I cannot speak for all REUs, but the ones that I have experience with usually look for a few things:
- Good statement of purpose with a clear research objective. Even if this statement of purpose is a bit broad, it is important to show that you are able to ask good questions in relation to mathematics.
- Good letters of recommend.
- Specific coursework requested by the REU. I always found it odd that the REU at my university would specifically say a student needed understanding of Galois Theory OR Complex Analysis OR Graph Theory, and we would have students with none of these applying.
Data science (DS) internships are not scarce, as long as you are willing to go anywhere in the US. They are, however, often times competitive. I would suggest that you look very broadly at many fields for data science opportunities. (I, for example, got a DS internship one time working for a company that makes marine engines). Places like Google, Amazon, Apple, will be insanely competitive. Others, perhaps will be more tractable. If you have a background in chemistry, places like pharmaceuticals (Pfizer, Eli Lilly, etc) and chemical companies (Dow, DuPont, etc.) may be of particular interest.
Data Science as a Field
I cannot address every possible career path for math. I know people in law, medicine, engineering, academia, data science, psychometrics, business, athletics with math degrees. Given ten people with an undergrad in mathematics, chances are high that they will work in ten different fields.
I will specifically address data science as a career. DS relies on a trident of core topics:
- Computer Science
You need to be good in all of these. I would hear (and was given) advice to math students such as
A math degree teaches you to think & people will hire you for you ability to think and problem solve.
While this is true, it takes much more than a BS in mathematics (especially pure maths) to get a job in DS. You need to be competent in the trident of fields I mentioned above.
I would suggest becoming as expert as you can in PyTorch or TensorFlow, pandas, numpy, SKLearn (all in Python). I have never seen a job reject me for knowing those skills. Learning an object oriented language (Java, C++) is also helpful.
If you are also interested in chemistry, I would suggest getting a minor in it (or something else crosscutting). Read up on GANs and drug/molecule discovery. (See for example https://thischemicaldoesnotexist.com/) And, as I mentioned, fields like law and medicine (chemistry) are on the table.
Always willing to chat if you start a private chat and what to know more.