With one exception, 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 7-10 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. Typically, about 85 applications are received each year.

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 discrete mathematics 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 visitors 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, 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" and "Who Wants to be a Millionaire" where he won $500,000. Alison Miller is shown finishing third in the 2000 National Spelling Bee broadcast on ESPN. Next year I will include clips from the documentary film "Wordplay" about the 2005 annual American Crossword Puzzle Tournament in which Kiran Kedlaya places fourth. (Kiran was second in 2006). In addition, I include some videos from the annual program talent show.

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. Through 2006, the program has had a total of 143 students with many participating more than once. To date, the program has produced over 100 papers that have been published in well regarded profession journals. They include papers on graph theory, combinatorics, number theory, group theory, ring theory and field theory. A complete program bibliography is available at www.d.umn.edu/~jgallian). Of the 129 program participants who have received their Bachelor's degrees through 2006, more than 90% have gone on to graduate school and two thirds have received fellowships. Sixty-four participants have the Ph.D. degree. Many participants from the program have received the Morgan Prize given jointly by three professional organizations for research by an undergraduate and many have won the Alice Schafer Prize given by the Association for Women in Mathematics for excellence in mathematics by an undergraduate women. In large part, the success of the program is due to the extraordinary contributions of the advisers and visitors.
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