I am a first year undergraduate student studying natural sciences at highly reputed university, and am pretty sure that in the future I would like to pursue studies in philosophical theoretical physics and mathematics, and philosophy of artificial intelligence, perhaps also dappling in philosophy of mind. I wanted to explore this during the summer, however there aren't really any philosophy summer programs for undergraduates (although I would be very interested to hear any suggestions that anyone has. I have come across the Summer School for Mathematical philosophy for female students at the University of Munich for example, however it is only a one week long course and I have a 3 month long summer vacation!).

I was wondering if there are any other options, perhaps I could email a professor at another university and I could spend the summer there? The problem is, I don't really know what this could entail, so I am not quite sure what to put in an email. If I were to spend, for example, 6 weeks in a department, what could I hope to achieve? Is it common for a humanities student to write a short paper during the summer while working under a department? I would rather not spend the summer at my university- I think it would be good for me to spend some time in a different environment as well.