in your personal statement, so yeah. Granted, just like over half of undergrads change their major, something like 2/5 grad students change their research focus somewhere along the way.

I am actually talking about being up to date with the professor's research (reading full articles). There is one professor who's work interests me and I happen to know just enough algebra/computer science/category theory to read one or two articles in order to be able to look at his publications with a good degree of understanding. For most of the professors I am looking at this is not necessarily the case, although I have put in a lot of time into looking at faculty with research that interests me and I spend a lot of time learning about my areas of interest on my own.

I think you've probably got your basis covered. The goal is to know their work well enough that you're asking to work for them for better reasons then their name showing up in a keyword search.

My main concern is developing connections at schools that have researchers who interest me.

I don't know what year you're in, but do you still have time do an REU or research at a local school? Also, who are you currently working for? Do they have friends/connections at their old schools? They've been grad students and done post-docs, and if they like you they might be willing to rec you to a friend.