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I'm planning to apply to top US grad schools in the fall, and out of all the required documents, I would say that my weakest link would be in the quality of my recommendation letters.

I'm currently planning to ask the following people:

  1. Professor X: I'm doing research with this person in the summer, and we already have a significant result that we are planning to turn into a joint paper. (Subject: discrete math)
  2. Professor Y: I received an A+ in this person's undergraduate analysis course last year, and he offered to write a letter of recommendation to those who received an A+ in his course.

Then, the rest I'm not sure about, I have the following to choose from:

  1. Professor Z: I did a research project with this professor in number theory, but it was more like a reading course. I don't think I left a significant impression on him, since the topic I was reading was fairly elementary in the field.
  2. Manager A: I did an internship under this person at a Big 4 Tech company last summer, and he had high reviews of me, and gave me a returning offer at the end, which I declined.
  3. Postdoc B: I did a research internship with this person in applied computer science (not math heavy) two summers ago, and it culminated in a joint conference publication.

The problem with Manager A and Postdoc B are that they are not professors, and I did not do any pure mathematics with them, which I heard should not be a part of my application package.

I was briefly in engineering. I switched into my current math and computer science program about 1.5 years into my undergraduate degree. I started becoming serious about going to math grad school last summer, after testing the waters with industry.

My GPA is probably among the top 1%, and I have taken most of the upper level undergraduate math courses. I will be taking some graduate level math courses at the same time as my applying to graduate schools in the fall.

I've also been learning more graduate number theory material with a mentor on the side, and will be writing some expository pieces. But again, a graduate mentor cannot write me letters of recommendations.

Of course, if I choose Professor X,Y,Z, then I will have 3 letters, but only one of them will be strong. Should I explain this in my statement of purpose? Can I still fix this situation by working on a more meaningful research project in the fall?

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I think X, Y and Z with both X and Y strong will be just fine. Few undergraduates have had enough contact with faculty to generate three strong letters.

The work you did with A and B will be on your CV and you can discuss it in a cover letter.

Good luck.

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