In terms of the actual math, Duluth is a discrete math-combinatorics program (which generally, although not always, means graph theory). Joe Gallian (see the program web page), the director, is generally pretty good at assigning problems; almost everyone was happy with the problem they were working on, and if you weren't getting anywhere or didn't like your problem, Joe was very ready to give you a different problem. Perhaps most importantly, the problems that you get are very open-ended; it's not like "here's this problem, solve it," but more like, "here's this concept; play with it and see what you can discover about it." The logistics of this basically are comprised of Joe giving you a paper or two on a subject, and of you reading it and letting your creative inspiration roam freely.
As far as the social environment goes, participants are lodged in very luxurious apartments next to each other; this makes for a very bonding experience (especially when combined with the fact that participants are generally very bad at cooking.) The weekly field trips are also very exciting and bonding (partly due to lacerations incurred by some of the participants and, amusingly enough, visitors during alpine sliding (think luge, except with stone instead of ice and plastic instead of a luge board.)) As for Duluth itself, it is a relatively boring town, but there is miniature golf, th-th-th-thunder bowling, and, of course, Lake Superior, over which we saw many a sunrise.
All in all, I had an excellent time at Duluth. The only complaint I had
was about the specific people there- however, I'm sure that will be
better in the future. Please feel free to email me if you have any questions.
--Mike Develin (develin@math)