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I'm a sophomore studying computer science and mathematics at a well-known university in the US who is interested in doing a PhD in computer science related to graph algorithms, theoretical deep learning, or something else in these areas of interest.

I'm currently taking a graduate level measure theory course and a senior level (i.e. 4000-level) mathematical statistics course. I'm concerned that I may get a B in one of these two courses, but likely not both. Assuming that my GPA is otherwise a 4.0/4.0, will this seriously affect my chances of getting into strong graduate schools for computer science?

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Yes, they care. Or at least those on admissions committees in the US are very likely to care. But one or two grades below A shouldn't be a problem. It isn't a numbers game, but an overall evaluation of your likelihood of success in grad study and beyond. But GPA in major is more important that overall GPA in the US educational system, assuming that you want to continue in that field.

If you are taking measure theory in the second year, I suspect that you are good enough in grades. Make sure you have enough contact with professors to get good letters of recommendation. That is very important.

Also note that competition at the best schools is intense. Cast a broad net when you get to the point of making application.

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When I was on my department's graduate admission committee, we paid a lot of attention to grades in our field (mathematics) and nearby fields (physics, computer science ...). That involved looking at the courses the applicant had taken and the grades, not some mechanical average like the GPA. We would certainly view a B in measure theory (for a sophomore!) more favorably than an A in a typical sophomore course (calculus 3, introduction to proofs, ...).

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