Eight undergraduates will assemble for eight weeks at Auburn University in each of the summers 2013-2015 to conduct research in areas of algebra and discrete mathematics. Our aim is to provide participants with an authentic research experience and get them excited about graduate school and research careers. The essential part of our program is that we lay out a lot of research problems, and participants can work on any one of them with faculty, graduate students, other participants, or by themselves. They can work on more than one thing; they can work on questions imported from elsewhere, or on questions of their own devising. We conduct the program this way because we believe that this is essentially how mathematical research has always been done for at least 2500 years. So the pattern of activities will therefore be as in our previous REU programs: intensive introduction to problems and problem areas in the first two to three weeks, capped by an obligatory "ice-breaker" presentation by each participant in the third week, followed by a "research institute" in the remaining five weeks, capped by a final presentation by each participant at the end of the final week. During the research institute phase, there will be at least one research presentation every day by faculty and graduate students of our Department of Mathematics and Statistics, visiting luminaries, and the participants themselves, but the main feature of that phase will be research carried on by the participants in various combinations with faculty, graduate students, and themselves. Publishable results will be written up either by the participants themselves, with advice from the project directors, or, in the case of joint work with faculty, by a faculty member in consultation with the participant(s). Communication will be maintained with participants after the program ends for the purpose of conducting further research, presenting results at national and international conferences, recruiting for subsequent programs or graduate study, and for assessing the impact of the program on their lives.
By the measure of mathematical discoveries made by the participants, we have been quite successful. By the time all the results from our 2011 and 2012 programs have been published, there will be well over 30 papers in refereed journals and numerous others still in preparation arising from our nine programs. However, the success we aspire to is not so easily quantifiable: we want the participants to emerge from the program enlightened as to what mathematical research might be like, that they may better decide what they want to do with their lives. So far, around half of the alumni have gone on to graduate study in mathematics, and another significant fraction has gone to graduate school in computer science, statistics, or mathematics education.
