2

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.

BCLC
  • 3,157
  • 7
  • 29
  • 64
  • 4
    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 07 '16 at 13:06
  • 3
    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. –  Jun 07 '16 at 15:17
  • 3
    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 07 '16 at 23:18
  • 2
    It seems biased to pure math - From the description, I would only categorize the "abstract algebra/number theory" as not something I would expect to study for some pursing applied math or probability/stats. This is only one of 3 topics listed in the algebra category, which itself only comprises 25% of the exam. – Kimball Jun 07 '16 at 23:33
  • 2
    @anonymous I believe that the OP wants to not look at the practice exam until he/she takes it, so as to have an accurate measure of his/her score. – Plutoro Jun 08 '16 at 00:10
  • 3
    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 08 '16 at 01:33
  • 1
    The choice of topics for the Math GRE is, as far as I know, based on the knowledge that one should have in preparation for graduate study in mathematics. It is not based on what is or is not covered in particular undergraduate programs. – Andreas Blass Jun 08 '16 at 03:54
  • I think this question is opinion-based. The only real answer to "why does the test cover this and not that" is "the test designers felt that would make the best product". Certainly others may disagree, or would have done it differently if it were up to them, but as you know, discussing opinions is not the purpose of this site. – Nate Eldredge Jun 08 '16 at 21:36
  • @user37208 My grades in basic discrete mathematics and basic statistical theory were low. I dread those kinds of questions but can accept them because they were in my bachelor's. Anyone with pure or applied math bachelor's or master's is expected to know those. – BCLC Jun 08 '16 at 21:43
  • @JonCuster So how does anyone with a bachelor's and master's in applied math get into a PhD program in the US? I can learn all those courses in the PhD program anyway. i'm thinking, if they were so important, why aren't they covered more in the GRE? and if they aren't so important, why are they covered in the GRE at all? – BCLC Jun 08 '16 at 21:45
  • @OswaldVeblen What do you mean by "last two years" ? – BCLC Jun 08 '16 at 21:48
  • 1
    @AndreasBlass i'm thinking, if they were so important, why aren't they covered more in the GRE? and if they aren't so important, why are they covered in the GRE at all? Graph theory for example is likely going to be in 1 or 2 items on the test. Why 1 or 2? If it's so important for grad studies, how about 10? If it's not so important, how about 0? – BCLC Jun 08 '16 at 21:49
  • @NateEldredge Did you VTC? How is this opinion based? I'm asking for the opinion of the ones who make the GRE and the ones who require or give credit to the GRE. The GRE is really expensive! – BCLC Jun 08 '16 at 22:01
  • 4
    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 08 '16 at 22:01
  • 2
    @JackBauer The Math GRE is primarily focused on pure math, and the further a graduate program is from pure math, the less importance will be placed on applicants' Math GRE scores. Most pure math undergrads are not expected to know statistics or discrete math. The core subjects of a BS in pure math are calculus, linear algebra, basic real analysis, abstract algebra, topology, and complex analysis, and the Math GRE reflects this reasonably well. –  Jun 08 '16 at 22:03
  • 2
    @JackBauer Presumably the number of questions on any particular topic reflects the test-designers' view of the importance of that topic for graduate study in mathematics. I would hope that this view is based on information from mathematicians who supervise such study. (I've never been involved in designing such tests, so I'm only describing how it could reasonably be done.) If the coverage of topics in the GRE exams deviated too wildly from what's actually appropriate for graduate study, then mathematics departments would stop using the GRE in their admissions process. – Andreas Blass Jun 08 '16 at 22:04
  • 2
    You've got some really weird (and unnecessary) assumptions in this question. You think that a Ph.D.-bound economics student doesn't know calculus, or that an engineer doesn't know probability? Huh? –  Jun 08 '16 at 22:05
  • 1
    "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." One - it's not like there's a shortage of practice material available... sadly there's a for-profit industry around making sure of that. Two - do you really think an untainted estimate of your own ability is really the best way to prepare for the exam? Sounds like you're confusing training and performing. –  Jun 08 '16 at 22:11
  • This question really should be closed as too broad or opinion based. I can't tell if you're asking 1) what's actually on the test (which is reasonable to answer), 2) how the GRE company decides what to put on it, 3) what admissions looks for in students from math v. non-math backgrounds, or 4) how admissions committees reconcile GRE scores among different students. You kinda need to pick one and ask it. –  Jun 08 '16 at 22:14
  • 3
    I don't see the point of objecting to the graph theory part of the GRE because lots of people haven't studied graph theory (Question 2) while recommending inclusion of topics like basic statistical theory (Question 1) which many people (including me) haven't studied. It seems that a very similar question (or rant) could be raised no matter what topics were on the GRE and no matter how they were weighted. – Andreas Blass Jun 08 '16 at 22:18
  • @djechlin In my university, engineers don't have basic probability theory as in with random variables, probability distributions, sample spaces, bayes theorem, etc. Maybe just basic probability. I would expect a math PhD-bound economics student to know or have studied calculus as much as someone with a bachelor's or master's in math. I wouldn't expect someone with a bachelor's or master's in eco to know epsilon-delta, mean value theorem, LHR, double integrals in polar coordinates, derivatives or integrals of trigonometric functions, integration by parts – BCLC Jun 08 '16 at 22:28
  • @AndreasBlass basic statistical theory? as far as i know all math majors take up a statistics course which should include topics like hypothesis testing, properties of estimators, etc. anyway i was just assuming. the point is i think the GRE should include only topics expected of all math majors. if that means no stat, i would be glad. there's no argument for calculus, linear algebra and intro real analysis. Ordinary differential equations? I would expect but could be wrong. The point is only subjects like calculus, linear algebra and intro real analysis should be included. – BCLC Jun 08 '16 at 22:31
  • You could just remove the unnecessary assumptions rather than argue them. –  Jun 08 '16 at 22:35
  • 1
    @JackBauer - clearly no applied math graduates are admitted to grad school. Oh, wait, yes they are. Why? Because they take a wide range of courses, including ones valued by math programs. – Jon Custer Jun 09 '16 at 01:16
  • @Jack Bauer: sorry - by "last two years" I meant the last two years of some kind of stereotypical four year undergrad math degree in the U.S. The majority of the subject math GRE is calculus, differential equations, and basic linear algebra - which are rarely senior level courses in my opinion. On the other hand, topics that students may see in their last year are covered much more lightly, based on lists like https://www.ets.org/gre/subject/about/content/mathematics – Oswald Veblen Jun 09 '16 at 20:26
  • 2
    At the same time, I think there is a rumor, or urban legend, that the mathematics subject GRE is particularly difficult in order to make the scores have a wider distribution. If the rumor is correct, then the test is intentionally designed so that few people (at least few U.S. takers) will have perfect scores, even after having a bachelor's degree in math. The figure in this answer: http://academia.stackexchange.com/a/13965/16122 shows that the median percentile for U.S. students admitted to Ohio State over some period of time was only 67. – Oswald Veblen Jun 09 '16 at 20:37
  • 1
    @OswaldVeblen But why majority and not all? Everyone with a bachelor's or master's in math, applied math, statistics or physics is expected to know those 3. Why include anything not expected from everyone with a bachelor's or master's in math, applied math, statistics or physics? – BCLC Jun 17 '16 at 10:39

3 Answers3

3

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.

Oxonon
  • 265
  • 1
  • 5
  • 1
    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 08 '16 at 00:00
  • 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!
    • – BCLC Jun 08 '16 at 21:38
  • 2
    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 08 '16 at 21:38
  • 1
    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 08 '16 at 22:41