To what degree do you have to transform notes to avoid copyright violations? I’m thinking in particular of taking notes on a lecture, but it could also apply to something like creating a Cliffs Notes sort of thing for a textbook, or creating a set of flashcards for studying. Would fair use for educational reasons change if you shared them among a study group, versus put on a non profit website, versus a website with ads? What about creating a public wiki where students could share their own lecture notes, summaries, and study guides?
I think with lecture notes there is an implicit copyright that you may copy the note for your personal use pertaining to class but not that you may copy it for others outside of class or profit from it. That being said, facts cannot be copyrighted but the style of presentation can be.
The essence of “copyright or not?” is how closely you repeat the words of the original. If you essentially reproduce the blackboard formulas verbatim, you are violating copyright. If you capture entire phrases of the lecture word for word, or with minor rewording - that’s copying.
As mentioned above, it gets tricky because facts and common math formulas cannot be copyright. Pythagoras or the sine law or geometric proofs have been repeated so many times nobody can say “when I said and wrote that, it was my copyright”. Ditto for a list of public statistics.
Few people bother to enforce copyright on lectures (unless they’re broadcast). Technically, the copyright belongs to the lecturer (assuming he wrote the lecture), but it’s unlikely it would be registered and thus legal options are limited for him.
Lecture notes are not usually verbatim and they are often just covering factual matter which could presumably be found elsewhere. If you took it down in shorthand for your own use and for the use of others in the class, you can argue that this was the entire point of giving the lecture – so students in the class had access to the information – and thus there was both fair use and an implied license.
If you copied the lecture verbatim and sold booklets of it, then you’re in potential copyright infringement territory, but ultimate there is no hard-and-fast rule that is clear in every situation.