Next week I finish my summer internship. Am I supposed to give a thank-you note to my manager when I leave?
Thank you notes are always a good idea when they won't come across as being a "suck up" which I don't think is the case here.
I would send one. It will leave things on a very positive note and since most people don't send thank you notes anymore, it will make you stand out. It's never a bad idea to network and you never know when you'll encounter this person in the future, either for a reference or for a job.
I wouldn't say you are "supposed to" however. If you don't, there is nothing harmed.
I would not bother with a physical letter but an e-mail seems fine but its not going to harm things if you don't. If you did a good job they will remember if you did a bad job you will soon be forgotten.
Personally, I would send a team wide e-mail.
Saying thanks to everybody. If you had an assigned mentor mention them by name and try and put something specific that you learned about the big bad world.
For short period time I send a thank you email on my last day including everyone I know, have met, worked or didn't work. After those who appreciate you, will come for a small chat or at least reply to your email.
For longer periods I will also include a drink offer in the email but that depends if I have met people who would consider coming out and you would enjoy their presence.
First, you're not required to write a thank you note.
Second, there may be better ways to express your appreciation. You are, however, supposed to show your appreciation in some way, if you want to make the best out of the internship.
Way back, I made brownies and brought them in, and let the office know a couple hours in advance - by email - that there will be brownies in the lunchroom at 5. I'm not saying that's what you should do. I'm saying there are many ways to express appreciation and you should find/choose one that fits your own style.
In the United States, sending a thank you letter is optional. If you absolutely, positively have to send a thank you letter, do it by email - I find receiving and reading snail mail aggravating, given that I run around like a headless chicken, I am juggling multiple tasks and I have only so much time. And things go wrong all the time.
Send a thank you email to: 1. remind them that you are leaving at the end of the week; 2. you'd like them to act as your reference; 3. let them know that you are available for work during the semester - they can't and won't read your mind. If you are available, you have to spell this out; 4. that you had a great time working with them. If your internship was unpaid, discuss getting paid at the first opportunity when you are offered future work.
Don't send a "thank you" email just to say "thank you" :)