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I'm not a grad student, but I just want to add to what GoldenRule said about whether to use a professor's first name or not. I typically start off just as he said to, but every time thereafter I use whatever name the professor closes with. Most professors sign off an email with their first name, and if they do then I use it as well. But there are definitely some who end with "Prof. so and so", and in those cases I'm careful not to get too familiar.
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