I went to a top 5 university where I chose to major in an obscure corner of the humanities. However I did economics research and a software engineering internship at a machine learning startup, which piqued my interest in applied math. I also really loved my proof based math courses, and I'm now trying to assess what the best way to get back into mathematics would be for me. My primary motivation here is to experience more of the beauty of mathematics, with a secondary motivation of potentially finding math related employment.

Courses I've taken (all proof based): Calc 1 (B+), Calc 2 (B+), Calc 3 (B-), Real Analysis 1 (Withdrew first time I took the course, retook for a B), Linear Algebra (B).

- 1. Should I retake real analysis and linear algebra if I feel I can be more successful in those courses the second time around? Or would admissions committees look at my profile and think that I was unable to succeed in math at my top ranked department and was boosting my GPA with an easier state school? (Although I was a consistent B student in math in college, I feel that some personal changes in my life will enable me to be more successful in math coursework going forward.)

2. What math courses should I take before I apply to a math masters? From my reading online, linear algebra, real analysis and abstract algebra seem to be the basic requirements. But how much real analysis/abstract algebra is expected? And is there anything else I must take? I would prefer to take minimal courses before a masters program because of the high cost per course.

3. Would doing a masters from a lower ranked program count against me in academia? Among other things, depending on my aptitude and interest in higher level mathematics courses, I'm considering trying to do a PhD in a mathematical field like economics or statistics. And one lower-ranked university I applied to last year for a math masters program was willing to consider me with just the background that I have (1 term each of linear algebra and real analysis). I've also noticed online that more prestigious departments offer no funding, while less prestigious departments in less desirable locations in the US seem to offer some funding for masters students (although I have not contacted any departments directly about this).