Some background on me: I graduated in 2020 with my BS in Accounting with a minor in Mathematical Sciences from a non-special public university. I decided I wanted to make an educational career change with only 1.5 years of undergrad schooling left. Mathematics courses I took in that time were calc 2, calc 3 (taught myself calc 1), differential equations, linear algebra, and real analysis. I got A's in all of them. I was lucky enough to be admitted into an MS in applied math program in my state at a relatively well known private school in the tristate area knowing I didn't have a serious shot at being admitted to a PhD program. This first semester I am taking topology, numerical linear algebra for big data, and probability theory. I am concentrating in data science but still taking more pure mathematics courses as electives.
I plan on sending out PhD applications for the Fall 2022 cycle during the fall semester of 2021. At that time I would be enrolled in foundations of algebra 1 (which is just abstract algebra), functional analysis 1, and numerical analysis. I am hoping to do a research project with a professor this upcoming summer. With that said, I know some of the very important things for the application are the letter writers (of which 1 professor at my school is pretty well known). Other than that, I plan on retaking the standard GRE which i did not do well on the first time, and potentially taking the subject GRE. What would this community say my chances are at being admitted to a top 50 university with funding? I know it's kind of a hard question to answer but if theres any other info I can provide please tell me. I would also accept any advice you could give me. I will most likely just be looking to apply to pure math phd programs while planning to do my research in a more applied area. Thanks.