Colleagues working in space technologies discussed recently if fundamental education were necessary for a programmer, so just for a reference, here's a list of fundamental-ish areas I had trouble with in practice over a 30 year career.
Statistics. This should be obvious. Although in theory I'm educated in the topic, I always had difficulty with it, and barely passed my tests, decades ago.
Error correction. To be entirely honest, I blew this. Every time I had to do it, I ended either using Phil Karn's library, or relying on Kevin Greenan's erasure coding package. I think the only time I implemented something that worked was the UAT.
The DSP on Inphase/Quadrature data. This one is really vexing. I ended with some ridiculous ad-hoc code, even though it's very interesting. In my excuse, there were some difficult performance constraints, so even if I knew the underlying math, there would be no way to apply it.
Other than the above, I don't feel like I was held back by any kind of fundamental background, most of all not in CS. About the only time it mattered was when an interviewer asked me to implement an R-B tree.
