Mathematics GRE

[ezrast]

So, I'm scheduled to take the GRE Subject Test in math next month. Anyone ever taken it? Flipping through the practice exam they gave me, it looks like the plurality of questions are calculus (probably my worst area, yay) so I'm planning on studying mostly that, plus doing a solid review of algebra and a cursory one of analysis, geometry, and statistics. I still have all my math books from college, so I'm not short on study material, but if I do a straight read-through on the areas I'm muddy about it's hundreds and hundreds of pages of reading. If I do it that way I will have spent more time studying for this than for everything else in my life combined (which isn't saying much) though I will if I have to. Any tips?

[IainC]

The good thing about calculus is that most of it is very derivative.

[Merusk]

I hope that's the limit of the higher math puns.

[ezrast]

You can't talk about calculus without making puns. They're pretty much integral.

[Hawkbit]

Thread subject is absolutely irrational. 

[Lantyssa]

I'd look for all the practice tests you can online and study whatever is on them.

[IainC]

I'd look for all the practice tests you can online and study whatever is on them.

 

[Selby]

I'd look for all the practice tests you can online and study whatever is on them.

Get the study book from Kaplan or whoever is making the good one these days.  They come with a CD with practice tests like Lant says.  You can just take practice tests over and over again to get an idea of what kind of problems they are looking for (AND how the test is arranged as it is computer based with a time limit).  When I took it (back in 2002) it was really straightforward once you had taken some practice tests a few times and I did pretty well for not having overly studied the material in depth in a year or two.

The biggest thing to remember is they are after how well you can take a test, not how well you can do math.  While some of the problems may look complicated, they are merely repeat patterns of a certain type of problem that you can learn to do quickly, which is the big key to taking the GRE effectively.

This is all with the caveat that things haven't drastically changed in the last few years ;-)

[Ingmar]

The general ones are kind of a joke, but the subject GREs don't mess around, from my own experience and everyone else I know who has taken them for the most part. When I took one years ago (music) I came out of the quest feeling like I did terribly, and my score was not great in an absolute sense - but it was still 70th percentile. So, by all means, don't take it lightly, I don't know anyone who has come out of a subject-specific GRE saying "pfft, that was just a formality."

[Nebu]

Subject GRE's are to be taken seriously.  A couple of notes:

1) The general GRE just changed format recently.  Check to see if this is also the case for the subject exams as old study guides may be less useful if they haven't adopted the new scheme.

2) If subject exams haven't changed format, you can buy older study guides and practice materials used on Amazon for cheap!

3) The chemistry GRE was hard.  I imagine the math GRE is a nightmare.

[Lantyssa]

Yeah, Chemistry was a pain.  I did pretty well, but I didn't walk away from it with anywhere near the confidence I did with the general GRE, SATs, or ACT.

[Khaldun]

Subject GREs are to be taken seriously if you're using them to apply to subject areas.

The GRE in general blows: I measure the intellectual seriousness and independence of a grad program in inverse proportion to how seriously they take GRE scores. But I can do that because I'm in a secure situation, it's a luxurious opinion.

[Murgos]

The GRE in general blows: I measure the intellectual seriousness and independence of a grad program in inverse proportion to how seriously they take GRE scores. But I can do that because I'm in a secure situation, it's a luxurious opinion.

Hmm, MIT doesn't require the GRE so maybe you're on to something.  Then again, Harvard does, so maybe your not.

[Ingmar]

I suspect that like anything it varies from field to field just how useful a measure it is.

[Lantyssa]

GRE scores help, but they're a small part of what most programs will look at.  Having undergrad research, papers, extra-curricular activities, or a faculty member who 'sponsors' you will carry far more weight.  Short of a perfect or an abysmal specialty score, it won't matter much.

[Nebu]

Due to rampant grade inflation in the US, GRE scores help normalize ability.  I routinely see students with high gpa's and low GRE scores and it's a red flag.  When I'm looking for graduate students, I'd much rather take someone with a decent GRE, good letters, and experience over someone with a 4.0, low GRE, and no experience.  

MIT and Harvard are looking for stars.  They care little about these exams as the applicant pool they get is loaded with proven talent.  The rest of the programs in the country are begging for their table scraps.  (this is an obvious exaggeration, but you get the point)

[Khaldun]

MIT is full of real talent. Harvard's grad programs, to be honest, are a big mixture of real talent and asskissers who are chasing the name. MIT really puts a lot of intellectual food on the table; Harvard is about buying the name.

In the humanities, honestly, a good GRE score means absolutely zilch to me if I'm evaluating whether someone's got the chops to do well in a doctoral program. GPA isn't altogether that interesting either--it's really about how they write about what they want to do in their program of study and research, which tells you instantly whether they know what they're getting into. In fields where the outputs and expectations are more standardized, maybe a standardizing measure on the way in is a better way to figure out who is going to flourish.

[Goumindong]

Science is all about defining a formal system and then empirically testing the results. To do that you need a lot of math. But its real math, logic, proofs, knowledge of past proofs and techniques that make solving (and therefor proving things) easier. I am going to assume that this is as true in Chemistry or biology as it is in Physics or Economics

Since none of that requires computation and that is mainly what the general GRE is; I am not sure how anyone can really use it as a basis for the quality of students. I say this mainly because there is no doctorate program in econ that I know of that takes any scores but the general GRE. Which makes me quite unhappy because I did not ace the test due to dumb errors(both times, different dumb errors at least), which for econ means you don't do well. [E.G. my percentile score on the verbal was higher than the percentile score for acing the general math section]

The tests seem like they should be a filter more than a criteria. Throw out the low scores since you can't be bothered to read the applications and then pick from letters and grades/institutions

Harvard's grad programs, to be honest, are a big mixture of real talent and asskissers who are chasing the name

I don't believe that. Maybe at the masters/law student level. But you can't get into a doctorate program at Harvard unless you're amazing. If you're an asskisser chasing the name then you've got to be an amazing asskisser. I don't believe that an asskisser can easily fool the professors that they did their undergraduate/masters with. And frankly i would wonder why you aren't having professors making your recommendations if you're not going into that field.

[Ingmar]

You're talking about the general GRE, though, which is just a glorified SAT. Pretty sure everyone else here is talking about the subject GREs, which are on a whole different level.

[Goumindong]

You're talking about the general GRE, though, which is just a glorified SAT. Pretty sure everyone else here is talking about the subject GREs, which are on a whole different level.

I know. I qualified my statement.

[ezrast]

Thanks for the comments all.

As for the general test being a joke, the stats on the GRE's website say 29.7% of test-takers going into math programs score an 800 on the math part. So it doesn't even distinguish between the upper 30% of my competition. We're just all in the 70th percentile.

[Murgos]

Good entrance scores are a requirement, if you need financial support.  The real secret is that if you're paying your own way they'll let you spend your money and find out for yourself if you can make it.

The magic words to put into your statement of purpose, "I will not be seeking financial aid." opens the doors, or at least lowers the bar to a reasonable height, to even the MIT's and Harvard's of the world.

[Khaldun]

That is terrible advice for a doctoral program in an academic subject.

If you are admitted in a doctoral program in any academic discipline, the normal 'package' is tuition waiver + a stipend. (Usually the stipend is conditional on being a TA or teaching in your 4th year, while working on a dissertation). If the program is very good and there is an advisor you especially want to work with, it might be worth going if you just get a waiver, and hope to be added to the list of students receiving a stipend. In academic disciplines, doctoral students are supported in this way by universities because they are on a net basis money-savers (because they supply cheap teaching labor).

A tuition waiver is rarely described as "financial aid". If you are admitted to a program of doctoral study and asked to pay tuition, it literally means they don't want you but they think you're not so awful that it will be embarassing to have you around. They see you as someone who is helping to pay for the students that they do want. You might think, "Well, I'll go and I'll be so awesomesauce that I will reverse this verdict on me" but this is an exceptionally hard thing to do, and might only work in a discipline that has extremely hard, well-defined, relatively objective standards for excellence. Most doctoral study involves more subtle and insidious kinds of standards for achievement, and much of what you achieve is negotiating the byzantine culture of your department, your discipline and the academy as a whole.

In general, I tell undergraduates who are applying to Ph.D programs in academic disciplines that if they're not offered a tuition waiver anywhere, they shouldn't go to graduate school. The only time I'd ever say it's worth paying anything out of pocket to get a Ph.D is when it's a necessary credential for a high-paying profession outside of academia that has a fairly large number of jobs. Say, if someone wanted to do a Ph.D in engineering and had zero interest in being a professor of engineering, and they were confident they had the basic skills to get through the program, that might, just might, be worth it. It is never ever worth it in most disciplines.

[Murgos]

That is terrible advice for a doctoral program in an academic subject.

If you are admitted in a doctoral program in any academic discipline, the normal 'package' is tuition waiver + a stipend. (Usually the stipend is conditional on being a TA or teaching in your 4th year, while working on a dissertation). If the program is very good and there is an advisor you especially want to work with, it might be worth going if you just get a waiver, and hope to be added to the list of students receiving a stipend. In academic disciplines, doctoral students are supported in this way by universities because they are on a net basis money-savers (because they supply cheap teaching labor).

A tuition waiver is rarely described as "financial aid". If you are admitted to a program of doctoral study and asked to pay tuition, it literally means they don't want you but they think you're not so awful that it will be embarassing to have you around. They see you as someone who is helping to pay for the students that they do want. You might think, "Well, I'll go and I'll be so awesomesauce that I will reverse this verdict on me" but this is an exceptionally hard thing to do, and might only work in a discipline that has extremely hard, well-defined, relatively objective standards for excellence. Most doctoral study involves more subtle and insidious kinds of standards for achievement, and much of what you achieve is negotiating the byzantine culture of your department, your discipline and the academy as a whole.

In general, I tell undergraduates who are applying to Ph.D programs in academic disciplines that if they're not offered a tuition waiver anywhere, they shouldn't go to graduate school. The only time I'd ever say it's worth paying anything out of pocket to get a Ph.D is when it's a necessary credential for a high-paying profession outside of academia that has a fairly large number of jobs. Say, if someone wanted to do a Ph.D in engineering and had zero interest in being a professor of engineering, and they were confident they had the basic skills to get through the program, that might, just might, be worth it. It is never ever worth it in most disciplines.

Or, you know, you have a job that pays tuition.  Then it would also be worth it to go to a better school.

Or, you have the money and would rather go to this top university that didn't offer you a position vs the middle of the road one that did.

Because, if you had read what I said I was explicitly talking about top tier schools.  A PhD from MIT or Harvard or Stanford or any of the top 10 or so, even if it's coming out of pocket (preferably not your pocket, just not the schools) is worth a lot more than a full paid ride to Podunk U.  I doubt if any university in the world is going to ask how you funded your education as a hiring decision (because that would be a logical fallacy, how you funded your education has no bearing on your ability to perform a task).

Anyway to address the point you did make, even if it wasn't really mine that you were addressing, if someone wants to go get a PhD in a subject and they can afford it, really who the hell are you to tell them not to?

[Nebu]

A PhD from anything but a top 25 school is essentially worthless in most fields outside of business and education unless a) you already have a job you love that will promote you because of it or b) you're an underrepresented minority in that field. 

Aside from that, Murgos said it well enough already.

Anyway to address the point you did make, even if it wasn't really mine that you were addressing, if someone wants to go get a PhD in a subject and they can afford it, really who the hell are you to tell them not to?

[Khaldun]

This is only sort of the case if what you're looking for is an academic job. There are in a few cases fields where a particular university has an overwhelmingly strong reputation in that field but not in general where it is very worthwhile for a doctoral student to be studying. Equally, there are general "top 25" institutions where you absolutely do NOT want to be studying certain fields because they don't have good people in that field. In many academic disciplines, it's less the institutional reputation and more the reputation of your advisors that gives you social capital when you go onto the academic job market.

In any event, if what you're looking for is to be a professor, never pay to do a doctorate, no matter how prestigious the institution. If you have other professional goals in mind where a Ph.D is an important credential, it might be worth it to pay (or have an employer pay). For fields where the major (or only) professional opportunity is an academic job, it's not only not worth it even at a top school, it almost guarantees you won't be strongly positioned to get a good academic post when you're finished 6-8 years later.

[Goumindong]

PHD students are not net money savers, its the other way around, they are incredible expensive to educate. Yes you get some low cost labor out of them, but not compared to the time and other resources you put in.

The real issue is that the cost of tuition only makes a small dent in the expenses to educate a doctorate student. Graduate students are only "free" if you consider that they're a byproduct of research and that you're educating them so that they can do research later.

Of course considering the recession, if you're at a school with public funding, the money thing is no longer true as well. States have cut back and they just don't have the money to spare even if the costs are only a dent, the difference between a 120k grad student and an 80k grad student can take you past your marginal values.

* here is an article that discusses a study attempting to analyze the costs of educating particular students by specific expenditures towards those students. Though i would bet allocating the fixed costs tend to make it look like some aspects are cheaper than others since use of facilities is highly variable.

http://www.insidehighered.com/news/2009/05/19/degree

Edit i suppose i should link to the article if i mention it.

[Khaldun]

It's just incorrect. Ph.D students in most academic subjects in most of the top universities are a source of cheap teaching labor, they're a measurable output in public universities that helps document the labor of faculty for skeptical political eyes, in the sciences they're a flat-out necessity for conducting research projects of even the smallest scale. Universities subsidize the desirable candidates because they *must*. If they want money from you, it's because the field in which you're seeking a doctorate has value outside of academia and they think they can charge for it. If that's not the case and they're trying to charge you, it's because you have "sucker" written on your forehead.

[Nebu]

Don't forget that having graduate students makes you eligible for $millions in indirects from training grants. 

Skimming the article he cited it appeared to be about measuring the real cost of undergraduate education.  If that's the case, it hardly applies to PhD programs particularly in scientific disciplines. 

[Torinak]

Don't forget that having graduate students makes you eligible for $millions in indirects from training grants. 

Skimming the article he cited it appeared to be about measuring the real cost of undergraduate education.  If that's the case, it hardly applies to PhD programs particularly in scientific disciplines. 

Yeah, no kidding. I wasn't a particularly prolific or "good" PhD (in a monetary sense) compared to my peers, but even I obtained about a quarter-million in research grants for the department, plus spin-off applied research work that at least doubled or tripled that over a few years. The amount a guest lecturer would have been paid to handle the classes I taught was much higher than my tuition+fees+living stipend.

I don't know of a single one of my colleagues (forward or back several years) who had to pay out of their own pockets for their PhDs. All had teaching stipends, research stipends, and/or fellowships or scholarships. This was in Computer Science, at a top-10 CS program.

Based on the small amount of politics I was exposed to while in grad school, I know things weren't as rosy in non-science departments--they kept trying to appropriate our department's money...especially the English department. Apparently, there are fewer multi-million dollar poems written than there are multi-million dollar patents or spin-off companies. :)

[Khaldun]

Don't forget that having graduate students makes you eligible for $millions in indirects from training grants. 

Skimming the article he cited it appeared to be about measuring the real cost of undergraduate education.  If that's the case, it hardly applies to PhD programs particularly in scientific disciplines. 

It's a study that used the University of Central Florida as its source of data. Which tells you exactly shit and nothing about the value of doctoral students to the top R1s.

[Miguel]

It's just incorrect. Ph.D students in most academic subjects in most of the top universities are a source of cheap teaching labor, they're a measurable output in public universities that helps document the labor of faculty for skeptical political eyes, in the sciences they're a flat-out necessity for conducting research projects of even the smallest scale. Universities subsidize the desirable candidates because they *must*. If they want money from you, it's because the field in which you're seeking a doctorate has value outside of academia and they think they can charge for it. If that's not the case and they're trying to charge you, it's because you have "sucker" written on your forehead.

I'm halfway through a PhD program in Computer Science:  I also work full time (with full time meaning 60+ hours a week plus some weekends).  I was actually surprised at the number of universities that immediately became disinterested in talking with me as soon as they found out I did work full time and would not be available to do any teaching, tutoring, TA'ing, grading, etc (even given that fact that I've received nothing other than A's during two Master's programs).  So what you say rings largely true.  All of my paper-writing and advisor meetings are on my own time.

I'm doing the PhD to enable the option of entering academia later in my career, you know, after all the other technical jobs are being done in India or China. ;)

[ghost]

I started in a PhD program in pharmacology.  I honestly can't imagine why anyone would put themselves through all that shit for what is, in most instances, a mediocre job in the end.  I'm thankful I had the good sense to get out while I could.

Also, I'm very tired and thought that the title of the thread read, "Mathematics GED" and couldn't for the life of me figure out why you would be getting a mathematics GED when you've already been to college.  Ah, the sleepless nights with two small children are wonderful.   

[Goumindong]

Don't forget that having graduate students makes you eligible for $millions in indirects from training grants. 

Skimming the article he cited it appeared to be about measuring the real cost of undergraduate education.  If that's the case, it hardly applies to PhD programs particularly in scientific disciplines. 

He did measure the costs at different levels, the undergraduate is what was focused on because that tends to be what people think about when they think about college.

They're a source of cheap teaching labor and they're valuable as assistants but that does not account for their tuition, nor the real costs of educating them.

If you think "they're a measurable output" then clearly you're saying that the real costs of educating them are higher than they're tuition. If it was not they wouldn't care. Saying that they're justification to politicians is even more funny given the current political climate.

Let me make an even simpler argument which should explain why your position doesn't make any sense.

If doctorate students were net money savers, institutions would fill up with doctorate students until they were not. Now let me ask you a simple question, when you judge candidates for your programs do you determine the number of applicants you're going to accept, do you set up a profit maximizing function to determine the optimal number of graduate students?

Maybe I can be even more clear. If what you're saying was true, then total spending per student would be LOWER at research institutions than at institutions where only masters degrees were offered which would be even lower than teaching colleges. This is because for every doctorate candidate that you added the cost of teaching him would be lower than the reduction in cost associated with his teaching.

Except that we find the opposite trend, total spending per student increases as we move from places that teach up to masters students only (and don't do research) and is cheapest at teaching colleges. (and noted that this doesn't include what is spent on research, its only student costs) cite

Similarly we would expect that there would be lower faculty costs as a percentage of our total costs devoted to education.  This is especially true if spending per student increases, since we must then expect that that spending is not represented in more faculty working with students as we have surmised that we have less faculty working with students, but other resources. But again, per the cite above, we find the opposite to be true. As a percentage of total education spending, instructional spending is a full 10% higher at research institutions than community colleges! Now you could say that the faculty is more expensive (and they have less per student than at teaching colleges)

Now it is true that its cheaper for a grad student to teach a course than a professor, but only when the margin is not adding another grad student.

Furthermore, if you're taking my position and you go ahead and read the full report you would find that spending at private research institutions per student is quite high. Not surprisingly they also have the highest proportion of graduate students to undergraduate and spending per student universally increases the higher proportion of graduate students you have on average. They also have higher raw grant funding/student but not nearly enough to make up the increase in grad student percentage.

Per student subsidies are decreasing in leaps and bounds as public research institutions. The data suggests that its quite more expensive to educate doctorate students than other types. You only "make money" if you value the non-pecuniary costs of the research. Oh, and students at public research institutions do not get significantly more subsidies per student than those at community colleges(from all sources), so it can't be marginal on revenues from the research or producing doctorates.

Maybe we should go back to the economic argument. Research institutions are not hurting for qualified applicants, especially at the top institutions. If they were generating that kind of revenue with no cost increases then the departments would be letting in many many many times more applicants than they are. The best ranked institutions would have cannibalized the top 20 let alone top 50.

Maybe that has happened in the engineering fields. I don't know. But it hasn't happened in the bulk of graduate fields. There is zero dollars in ground breaking mathematical research; nearly all the benefits are external to the institution and the individual. The best research institutions in the world for economics let in ~10 people a year, the total number of doctorate seeking physicists and astronomists in the world is probably something around 3000 (at least it was in 2004, which was the highest number since 1994 according to a quick perusal of a google search). These numbers simply would not be possible with the kind of returns you are talking about. There wouldn't be a top 50 school for PHD's because everyone able would have already been accepted to the top 10. There would be no qualified students left to do research at lower ranked universities.

What you're describing is an aberration.  

I mean, lets take it a little further. Lets assume that professors are more productive in terms of research than grad students. Lets also assume that since they're employees of the university the grants they achieve due to their research and the value derived return to the university. They university pays salary and in return gets teaching and research.

How much do academic professors make? Lets say you're the 90th percentile, so you make about 187 grand[compensation iirc]. How much of that is research? How much of that is prestige due to your name, how much of that is teaching? Is there any of that that isn't attributable to productivity?[note 50th percentile is 75k compensation or so]

OK, now the teaching time is reduced because you have to be taught. The prestige is none (you cannot attract students or increase the ranking of your school generally until you're done and placed... which is more a product of your professors anyway since ranking is likely a dynamic system). What you're supposing is that with all the associated expenses grad students, even the best, are productive on levels similarly to professors. They aren't. You're wrong. The logic and evidence all suggest otherwise.

I was actually surprised at the number of universities that immediately became disinterested in talking with me as soon as they found out I did work full time and would not be available to do any teaching, tutoring, TA'ing, grading, etc (even given that fact that I've received nothing other than A's during two Master's programs).  So what you say rings largely true.  All of my paper-writing and advisor meetings are on my own time.

This is not because its these things make it profitable to them, its because they only have so much space. They have a goal to graduate PHD's who can research and if they have to choose between one who is not going to be a part of the department then they're not going to be as interested as one who can.

[Khaldun]

You are trying to derive a bunch of stuff from a generic theoretical knowledge of economics and a paper-thin shred of empirical evidence. What you're leaving out is any specific inside knowledge of the culture, norms or functioning of actually-existing research universities. So you end up with a picture of "how it must be" which is really not anything like "how it is", partly because you don't have a full picture of the weird, intricate institutional economics of academia and partly because you don't know anything about the internal culture of top R1s.  If you don't mind me saying so, that's something of a pattern for you.

It may well be that doctoral students do not pay for themselves in some absolute sense. They return value (both monetary and abstract) to a research university in a fashion very different from undergraduates, however. Moreover, in some ways, they're also benefits designed to attract highly valuable employees--a top academic researcher often expects to have graduate students who both assist his/her research and who extend his/her prestige and social capital when they go on to take academic posts themselves at other institutions. On the labor side, in many disciplines, doctoral students do not impose the same labor costs on faculty as undergraduates. To be honest, in more than a few programs, very little of what might be called "teaching" actually goes on between tenured faculty and doctoral students. In one department I know well, the faculty who will exam doctoral students in a field of competency hand those students a long list of books to read and tell them to come back in two years to be examined, more or less. All the students who are working with that advisor often meet in a seminar, but at least some advisors don't even bother to show up for the seminar itself. Once a student is ABD, this is even more the case: a vast amount of your dissertation work is self-guided, and this is precisely the point at which the ABD is often serving as an assistant in a lab, a teaching assistant and/or teaching their own class. The cost to the institution at that point of hosting that student is usually embedded in costs it would incur anyway (a lab, a library, etc.). ABDs who are doing work for their host institution generally do not get their own offices or impose other costs of that kind (there may be one office for all the teaching students to share for meeting with undergraduates), many do not receive health or other benefits, and if they have research costs of their own (for fieldwork or equipment) those are often funded by external grants.