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PhD in Applied Math with a low math GRE score


hkcool

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I only took the exam once and did poorly. I scored in the 46th percentile (640).

My undergrad education was in computational math, and honestly, the exam was quite difficult for me. The questions I knew, I could answer easily. But a lot of the material was unknown to me. I did some self study on those subjects, but focused my time mostly on material I knew I could master. 

None of my applications (applied math PhD programs) require the subject test score, per se. Stanford's ICME program, which is probably the highest reach school I am applying to, says the subject test is "highly recommended, but not required." Lots of my programs go this "optional, but recommended" route.

I'm just curious what to do in this case, especially for a top program like Stanford. Without getting into too many details, my GPA and general GRE are good. I have a lot of research experience, first author on a publication in my desired subfield. Good to great rec letters. I feel like the low mGRE score drags down my application. The two choices I can make are:

1) Submit the score. Risk getting weeded out immediately without the rest of my application looked at.

2) Don't submit the score. Let the rest of my application speak for me. But in this case, does the school see a red flag in the lack of a score, and then it counts against me anyway?

What would you recommend I do? My undergrad study was in computational math, and I covered the basics of Calc 1-3, ODEs, PDEs, linear algebra, real analysis, but subjects like abstract algebra, discrete math, etc. weren't part of my study, and this is reflected in my transcript. I did cover numerical analysis, optimization, and numerical methods for PDEs (theory and implementations) in detail, which is more tailored to the dedicated applied math programs I am applying to. 

My undergrad institution was a dedicated computational math dept that did not require mGRE scores for PhD applicants, so I'm not sure they can advise me at all in this matter.

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