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I'm in the process of selecting courses for my third year, and I wasn't planning on taking certain mathematics courses (in particular, "pure" courses, such as Algebra). However, upon speaking to come colleagues, I've found that I might want to substitute Advanced ODEs for Algebra, given that I could probably learn the former on my own, and the latter weighs more on the GRE Subject Test, so I should have a good handle on it.

This has made me ask two things:

1) Is the Subject Test even required for all Grad Schools? I'll be doing the GRE, and the schools I'm planning on applying to fall into sort of an "Applied/Computational" category, so I don't know how much of the Subject Test they'd be interested in.

2) Do courses (and their subsequent grades) matter more than scores on the subject test, or is it vice versa, or are they both pretty equal?

I'd love to hear any and all advice. I'm doing a combined honours in general sciences and mathematics, if that makes any difference. I'm close to course selection, and I'd like to have a good idea of what would be useful to take.

Thanks!

  • The apparently-traditional partitions of mathematics into "pure" and "applied", or, currently "pure" and "computational-applied", are not genuine scientific divisions, certainly not at all disjoint in terms of underlying mathematics. It might seem so from course catalogues and naive descriptions, but it is not so. The subject-test GRE is a highly stylized, multiple-choice mock-up of one picture of what undergrad math is... so nowadays many good math depts don't care about it too much. It does not substitute for coursework or self-study! [cont'd] – paul garrett Jun 12 '16 at 17:21
  • [cont'd] Coursework (or self study) counts much more than the GRE, in general, because it shows sustained effort (and knowledge that might be retained for longer than a Saturday afternoon). As much of any of this is letters of recommendation, in the U.S. (and personal statement), since the issue for grad admissions is prediction of future success (in a rather different enterprise, namely, higher level scholarship and research) rather than past success (in lower-level coursework in a highly structure environment). So, in some sense, the real answer to the question is "neither"... [cont'] – paul garrett Jun 12 '16 at 17:24
  • [cont'd] ... though if any kind of a mathematician has no idea about basic abstract algebra they'd be in a bad situation almost all the time. Try to take basic courses in "everything"... :) – paul garrett Jun 12 '16 at 17:24
  • @paulgarrett I truly appreciate this comment, it's given me a lot of motivation to go out and learn. I think you've given me a lot to think about wrt courses and my own ability to self-study. – Turra Jun 12 '16 at 21:56
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It's difficult to answer this question because a lot depends on the programs that you're applying to and on the undergraduate program that you're currently in (because not all undergraduate programs are equal.) The GRE subject test in mathematics covers a broad range of undergraduate mathematics that anyone going on to graduate study in mathematics should have mastered. Your grades in undergraduate math courses should provide similar information to an admissions committee.

However, the graduate admissions committee might not be able to interpret your undergraduate grades (e.g. because they have no experience with students from your institution.) At some places grades are now so inflated that even a 4.0 GPA in math courses with the appropriate GPA says little about what you actually have learned. A good score on the GRE subject test in mathematics will help to confirm your good grades. Highly ranked graduate programs will want to see both good grades and a good score on the GRE subject test and for the very best programs this is simply a bare minimum- they'll want to see something beyond this in your admissions packet.

The subject test is really written from the point of view of traditional programs in mathematics. For programs in computational applied mathematics, the test content isn't as relevant and the subject test is not always required.

To answer your specific question about taking an advanced ODE course vs. a course in Abstract Algebra, you'd probably be better off taking the advanced ODE's course. In the other direction, if you were applying to a mainstream PhD program in mathematics, than you would almost certainly want to have an undergraduate abstract algebra course on your transcript. Certainly if you were applying to my graduate program I'd rather see a second course in ODE's than a course in Abstract Algebra (although both would be even better.)

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    Even for grad schools in pure math, the subject GRE is not always required. My dept (primarily pure math) does not require it (and we only require the general GRE because the university does). – Kimball Jun 12 '16 at 11:24
  • Thanks so much for your answer. I was thinking the exact same way as you described in the last paragraph about those 2 courses. Some of my conflicts arise from the fact that I'd be interested in taking non-maths courses, and taking courses that would be beneficial for seeking a research supervisor for a potential future research project. Thanks again for your insight, I have a lot of thinking to do! – Turra Jun 12 '16 at 21:54
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First, I'd like to give you some perspective. When I was beginning my fourth year and picking my courses in preparation to applying to Ph.D programs, I met with my advisor to go over my choices. Since I was in an "Applied Math" concentration, my course load was comprised of:

  1. Combinatorics and graph theory
  2. Advanced ODEs
  3. PDEs
  4. Operations research (I & II)
  5. Mathematical modelling
  6. Foundations of applied mathematics

My advisor suggested that I drop out of the concentration and stick to the regular math curriculum. The reason being that in grad school (even in the applied math program), you will be expected to have gone through a good range of subjects, including of course, pure math.

Moreover, the qualifying exams you will be expected to take and pass will include these pure subjects, so the idea is for you to have some exposure before you arrive. To this end, my final year ended up looking like:

  1. Abstract algebra
  2. Advanced Calc. (I & II)
  3. Numerical analysis
  4. Complex variables (intro to complex analysis)
  5. Mathematical modelling
  6. PDEs

His decision was seconded by a senior professor, and the chair of the department. Looking at my course load now, and the subjects to be covered in the exams, I'm sure glad I listened.

Now, to answer your questions:

1) No, not all schools require it. In fact, none of the schools I applied to required it (they recommend it). I was told by my advisor that if they don't require, it's because they don't care about it.

2) Depends on the school. Some schools weigh performance in grad level courses more heavily than scores on the test (this coming from a member of the admissions committee at my current institution). Other schools use scores on the test as a metric to determine how well you'd do on the qualifying exams. (Sean Carroll told a story about how in the U of Chicago, they found an almost perfect correlation between good scores on the Subject GRE and passing the exams. See this: unsolicited advice)

I hope my answer is of help to you. Good luck!

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  • One point to keep in mind is that even schools that don't require the subject exam may still take note of subject exam scores if they receive them. Some amount of careful planning is necessary in that regard. – Oswald Veblen Jun 12 '16 at 19:34
  • I'd like to thank you for your insight, as your initial course load is similar to, if not, exactly what I saw myself taking in my senior year. As part of my degree, I've already taken Calc I and II and will be taking Real and Complex Analysis this upcoming year. I was planning on taking 1,2, and 3 from your initial list, and the way my school works is I must take 2 from that list to take 3. I'll have to do some thinking it seems. Thanks again! – Turra Jun 12 '16 at 21:51

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