My preliminary verdict is that I think I will have gotten what I had hoped to receive from this class. I was very interested in dimensionality in high school, and the local public library was callously disinterested, so my curiosity was frustrated. Exploring general topics of dimensionality with a group of peopleto back me up has so far been more rewarding than I'd hoped. The extremely good news from my point of view is that I'm beginning to gain a sense of intuition about higher dimensionality. Perhaps this means the child-like awe will wear off soon, but I'm ready to trade the slack-jawed wonder of it all for a little more facility with the subject at this point.

I feel that I'm still up in the air to some extent, however. Basically, every week there is an entirely new, huge subject for me to explore. Each chapter suggests at least one detailed project to me, with the result that I feel somewhat guilty for never getting to finish all of these fun projects. My last great hope is the final project. Hopefully I'll be able to get a few folks to sign on to some of these ideas of mine and I'll see at least one to fruition. Nevertheless, I sense that this course will be one where I feel that I could have done better. This is not really because there is terribly much more time and effort I coud reasonably devote to it, but because it is leaving me with a feeling of being at loose ends because of all the territory I'd like to explore.

Prof. Banchoff's response
Obviously, it's a little self aggrandizing to pretend that all of these ideas could be neatly explored in a single semester course. Dimensionality is the sort of thing one devotes a career to. This is the closest thing to a complaint that I could muster at this point; every day I find some concept that I would like to spend a year developing, and then tomorrow comes and the same thing happens. This makes for a fascinating class, but not a very satisfying one: you never have that full, after-dinner, I-have-just-fully-conquered-this-subject sensation. That's all well and good, mind you, and I wish most introductory level classes were less pat and simplistic. In fact, I appreciate that this course doesn't even have the pretense of being a complete treatment of dimensionality, or even a complete introduction. It's more intellectually honest than most other intro courses, where the tendency is to pretend that everything has already been figured out, and you, as student, must accept what has come before you as fact. It is intriguing that we seem to bump our heads against the limits of human knowledge almost daily, and I wish more of my classes were like that.