I'm currently a student on an co-op term. I work in a fairly small team and my term is about to finish up. Since this is my first intern experience, I was wondering if it would be appropriate for me to ask my co-workers if I could maintain a professional network with them (such as adding them on LinkedIn). If so, any advice on how to go about asking would be appreciated!
I was wondering if it would be appropriate for me to ask my co-workers if I could maintain a professional network with them
It's perfectly appropriate to invite anyone who you think would add value to your network.
Depending on how you worked with them during your internship, and how they feel about you, they may not all accept your invitation. Don't take that personally.
Absolutely! Not only do I think it's OK, I think it's an excellent way to start building your network. Internships don't always get counted as real work experience by interviewers, but if your new network contacts from your internship endorse your skills, that might help you when you go out for your first real paid gig. Showing that you have not only passed classes in which you learned something, but can actually apply it in a real work environment is going to help put you ahead of someone with similar credentials.
Also, I would love for interns I've worked with to add me to their network. When I'm working with an intern, it's part of my job to act as a mentor in both technical skills and professionalism/career-building. If I've done a good job of that, having interns that I mentored in my network can help me as much as it does them.
For the coworkers you just want to stay casually connected with, just send them the invite.
One other thing you may (should) be thinking about when building a network is references. In your job search, you will be asked to provide references, and it's proper etiquette to have had some conversation with the person whom you put down before they get the call. Leaving an internship is the perfect time to have those conversations. You may start the conversation with "Hey, do you mind if I add you on linkedIn" but end with "Do you mind if I put you down as a reference in my further job searches?"
I disagree with most answers about the fact you don't ask, specially in the case of using my personal mail.
If I gave you my personal mail, it's not to give it to some sites/anyone without my consent (like a phone number). Those sites may start to spam me or sell it eventually to some advertising spammers.
So I would prefer that you ask me first.
Note that probably not most people would care about that, but in doubt, ask.
Yes, it's perfectly normal to add coworkers on LinkedIn, especially if they're already members. The fact that you're an intern doesn't really matter - you still worked with them.
You don't really need to ask in advance of sending them an invite IMHO. Honestly, I'm not sure what their incentive is to refuse or object (I certainly wouldn't). Being connected with someone on LinkedIn is very different from being a Facebook friend, for example - being a Facebook friend tends to imply a certain kind of social connection with someone, but there's less of an implication of a particular social relationship (beyond some kind of professional relationship) for LinkedIn. (I'm connected with a fair number of headhunters that I maybe worked with once, for example; that's actually fairly common in my industry).
As your term nears its end, you can send out an email which thanks your co-workers for the internship, details how much you loved it, and say that you'd like to keep in touch. Include your personal or student email address (whichever is more professional for you) and a link to your linkedin account.
If you are closer to some of your colleagues than others, let them know you want to connect on linkedin before the internship ends. Then, send out those invites.
If any of your colleagues seem particularly active on LI, just send it out.