I am in the last few semesters of my bachelors, and I have been preparing myself for applying to PhD programs in mathematics. However, as I was sitting with my research mentor today, he informally offered me a graduate assistance-ship for the masters program at my current university. He mentioned I would still need to go through application process but that I am a pure shoe-in for the GA position. I am unsure whether to chase after this offer on a more serious tone or apply for PhD programs, and as such I am seeking information. The real rub stands that I am attending a not too prestigious school for math and this worries me that I may be limiting myself. However, for personal reasons I am considering this potential offer greatly. Would the masters from a low/middle-tier prestige/ranking hinder my chances for getting accepted into top-tier PhD programs?
If you need some information about me. GPA 3.7, Major GPA 3.8, I will have some published works, I will have finished 3 Graduate courses before applications (Order Theory, Analysis, Graph Theory), GRE general in the upper crust, No Math Subject yet (Still studying for this). Two very strong recommendations from current and accomplished researchers, and two standard recommendations.
There is a note that I should include my location before posting. I am attending MTSU for an Advanced Mathematics Bachelors.