The Graduate School Series: Part 1

A few post back I said that I would document my experience with the whole graduate school application process. Well now that I have a little free time (only have 1 final to study for this semester) now is as good a time as any to write it.

Before starting I guess I should mention where I did and did not get into. Then I'll talk about the whole process, and a short part on what are some things to consider when you finally make your choice on which school to attend.

Rejected:
Carnegie Mellon University
Columbia University

Accepted:
Cornell University
Duke University
New York University (*)
University of Florida
University of Wisconsin-Madison
* accepted but without financial support

SELECTION
The first thing you have to do is select which schools you would like to attend. Talking to professor at your current (or most recent) institution is always helpful. So talk to them about what schools are strong in your area of interest, and which they think you have an reasonable chance of getting into. One way to group your schools is: dream schools, reasonable chance of getting in, and "safety". Now keep in mind these terms are pretty vague, since all programs are competitive when it comes to offering admission to applicants.
Now I am going to assume that you know what area(s) of mathematics you are most interested in, or even which area(s) you don't like. I can't really comment on the process for selecting schools when you are unsure since I did not fall into that category. Anyway, I suggest that you begin your research on potential schools during the spring semester of your junior year. A great place to start is looking at the U.S. News rankings, also here is another useful site, but keep in mind these should not be the end all say all. Also talk to professors and see which schools have papers published in journals you enjoy. Plus, you will be surprised at how many internet forums there are out there that discuss what schools are good in what areas.
At this point you should try to get a list as big as possible, put a school on the list if there is the slightest bit of interest in their program. For instance I had Washington University at St.Louis, and University of Michigan on my original list, even though in the end I didn't apply to either school. Another thing to keep in mind is that while you are in graduate school your interest might change, so you should also take into consideration the schools activity in other areas. More on this in the portion about making a final selection.

Then when you have some more "free time" in the summer you take more in depth looks at each of the schools on this large list. You can even send out emails to faulty and current graduate students expressing your interest in their program and if they could provide you with any information that isn't available on the website. That being said, you should throughly look through each website before asking questions about the program. Otherwise you might ask a question who's answer is easy to find if you had put in any effort, and thus come off as appearing to be lazy, and who wants that for a first impression?
Now either in the summer or the beginning of senior year you will shorten this list to contain only those schools to which you plan to apply. The size of this new list will vary from person to person so not much can really be said. Though I would suggest it contain more than one school.

With your list in hand you are now ready to move onto part 2.