Emailing a student corrections to their typed notes I study undergraduate mathematics at university. In one of my units, the lecturer does not provide any notes (typeset or otherwise), but has said that if anyone else who attends the lectures wants to typeset some notes, he'd be more than happy to check them over and then share them with the class.

Remarkably, one of the students is actually doing that, and is actively typing up notes for the course as it goes on, and those notes are being shared via the online course page with the class. 

Unfortunately, the notes have some errors. These are often, rather than just being typos, completely incorrect assertions. I don't blame the student who's writing them at all; I completely understand that having written the notes it's very difficult to then check them over properly. 

I want to email the student with a large number of corrections to the notes he's typeset, but I don't want to come across as overly assuming. I feel that emailing the student who's taken the time to make these notes to such an effect might come across as condescending - or worse, "I'm better than you, do it like this". Should I email the lecturer instead? What's an appropriate way to approach this situation without upsetting anyone?
Since the notes are shared via an online system, it seems like a good idea to collect all found errors and typos in the very same online system, e.g. if the system provides a kind of a forum. This would have several benefits: 


Everybody who spots an error can report it right away.
Everybody who suspects an error can check if it actually is one.
The author of the notes or the instructor can answer in the forum and indicate if this is an actual error and announce when it has been fixed in the notes.
There is the possibility of discussion around the issues - sometimes one thing appear as an error for one person, but not so for another one and in the end it may just be a matter of convention (this is also true for mathematics…).


Note that the etiquette of the forum is very important: Everybody has to be polite, ask and answer in good faith and no blaming shall happen. But if this is supported by a moderator (e.g. the instructor) this can work very well.

I used a system like this for the lecture notes I typed and I even announced and awarded bonus points for everybody who found an error in the notes (this seemed to be a good idea as it makes it pretty clear that all lecture notes may contain errors…).