I talked about my plan for undergraduate research last week. This week, I invited my linear algebra class to join a research team I am forming.
The class is roughly half sophomores and half first-years. They have had calculus and linear algebra. My plan is to come up with a research question based around either finite fields or group actions on cyclic groups. I feel like I have some questions at the appropriate level that have come up in my own research, although I cannot explicitly state them right now. I had better be able to by next fall if any students decide to join the research team.