My school recently developed a 1-year, intensive Masters program in Mathematics following the typical undergraduate B.A. In an effort to get more experience with more advanced math, I've decided to participate in the program. However, I've been told several times that I should apply for and (if accepted) participate in a summer REU. Yet, in order to work on my Masters, I must officially graduate from undergrad, which (I think) renders me ineligible for many (if not all) REUs.
Without an REU, I am concerned how my overall profile for graduate school admissions will be negatively effected. I have some modest research experience and possibly will have a paper published with a professor (though that is TBD). Between the summer of my junior and senior year then, what can I do to stay productive in math? How can I continue to better myself as a candidate for graduate school? Am I correct in assuming that I am now completely ineligible for REUs?
Thank you for your time.