Response from Prof. B.

Thank you for your reflections and for your fine participation throughout the course. I agree that this course is quite different from the other courses in the mathematics department, including the other ones that I teach, but it certainly is centered around mathematics even if it is not traditional in its content or its methods. Several students felt that it would have been better for them if I had provided sets of problems (and expected answers) on a regular basis. That might have worked for a great many people, especially if the problems were carefully written and graduated in difficulty, but it would have been a different course. Maybe I'll try to teach that one the next time and compare?

I'm glad to see that the class periods were engaging enough to encourage regular attendance in spite of competing demands on time and energy. That can often be a problem when students are taking three other courses with their own challenges, some much more directly connected with a concentration program.

The dialogue aspect of the class, which I agree is paramount, will be facilitated considerably by more standardized and easy-to-use html templates, with a good introductory session and paid TA support, something we will arrange to have in the future versions of this course. We will also almost certainly find some better conferencing software, and some ways to encourage people to go back and visit their own earlier pages and those of their classmates, to build things up over time, not just along the "wave-front of the present".

I was hoping to see more hypertext techniques in your final project, but I think you had to work primiarily on the content since you had chosen to cover such an ambitious amount of material! You did manage to cover a great deal.

Course grade is Satisfactory.

Comments on the Cosmology Group

Your group certainly did a thorough job with your substantial web pages and your presentation. I'm glad that we allotted a full class period to it since it covered so much ground.

The Field of Cosmological Dreams was a very creative and successful way of presenting numerous interrelated theories connected with the nature of the universe, especially in relation to geometric ideas. There was effective use of visual materials and historical links, a nice final presentation component which was both engaging and historically accurate (even if the spelling and pronunciation of the names was somewhat inconsistent).

Possible shapes for the cosmos covered a great many topics, some combined in ways that were not included in any of the references. It might have been better to decrease the number of topics and to try to find some new ways of presenting concepts already introduced in class or in the readings. As it was, it definitely invited the audience to look at the references for further elaboration (and it did provide references, something missing from several of the other final presentations).

The Haikube was a very imaginatively presented illustration of a slicing operation, although the edge-first slices are still hard to understand and corner-first is quite mysterious. It might have been good to start with a more conventional Haiku, to illustrate the literary form and to serve as a basis of an expansion into another space. Following along the space-time analogy, you might consider a poem where three slices in one direction describe the same scene or phenomenon at different times, past, present, and future. Then slicing perpendicular to a different direction could reveal some other aspect of the poem? The relativity of rotation of a person or of space-time itself was nicely illustrated by the plastic card demo (and I would like to have that model, or a copy of it, for the collection.) These examples were a nice counterpoint to the physics concepts.

The Relativity section made some good links to other sections of the presentation and within the topic itself, although it might have been more helpful to include some suggestions for linking at the bottom of the page. It is a bit disconcerting to come to a dead end with no good idea of the way to continue. The asides were effective uses of the hypertext. There seemed to be some duplication in the pictures of spheres on a quilt and the finger pushing against a grid, so some additional links might have coordinated Flatland analogies better, ultimately among the various final projects themselves.

The Expansion section also uses links well to explore a subject that was only alluded to in general terms in "Sphereland" for example. The Hawking speech might have been connected to other parts of the presentation, along with some of the philosophical comments. The sphereland analogy could have been tied in better with the shape section in this presentation. The overall design of the presentation is effective, and the reader is drawn to consider further reading. A suggested bibliography would have been nice, for the whole presentation, not just for individual parts.

All in all it is an impressive presentation, showing a lot of effort. Good work.