It is interesting, of course, to compare different responses from the class, especially when it comes to the amount of mathematics in the course. Some felt that there were too many approaches from subjects other than mathematics proper, and not enough "hard math". Others liked the mix as being just right for them. You seem to have found too much of an emphasis on mathematics, but since the course is termed "The Mathematical Way of Thinking", I suppose that that might be anticipated. I did try to bring up alternate approaches, in the book and in comments in class, and some people took me up on them in their weekly reponses, sometimes embarking on a few interchanges over the course of a few weeks, sometimes with other students entering in. I hope that that will happen even more in the future when we iron out some of the technical problems that wasted a lot of our time this past semester. I certainly agree that we need more clearly presented introductions to the software and easily accessible TA support, and that will definitely be a feature in future versions of this and related courses. Also we will standardize the html documents to the degree that they can be more easily be read. Several electronic messages I have sent have been lost, and I still don't know an effective way of getting apostrophes to print correctly without having to retype them all (as I did for your week 14 reflections page).
With respect to the final project, I liked your presentation of a single page with a number of interconnected items, but you could have gone further and provided more information for people unfamiliar with the different authors. This would have been a good place to link to a more complete analysis of the pieces for those with a more sophisticated literary background. How does the maze image interrelate with other ideas in George Eliot's work for example? (When I was a sophomore in college, I remember that the prize winning senior thesis was titled "Patterns of Imagery in 'Middlemarch'.")
I hope you continue to encounter the meeting of mathematics and beauty in art and literature--it is always there in some guise.
Course Grade: Satisfactory
Commentary to the Maze Group
Although your work has furthered the study of mazes and labyrinths beyond the preliminary investigation that some of you carried on in the book report exercise earlier in the semester, it does not seem that there has been that much progress in understanding the mathematical principles involved, in particular the function of dimension in the subject. It may be that there just isn't that much there, and the subject is too easily exhausted.
Let me comment on several aspects of your website. The overall structure is certainly fine, inviting the reader to explore the concept in literature, history, art, recreations, and algorithms, but there could have been more of an attempt to coordinate the form of the various sections. All of the pages seem quite wordy, unrelieved by illustrations, even though there were links to visual material.
It would have helped in the literary portion to include links to biographical information on the various authors, especially George Eliot with her Victorian connections. The Borges link is a nice one, although the material presented there is a bit rough and unscholarly in its writing. The background texture on the Auden poem makes it difficult to read, and it would have been better to analyze it somewhat, since it is a fairly good poem and it does bring up a number of interlinked images that can be related to other aspects of the topic. In particular it is one of the most "dimensional" of the literary examples in that it explores the concept of an overview. This overview notion shows up in at least one of the computer games, where a player can navigate a series of rooms without looking at the floor plan, or choose to see the plan of the maze "from above". That would have been a nice way to establish some linkages within the final project, to get away from the impression that the parts are separate somewhat unrelated entities.
The history section would have done well to link to some of the artistic representations of the Minotaur legend (there is an nice on in the "Mazes and Mathematics" link in the Recreations and Games subsection) as well as to some more serious sources of information of the encyclopedia variety. It should not be necessary to highlight the words each time they appear in the page, a very distracting feature. The link to Borges is not particularly historical, and the "Greece" link only goes to a very general source on mythology, with no further information on how to follow that thread. "Crete" appears to go to a travel folder, and "Nile" to a field trip, neither of which adds much to the narrative or gives any information that might be useful to labyrinths, mathematical or otherwise. There must be more legitimate sources out there. The material on Egypt was intriguing since mazes are not so commonly associated wht that culture. It would have been good to give the reader some more idea of places where additional material could be found to follow up this introduction.
In the art presentation, although the choice of images includes some that are quite striking, there is not enough elaboration to show how the mathematical concepts are suggested. The link to Escher for example does not lead to anything specifically related to mazes and there is little assistance provided in the text. There has to be some further biographical information provided about the unfamiliar artists, like "der Hundertwasser". The notion of a maze inside one's head is something that could be developed even further, in that the two-dimensional slice of a brain, in CAT Scan or MRI form, resembles a maze structure, which only can be navigated by moving into the third dimension, into the full range of convolutions of the brain. It is not clear to what extent the mandalas represent mazes at all. A link to the history section of the paper, with reference to the classical themes, would have held the sections together better. Hedge mazes as forms of artistic expression could receive more attention too.
The maze references in the World Wide Web could have been annotated more helpfully. Some of them are quite mathematical while others have little to add to the discussion. Singling out some of them for special consideration would have made the section more useful, especially if some of the games could have been linked to other sections of the final project.
The algorithm section, curiously enough, seemed less interactive than the earlier trio demonstrations that used hypercard stacks. Some visual illustration in the code sections would have been much more helpful in showing how to pair a simple maze up with a tree, and how to use the queues and stacks to make the various analyses. The in-class presentation made the comparison clearer, but it never had the force of the earlier demonstration. Some illustrations of weighted graphs could have motivated the Dijkstra method, and tied in better with the applications of maze algorithms to practical problems, as mentioned in the introduction.