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Currently, I'm applying for PhD positions at several universities in pure mathematics and computer science. Despite the fact that these two fields are content-wise different and do not have too much in common, I'm open to do a PhD in both of them. However, if I ask a professor to write a letter of recommendation for each them, I'm not sure if the professor would negatively understand it. He may think that I should choose only one of these fields for PhD positions.

My question are the following and may be based on common (best) practices/experiences:

  • Is it recommendable/valid to apply PhD positions in different fields at different universities?

  • Does a professor perceive it as inappropriate/negative when he is
    asked to write recommendation letters for two different fields?

Furher recommendations regarding this issues are very welcome.

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You can and should apply to any position in any field in which you are interested and have the background. But it is probably useful to give a lot of thought about what you want to do with your future before you make any applications at all. I suspect nost mathematicians are driven to math. Nothing else will do. If you don't have that sort of drive/compulsion for a field, evaluate carefully. It isn't like choosing McDonalds v Burger King.

Before you ask anyone for a letter of recommendation first have a conversation with them about your long term plans and get some advice from them. If you just make a blind "ask" you don't know what you are likely to get. And, of course, some professors will guide you to one field or another whether that is the right choice for you or not. If you really need a letter from an individual for both fields, make sure, in your conversation, that they happily buy in to the plan.

But if you are doing very well in both fields, it might be best to ask professors in the specific field for a recommendation in that field.

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