[Turing_Machine]

Well, it depends on what you consider challenging:

Most work in terms of hours spent: compilers (you had to write one from scratch)

Hardest due to inherent difficulty of the material: theory of computation. Turing Machines and the Halting Problem and such weren't too bad (well, duh) but some of the more advanced stuff was pretty challenging, at least to me.

Hardest due to the material being a collection of bizarre recipes and jumping all over the mathematical map: tie between an undergrad numerical methods course and a graduate modeling and simulations course. It wasn't conceptually difficult to write the code, but understanding exactly why it worked was a different story. I've never been good at memorizing stuff unless I understand how it works (advanced statistics suffers from a similar glut of "magic recipes", in my experience).

Edit: the compilers class was the one that's proven to be the most useful over the rest of my life. I've written specialized parsers and so on a bunch of times.

I've never used the stuff from theory of computation again, nor can I imagine that anyone would who wasn't a researcher in that area.

I could see numerical methods being useful if I did a lot of down and dirty work with the physical world, but I mostly haven't done that..