The Michigan Tech REU (Research Experience for Undergraduates) is an 8-week experience in Combinatorics or Number Theory research in middle-of-nowhere Upper Peninsula, Michigan. I highly recommend it.
The REU is run by a wonderful man named Anant Godbole. He chooses six undergraduates to come work alone or in pairs with him on problems he has collected.
The atmosphere is relaxed. We supposedly arrived at MTU around 9:30 every morning, took a two-hour lunch break from noon to 2 and left MTU around 5 each afternoon. In practice, we spent even less time than that at MTU. The important part was to think about math. And Anant knows that thinking can't follow a 9 to 5 schedule. We each had keys to our shared office so that we could keep whatever schedule was best for us. The time in the office was spent thinking or talking to Anant. (Everyone talks to Anant at least once a day.)
Originally, we were divided into three pairs of two and started on a problem. Some of the problems didn't go anywhere so Anant put those groups on other problems. Two of the groups split up after a few weeks. (I was sure the h>2 case was solvable but my partner was bored with the problem so he started another problem while I extended our h=2 proof.) One of the groups worked together for the whole 8 weeks.
If you want to publish, MTU REU is the place for you because Anant does too. He works very hard to get publishable results from as many people as possible.
Not only is the REU a good math experience, it is also a chance to live on your own. The four women shared an apartment two blocks from campus; the two guys had an apartment one block from that. There's a grocery store a block from MTU. We cooked for ourselves, entertained ourselves, worked. This was as close to real life as those of us who enter academia will ever get.
Houghton, MI is prime vacation country. It's 65 degrees in the morning. The sun doesn't set until 10:30 pm. We were lucky to have wheels which meant weekend camping trips, trips to Copper Harbor, weekend hikes, berry-picking. But if we didn't have a car, we could have rented one at quite reasonable rates.
If you're looking to do research in Number Theory or Combinatorics, think about the Michigan Tech REU.
--Rebecca Rapoport '95(rrapopor@math)