<p>robcol - First and foremost, there is absolutely no harm in asking (even as a freshman). I personally know quite a few people (including myself) who did/are doing math research with their professors immediately after their freshman year. In all of the above cases, the professors were more than willing to work with the students in question.</p>
<p>On the other hand… to be honest, it would (generally) be better if you had more background than that to be doing research. The work is, after all, quite advanced. All of the people I know involved in research have had at least some working knowledge of algebra as well as real and complex analysis (because even seemingly unrelated areas of math tend to rely on basic knowledge of all of the above). Personally, I would probably wait a year, because I wouldn’t want to be overwhelmed.</p>
<p>However, that shouldn’t stop you from trying if you feel you’ll be okay. Look at your professors’ web sites and try to skim through some of their work (don’t expect to fully understand it or feel discouraged if you don’t). If you think you could realistically pick up the background as you go, then go for it.</p>
<p>Also - I’m sure the faculty at your school will give you advice (if you ask) on what they think is best in your situation.</p>