What do you think are essential, pen-and-paper, math skills?
Maybe this is a non-sensical question but here is where I'm coming from.
I'm in the middle of a bioinformatics program. Growing up I always struggled with math. I do a lot of analytics work now and I've been learning more and more about Linear Algebra, Calculus, Probability Theory, and Statistics, so I'm a little bit late to the party when it comes to learning math and I don't have a good pen-and-paper math skills. I do basically all of my work on the computer, in programs like Python, R, and Julia, and I understand the concepts pretty well and how they related to each other (example an integral being the limit of the Riemann sums, a determinant of zero meaning a linear transformation collapses space into a lower dimension, etc), but if you ask me to even do a basic integration or determinant calculation by hand, I wouldn't even know where to start. I just compute them with functions of code.
I guess my worry is that if I was ever working on a team and we were having a discussion about some concepts and mathematics came up, if I had to go up on the board and do some basic math I would not even be able to do anything apart from basic arithmetic and pushing around variables.
I guess my question is do you think there are some pen-and-paper skills that are still essential nowadays (e.g. factoring, derivatives, integrals, etc.)? Curious to hear people's thoughts.