You also may wish to avoid mimicking the formal style of textbooks, e.g., "exercise for the reader," "question to confirm understanding." This tone of voice can be easy to use, but it's odd and unpleasant for me to read it, given that (in theory) we're all peers here. You may have something to teach us, but you're not exactly my professor.

I would add that this is another reason to simplify the math - doing so eliminates the need for exercises by making the answers less confusing.