I am a junior mathematics major at a relatively unknown liberal arts college planning to apply to Ph.D. programs in pure math next year. I have a near-perfect math GPA and a pretty solid background in terms of my coursework, including every intermediate and advanced-level pure math course offered by the department and several directed independent studies. In terms of research, I spent one summer assisting a physics professor with a computational physics project at my home institution, but it is an unrelated field and did not yield any publications. I recently accepted an offer to a pure math REU program for this summer, and I am considering the possibility of a senior thesis. The problem is this: the REU ends a week before the fall semester of my senior year begins, and ideally I would want to spend time working on tying up loose ends from the project and prepare a paper for possible publication. I also don't want to be working on two research projects at the same time (REU wrap-up + senior thesis), especially since I will also be very busy with a heavy courseload, studying for the GRE math subject test, and applying to Ph.D. programs. So basically, I have two options. First, I can stop working on the REU project after the program is over and focus my attention on the senior thesis. Second, I can spend time wrapping up my REU project and hopefully get a paper prepared and submitted, and replace the senior thesis on my schedule with more coursework (possibly a year-long independent study in intro graduate algebra). I understand that this is my decision to make, but I do welcome others' thoughts about the matter. I am especially curious as to how the two options may comparatively affect my preparation/chances for Ph.D. program admissions.