Here's an old mathematical perspective that treats dynamic programming as analogous to the calculus of variations. Very different from a how it's usually talked about, I think. I haven't read much of it, but perhaps the change in perspective will be helpful to you:
i'm familiar with this (through stochastic control and reinforcement learning and general econ stuff) but it's not really useful for the whiteboard coding style DP that FAANG asks.
https://www.rand.org/content/dam/rand/pubs/reports/2006/R441...