PhD Mathematics Admission Advice

Question

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.

Answer 1

Although some people might reasonably think that "pure math" courses are irrelevant to your larger goals, I would claim that the popular distinction between "pure" and "applied" math is both scientifically meaningless, and potentially hazardous to people trying to get started.

Having fluency with basic ideas of abstract mathematics ("algebra", "topology", and such) is inestimably useful. Illiteracy in these things makes it impossible to really know what the substance of many "applied" conversations may be.

The ideas in "pure/abstract" math are not at all disjoint from "the real world". They were all motivated by the desire to understand things. Yes, some self-styled "applied math" people pretend that all they need is computer time, and some self-styled "pure math" people pretend that whatever they do is disconnected from reality, and is practically useless. This is all silly, in my opinion.

In particular, having a basic grounding in "abstract" math will make you a far better candidate for any reasonable math program, whether eventually aiming at something "applied" or "not".

Answer 2

If you mean a TA by "funding" then you would probably be fine. But it is impossible to say until you apply. Make sure you have good letters of recommendation.

But "free ride" funding is not so obvious. A TA normally comes with free tuition as well as a living stipend.

And note that the GRE is being de-emphasized now in many places. But it is the application that gives you real information. Apply to a variety of places to give yourself more options.