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TL;DR My understanding is that the Math GRE is supposed to test knowledge that is expected of someone who wants to pursue a math masteral or math PhD. So shouldn't it test knowledge that is expected of someone whose bachelor's or master's degree is pure math, applied math, physics or statistics? It seems biased to pure math. Also why is numerical analysis in the Math GRE? How much of the Math GRE is the pure math stuff?


Those who pursue a postgraduate degree in pure or applied math usually have a bachelor's or master's in pure math, applied math, physics, engineering or statistics. Less common would be economics, chemistry or biology.

The Math GRE includes topics that not everyone from those backgrounds have taken up in their bachelor's or master's.

It would make sense that some people would have to study more in preparation for the math GRE (and their intended program). For example:

  1. Those from less common backgrounds likely haven't had much calculus or linear algebra. They likely haven't had any linear algebra, ordinary differential equations, basic probability theory, basic discrete mathematics or introductory real analysis.

  2. Those from engineering likely haven't had basic probability theory, basic discrete mathematics or introductory real analysis.

However, the Math GRE apparently:

  1. includes pure math topics such as abstract algebra, graph theory, group theory, advanced discrete mathematics, topology and complex analysis and seems to do so at a greater extent than ordinary differential equations, basic probability theory, basic discrete mathematics, basic statistical theory and introductory real analysis.

Those from applied math, physics or statistics are expected to know ordinary differential equations, basic probability theory, basic discrete mathematics, basic statistical theory and introductory real analysis but are not expected to know abstract algebra, graph theory, group theory, advanced discrete mathematics, topology and complex analysis.

However, those from pure math are expected to know the latter topics.

  1. includes numerical analysis, an applied math topic.

I would expect very few people who have a bachelor's or master's in pure math to have taken numerical analysis. Far fewer for and.

However, some of those from applied math, physics or statistics may be expected to know numerical analysis.

Questions:

  1. Why doesn't the Math GRE test include more basic probability theory, introductory real analysis, basic discrete mathematics, basic statistical theory and ordinary differential equations than abstract algebra, graph theory, group theory, advanced discrete mathematics, topology and complex analysis?

  2. Why in the first place does the Math GRE include pure math topics such as abstract algebra, graph theory, group theory, advanced discrete mathematics, topology and complex analysis that aren't expected of those with a bachelor's or master's in applied math, physics or statistics?

  3. Why does the Math GRE include numerical analysis, an applied math topic, when very few of those with a bachelor's and master's in math would have taken it up?

  4. In your best estimate, around how many questions out of 66 would one expect to cover topics other than calculus, linear algebra, basic probability theory, introductory real analysis, basic discrete mathematics, basic statistical theory and ordinary differential equations?

I don't really want to look at some of the past or practice exams out of fear of having the exam compromised for me if I were to try them out.

closed as primarily opinion-based by Nate Eldredge, Andreas Blass, Buzz, ff524 Jun 9 '16 at 7:22

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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    You appear to be projecting based on your personal background and biases. If a department requires the Math GRE, I would presume that they find the data moderately useful. Specifically for your first question - why should they include questions on those topics - they have little bearing on graduate level research abilities? – Jon Custer Jun 7 '16 at 13:06
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    Why do you place so much importance specifically on "basic probability theory, introductory real analysis, basic discrete mathematics, basic statistical theory and ordinary differential equations"? One gets the feeling you want the Math GRE to be focused on the particular subjects you happen to know about. – user37208 Jun 7 '16 at 15:17
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    What does this mean? "I don't really want to look at some of the past or practice exams out of fear of having the exam compromised for me if I were to try them out." ETS has a practice exam available on its website and looking at it is certainly not cheating. If you want to take the real GRE, I would strongly recommend that you attempt it and then review your answers. – Anonymous Jun 7 '16 at 23:18
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    Most of the math subject GRE is lower-level material: calculus, differential equations, linear algebra. There is little "pure math" on the exam, in the end; most of the exam is on background material that is useful in all areas of math, but is actually less useful in many areas of pure math than in many areas of applied math. One challenge with the exam, for some students, is that in their last two years they may begin looking at pure math topics which will not be reflected on the exam. – Oswald Veblen Jun 8 '16 at 1:33
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    A lot of this can be explained by the notion that breadth of knowledge is a positive factor in preparation for grad school. Indeed, not everyone will have taken all the subjects covered on the exam; but those who have will get a better score, thus signaling their better preparedness. – Nate Eldredge Jun 8 '16 at 22:01
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1) Why doesn't the test include more basic and introductory topics? Well, if you're applying to do research in mathematics, one might expect you to have a good coverage of broad aspects of the field beforehand.

2 and 3) The majority of the material on that paper is first year engineering level maths, and first term for people studying mathematics. Other areas shouldn't take longer than a couple days to cover to the level required for that paper.

4) Look at a past paper. The fact that you have an idea as to what is on the paper does not 'compromise' it. 50% calculus, 25% algebra and 25% advanced topics.

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    When I was preparing to take the old computer science GRE subject test I tried not to look at complete sample tests to keep them for timed practice runs after study. – Patricia Shanahan Jun 8 '16 at 0:00
  • 1) The GRE is essentially faulting its takers for not knowing graph theory or numerical analysis even if the faulting is worth 1 or 2 points. Seriously, what portion of those with bachelor's or master's in math know numerical analysis? Do you consider such expectation to be valid? If it's so important, why not include more items like those in the test? Why are Calculus and Linear Algebra so important? 2,3) What do you mean shouldn't take longer than a couple of days? If I'm going to study Group Theory for the first time, I'm going need to take at least a month which will be just 1question! – Jack Bauer Jun 8 '16 at 21:38
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    AFAIK, actual past exams of the GRE are not publicly available. There are sample tests (by ETS and third parties) that are claimed to be representative of the contents of the actual tests, though. – Nate Eldredge Jun 8 '16 at 21:38
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    Read the first couple chapters of a group theory textbook, do a couple exercises - couple days work. Its a trivial paper, you're over-thinking it. – Oxonon Jun 8 '16 at 22:41
  • @Oxonon Thank you! Any recommendations? – Jack Bauer Jul 8 '16 at 6:33
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Nobody expects you to get a perfect score on the subject GRE. That's not a personal judgement, just a fact. The body of graduate mathematics candidates is diverse in their backgrounds and areas of interest. True, most have undergraduate degrees, but their research interests range across all fields of mathematics. You will score well in the areas in which you are experienced, and you'll probably miss a few questions from the subjects with which you are less experienced. Thats okay; it's expected. The GRE does not discriminate against any area of mathematics.

Also, the vast majority of questions are from fields every math grad student really ought to know, like calculus, linear algebra, and basic analysis. If you have had little exposure to, say, graph theory, don't worry. There will be maybe one or two questions on it, if any.

It is not important that new graduate students be proficient in all of the more obscure topics covered on the GRE, just that they are proficient in some.

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    Documentation specifies that half the questions are from calculus, 25% from linear algebra and the remaining 25% cover topology, number theory, etc. if you define the subjects that every math student ought to know as "calculus, algebra and basic analysis" then you can't take "vast majority" to be anything larger than 75%. – user18072 Jun 8 '16 at 21:42
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    @JackBauer no, I'm not sure why the OP thinks the GRE covers some things that grad students really not ought to know, or what examples of such things might be. TBH I'm reading that sentence as "I have no idea what I'm talking about so I'm going to throw in a few random hedges." I've downvoted... if OP can explain or revise that'd be great. – user18072 Jun 8 '16 at 21:43
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    I guess the thrust of the argument is that grad schools only are really concerned with calculus, algebra and analysis, and not with number theory, graph theory or topology. But I'm not sure how that works with "does not discriminate against any area of mathematics." I also don't know the evidence for the diversity of math grad candidates? I was always under the impression students with strong bachelors degrees in math had some sort of leg up when getting into grad school, and maybe physics or C.S. students do well. – user18072 Jun 8 '16 at 21:51
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    @djechlin: I would say the GRE is primarily concerned with calculus, algebra and analysis. I would disagree that grad schools are only concerned with those areas. I think many people feel that the GRE isn't a very good measure of what grad school success really requires, and is used mainly because it's better than nothing and there are no other viable options. – Nate Eldredge Jun 8 '16 at 21:56
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    @JackBauer sorry, meant the answerer when I said OP. – user18072 Jun 8 '16 at 21:59
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To supplement other comments and answers: first, it is simply not the case that people with (typical...) engineering backgrounds or comp sci backgrounds or economics or ... know nearly enough mathematics to be ready to go to grad school in mathematics.

Also, it's not at all the case that the GRE subject test in math tests what it may claim to test, e.g., as in the question, "what is expected of someone wanting to pursue graduate work in math". It is, after all, simply a multiple-choice test, timed, and very superficial.

It's not that every undergrad in math in the U.S. is expected to know all the introductory-level stuff about complex analysis, Fourier analysis, graph theory, group theory, Galois theory, and so on, but, yes, some good swath of it. So then they'll get a pretty-good score on the subject-test GRE.

I am not so much a fan of the subject-test Math GRE, since in my experience (some decades involvement with grad math admissions) it is a highly flawed diagnostic, and full of curricular inertia besides.

For me, as admissions person, letters of recommendation and personal statement, on top of evidence of substantive coursework or self-study of advanced undergrad or beginning grad-level mathematics, is/are far more important than the subject-test GRE. A thin-coursework background + pretty-good subject-test GRE indicates to me mostly that the candidate is a good test-taker, or prepped specifically for the GRE, but not that they have a solid grounding in mathematics.

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