Logic behind masters programs admissions

Question

I'm 2 years out of undergrad and thinking about applying to some math graduate schools, specifically operations research and maybe financial engineering. I was a math major, with middling grades, and now I work in IT.

My question is this: it seems that even for not top-tier schools, a high GPA is crucial, as are great letters of recommendation, wonderful GRE scores etc. Why? If I'm willing to shell out 50k for grad school, and I've met the prerequisites, and I show an interest in the subject, why wouldn't a school want to have me? Is it purely so that they can claim they have a low acceptance rate?

In other words, if a grad school (again, not top 10 let's say) has a surplus of people who want to take that program, in a field like math, why not just hire as many professors as it would take to teach them?

I guess I don't get all this pressure to be perfect.

Thanks!

EDIT: I am referring to masters programs in particular, where stipends are not as common.

EDIT: Ok, Pete and Paul's answers make sense, given the current set up of grad school. I can imagine a different set up, however, that would make it less competitive for students, more profitable for professors and more about learning than prestige.

Answer 1

Some points:

1) The line that jumped out at me and probably most other mathematicians reading your message was "If I'm willing to shell out 50k for grad school". Stop right there. Most people who go to math graduate school get paid stipends; almost no one pays the full tuition themselves. It is a little unclear why you are so willing to do this: it certainly does not seem like a wise career move.

2) Graduate programs have limited resources. If they admitted more PhD students then it might in the long run lead to more faculty, but this is an indirect and uncertain process. Moreover every graduate student is a huge outlay of time and effort on the part of the faculty, and while programs are not being ranked according to their acceptance rates (I don't know that these statistics are even reported), they are certainly being ranked according to their completion rates. Math graduate school is a challenging proposition, and a lot of people who enroll realize it is not for them.

3) The requirements for getting into a decent math graduate program are not "perfection". (In fact, a "perfect" academic record may in practice mean that the student did not suitably challenge herself.) They are looking for an academic record that gives them confidence that the student will actually succeed in the program. If you admit a student who is merely interested and willing to pay but turns out not to have the skills and the drive to complete the program, everyone's time has been wasted, and lots of the student's money has been wasted. This is not a desirable outcome.

Added: Yes, the above remarks apply primarily to PhD programs. (In fact I didn't understand the meaning of MFE, and I thought that OR stood for "Oregon" rather than -- my next guess -- "Operations Research". It's best to err on the side of spelling out abbreviations on a site like this.) Master's programs generally do have lower entry requirements compared to PhD programs at the same institution, and yes, paying your own way is somewhat more common, although I would still not recommend it to any but the wealthiest students. There are in fact some good master's programs in mathematics that one could get into by making clear in advance that no financial support was being requested.

To say more than this really depends on the department. Some places have extra resources for master's programs, but many do not: the master's program takes place alongside the more populous PhD program and is administrated and taught by the same faculty members with limited time and energy that they are trying to apply in the best possible way. Master's students who are not strong enough to receive funding may in fact be the ones who require significant extra effort to get them to finish the program. They may also require faculty to meet and discuss tough questions like whether or not they should be allowed to continue in the program. Speaking from my own experience: a few years ago I was largely open to the idea that anyone who has the appropriate undergraduate degree and coursework and is willing to pay their own way should be given a shot in our master's program. I do not feel that way any longer.

Answer 2

You should not pay tuition to attend grad school, excepting possibly certain "professional" schools like medicine, business, law.

That is, grad programs admit a number of students for which they have funding, and have faculty/mentoring support.

Programs do not get tuition money back directly (as counter-intuitive as this might seem), but have to calibrate grad admissions to match the faculty they have ... the numbers of which are determined by essentially unrelated issues. But, approximately, programs will not admit you if they are not confident that you can succeed in their program. So you should not begrugde that judgement. And, srsly, such judgements are made with much experience.

Yes, there is the issue of prediction of success, which is an element that did not enter in undergrad studies. That is, programs do not "admit everyone" and then allow people to fail. Nor is it just a matter of "trying hard". Beyond a certain point, there is an issue of natural ability. It is true that this is highly non-trivial to understand/detect/encourage.

Yes, there is a considerable amount of disingenuousness in how we describe graduate programs...

Perhaps reaction-comments from the OP could help refine useful answers.