Lacking Research in Math

[World-Refusal]

Alright, time for some background.  I graduated with a BS in biology sometime ago, and while I was in college I did biology research.  The research is somewhat minor (at least in my eyes) and was not published, but I did present it to my school's Board of Trustees.  Also, my mentor is one of LOR writers.  I also worked as a service technician at my state's agricultural experiment station.  Now, I have decided to go to grad school in applied mathematics, not biology.  I have been taking math classes at a nearby college and will be done with abstract algebra and real analysis at the end of semester.  However, I finish with no research experience in mathematics.  

 

Basically, how much does this hamper my chances for applying to grad school for a MS in applied mathematics?  I have some experience and there are common traits desirable in researchers, but biology research and mathematics research are fairly different.  Some of the grad schools I am looking at seem to have their applied math MS programs designed around professionals and co-ops.  Other grad schools I am going to apply to seem more 'typical', in which they aim to produce researchers instead of professionals.

 

I figure REUs would be a good place, but there is the issue of getting LORs and being competitive compared undergrad math majors who likely have more math experience than me.  The college I am currently at is a typical four-year college, so I was wondering if I could ask some professors what research they are doing over the summer or look into other nearby colleges and universities.  Any advice on my situation?