This section briefly outlines some example research projects for the REU participants. When the time arrives for participants to select individual projects, each faculty member presents the participants at their institution with a greater number of possible topics than there are participants, so that each student will be able, within these limits, to choose a project topic rather than have one assigned. We feel that this is important in terms of having the student feel that the project is ``theirs.'' Also, we are careful to structure projects so that they have several possible levels of completion. This ensures that each student will be able to complete some (possibly simplified) version of their project and experience the resulting feeling of accomplishment. It also allows the more talented or ambitious student who works hard enough to achieve a substantial research publication. This approach has proven successful with our past REU participants.