Haha yikes that was a tad harsh. What sensible woman wouldn't want a smart, older man knocking on her door? I say as long as the rules permit, go for it! When I was an undergrad, I had a friend who dated a grad student after she finished his class and I knew another girl who even dated a teacher. I would imagine that the easiest person to ask is someone in the counseling center. if it's a no-no, I'm sure they have to deal with issues like that all the time.
Not trying to be harsh...just speaking as a woman who gets a fair amount of male interest. I know what it's like to be on the other side of the coin. For one thing, it's entirely possible that the woman is already in a relationship with someone. And there's the whole issue of what she finds attractive in the first place; I've only found maybe 5-10% of the guys who hit on me to be worthy of any attention at all. (It's a moot issue, because I'm married, but still...)
I imagined that I would be exempt from this in grad school since I'm so much older than everyone else, but NOOOOOO... I even have a freshman in one of my classes who flirts with me. I've mentioned that I have a son who's close to his age but that doesn't seem to faze him! Bleah.