I still don't feel like I have an answer about whether I need an agent for a math monograph which might be used for, but isn't specifically intended for, a class. I think the answer I'm getting from these discussions is "probably not." Is that right?
Yes, my answer is probably not. Sorry I can't be more positive.
No, that's good information. If not for you, my next step would be to approach an agent. Now, my next step will be to figure out which publisher to approach. Actually, my very next step will be to get a copyright. My research indicates that theft of submitted manuscripts is unheard of, but I just won't take the chance.