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This fall, I am planning on applying to PhD programs as a graduated student. However, I’m having to make up for an abysmal undergrad - 3.23 GPA, very very intro research experience, and not too many reasonably advanced classes.

In order to increase the competitiveness of my application, I am taking 3 graduate courses this fall, with the intent of proving my ability to excel in a graduate setting and getting recommendation letters from those professors (I only have one professor from undergrad that I’m close enough to to write me a letter - he’s also the advisor of the aforementioned research).

I’m also considering taking the continuation of these 3 courses in the spring in order to lighten my overall course load when I enter a PhD program. If I do this, I will be just shy of the requirements for receiving my master’s degree.

Would attempting to upgrade my status from Non-Degree Graduate Student to Master’s Student, and completing the accompanying Master’s thesis be worth the much-added effort? Namely, would it increase my competitiveness at all in the application process?

EDIT: I received my bachelor’s degree in Mathematics from a university in the US and am applying for PhD programs in Mathematics and am mostly considering US institutions.

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I would suggest doing that only as a backup plan and just make applications to doctoral programs, perhaps in parallel. The decisions for admission in US aren't made on the basis of GPA alone, and for a US undergraduate program the GPA for major courses is probably more important than the overall score; especially the upper division courses. If you did well in advanced courses a somewhat (not abysmal) overall GPA might not be much of a factor.

More important than GPA, however, is what letter writers say about you and what sorts of positive predictions they make about your future success. For many programs, writing a good Statement of Purpose that is well focused on your plans an how to achieve them can also be a positive factor.

You don't need a masters to enter a US doctoral program in math. Getting one will probably lengthen your time of study, since you still need to pass comprehensive/qualifying examinations and may need to take some coursework specific to that end.

But don't make assumptions about your chances. The only way to be sure whether you are already qualified is to make (several) applications to a range of R1 universities. You will need a couple more letter writers, though. Cultivate people who might speak for you.

Also, see this question and its answers. How are Ph.D. applications evaluated in the US, particularly for weak or borderline students? Am I likely to get into school X?.

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