With a few exceptions, every year since 1977 I have run a ten-week undergraduate research program in mathematics at the University of Minnesota Duluth. Graph theory, combinatorics and number theory provide the source of most of the problems. Recent programs have had 8-10 undergraduates along with two former participants who act as research advisers and a dozen or so former program participants who visit for a week or more during the program. In recnt years the number of applications ranges from 150-200.

Selection of participants is based on letters of recommendation, response to questions on the application form, performance in high school mathematical competitions and the Putnam Competition, reputation of home school and course work. The Putnam Competition has proved to be a good predictor but it is not foolproof. Many students who have done outstanding work in the program did not finish in the top 500 of the Putnam Competition or did not take it at all. Desire to succeed, enthusiasm and willingness to work are as important as raw talent. A special interest in combinatorics and the ability to interact well with others are also important considerations.

The program is loosely structured. Although each student has his or her own problem, it is quite common for participants to receive ideas from each other. Cooperation rather than competition is stressed. Each week the participants give talks on their progress during the previous week to the group. The visitors also attend these sessions and occasionally give presentations on their research. Participants, advisers and short term visitors who are program alumni live in the same on-campus apartment building and interact with each other on a continual basis. We have lunch as a group a three times a week.

Weekly field trips on Wednesdays are part of the program. It is important that the students enjoy their summer. We go biking, white water rafting, hiking, alpine sliding, walking along the shore of Lake Superior and visit the beautiful parks in the area (see photos at www.d.umn.edu/~jgallian) Watching the morning sun rise over Lake Superior is a program tradition. On Wednesdays and weekends the participants have access to university vehicles at no cost. This makes it convenient for them to see movies, shop and eat out.

One of the highlights of the summer is "Beatles night." On this occasion everyone comes to my home for dinner and to watch videos. In the early years of the program I showed various clips of the Beatles but it has gradually evolved to include videos featuring former program participants. One is of Melanie Wood on the syndicated TV program "To Tell the Truth" where panel members try to guess which of three young women is the real Melanie Wood, who was the first girl to represent the United States in the International Mathematical Olympiad Competition. Another is of Melody Chan playing the violin at Carnegie Hall with Itzhak Perlman and one other violinist and broadcast on PBS. Pat Headley appears on both "Jeopardy." Headley and Nathan Kaplan both were on "Who Wants to be a Millionaire." Alison Miller is shown finishing third in the 2000 National Spelling Bee broadcast on ESPN.

Although getting a publication stemming from an REU is not necessary for a positive research experience, having a paper published in a professional journal is highly desirable. Ideally, publication of work done in an undergraduate research program is a beginning rather than an end in itself. Many participants from the program have continued to publish as an undergraduate or graduate student.

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