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?