So, it's been a fun and illuminating semester; we've sliced clean across higher-dimensional mathematics in all possible ways, unfolded it into all manner of arts and science, and yet we have seen but a shadow of this rich and surprisingly informative field.
1) This class has greatly rekindled my interest in mathematics- I haven't taken any math since high school, and I had lost touch with much of the beauty of math and the thrill of discovery, the proud feeling of completion when a theorem is conclusively proven, and the humanizing embarrasment when a flaw in the proof is demonstrated. This class has helped me to return to the mathelogical discourse and given me new tools with which to examine and consider the many universes we know or will someday discover/invent.
2) The most positive aspect of the course, in my view, was the breadth and inclusiveness of the topic; the compartmentalization of a university, with each department in its own little building, often can lead us to believe the disciplines are wholly independent from one another. This semester, however, we have examined dimensional mathematics inside and out, and explored the complex interrelationships between mathematics and art, physics, literature, religion, biology, etc. The only thing I would suggest is having more in-class problem-type things... like the time we made formulas for the vertices of an n-cube or when we tried to define a "taxicab" circle. I liked the problem-solving aspect of these activities.
3) Paperless is the way to go; I really liked being able to use the web and all its resources as part of my assignments... as well as being able to update my comments after class, or after finding new web sites.
4) I enjoyed learning about HTML, and generally had no problem with it, though I think it may be difficult for someone who isn't a nerd like myself. Perhaps a more in-depth HTML lesson would be in order... is there an editor on the App Server? If so, it would be easy to train everyone to use it.
5) The weekly assignments were a good way to get us to think about things before class, especially with prof B's responses. I don't think the privacy thing is a problem; everyone knows that their comments are public, and it certainly made me develop my work more thoroughly, knowing that everyone would make fun of me if I didn't. Of course, it made for a bit of a contest to see who can have the most exciting links, the most bright colors, and the most blinking titles, but I think that serves to stimulate creativity and it wasn't really a contest, so we all just did what we wanted.
6) I took the "General Relativity" part of the experiment, and following that link is my stuff... also, I did some miscellaneous computer stuff for everyone: file transfers, scanning, etc.
7) Working on a team is a great idea, especially when dealing with a subject where so many topics interrelate; the group structure allowed the projects to express each person's strengths and interests. I think my overall effort was about the same as if I had written a ten-page paper, but my enthusiasm was much greater in the group context.
Thanks to everyone; I've enjoyed this class a lot...Prof. Banchoff's Response