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When applying to graduate programs in computer science, what are the pros/cons of having the professor who advised your project in an NSF REU in computer science write one of the required letters of recommendation? I ask since the duration of REU programs are so short (~10 weeks).

More specifically, assuming a good letter can be written by all professors, why might I have my 3 letters consist of:

Case A: 2 CS professors from undergrad, 1 CS professor from REU

or

Case B: 1 CS professor from undergrad, 1 math professor from undergrad, 1 CS professor from REU

or

Case C: 2 CS professors from undergrad, 1 math professor from undergrad

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    Have you done research with either of the faculty members from your undergrad institution? – aeismail May 18 '16 at 17:28
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It is extremely valuable to have letters that speak to multiple sides of you as a student, e.g. as a scientist, as an academic, as a communicator; letters that say you're not one-dimensional. If you have no one else who can speak to you as a researcher, I'd absolutely recommend asking your REU prof to write you a letter. Further, if you have truly made a connection, or they really think highly of you, or anything like that, they could trump a letter from your institution, to be honest. Internship advisors' letters from places like NASA centers were key points in some of my peers' applications in the past; 10 weeks is a good amount of time to show someone what you can do, although a longer relationship (stay in touch, etc.) certainly helps them understand your depths.

I'm not sure as to how much any particular program might value a diversity in your letters, but your professors at your school benefit from having their students do well; your REU advisors benefit too, but on fewer levels, which may make a letter from an out-of-school research advisor weigh a little more heavily. Your mileage may vary on the last, though.

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