reference request - dynamic discrete time optimization methods
As suggested by 1muflon1:
I don't really use dynamic discrete optimization (yet) in my work, but I did explore several books once. Here are some suggestions:

Economic Dynamics: Theory and Computation by John Stachurski: It's very easy to fall in love with this guy. He writes casually yet authoritatively. The book covers required real analysis and includes python codes and exercises.

If you like the above book do explore https://quantecon.org/lectures/

Recursive Methods in Economic Dynamics by Stokey, Lucas and Prescott