Why
not ask for their phone number? It doesn't necessarily imply that you intend on asking them out on a date...
Asking for fellow class members' phone numbers may even be helpful, ie, to ask someone when / if you get stuck with coursework off-campus, or miss a lecture, etc...
That way, you won't feel conscientious about appearing online, you can surf to your heart's content without worry,
and you'll have their number(s) which you can keep in contact with once in a while (besides, at the very least, you could
text them rather than
speak to them over the phone)...
And if they don't want to give you their number, then there's your answer!
Make it easy for yourself!