Earlier quoted context omitted.
I'm a data engineer for a startup that's trying to hire its first data scientist. The range of candidates that apply with this title is massive. Defining our expectations has been challenging. My phone screen "fizzbuzz" is having them calculate a standard deviation from an array of data w/out with only basic operators (no numpy.std). Then explain why they choose population/sample and explain the difference. I studied…
I have to admit this scares me just a little bit. I'm a senior sysadmin who is trying to lateral transition into data science, but I'm no math whiz, I'm just good at pragmatic use of tech stacks and have a generally analytical mind. If you are a math undergrad how could I ever expect to know more math than you? Of course a standard deviation should be easy, but your comment on math just stuck out to me.
Read through, and do all the exercises in, one textbook each for:
1. Calculus
2. Linear Algebra
3. Abstract Algebra
4. Analysis
5. Topology
6. Probability Theory
7. Number Theory
...more or less in that order. Make sure your calculus book covers single variable and multivariable calculus. Supplement with applied mathematical statistics. Do that, and you have the equivalent of a mathematics undergrad (as far as relevant courses are concerned).
You could even do this with something like UIllinois’ NetMath program, or some courses on Coursera. You can swap out Number Theory for Complex Analysis or deeper Probability Theory and it’d be more relevant.