Cryptography is one prominent example. Modern compilers would be another (though an amateur can go here a little farther than in others, because of parser gener

Cryptography is one prominent example. Modern compilers would be another (though an amateur can go here a little farther than in others, because of parser generators and such). Operating systems more sophisticated than a toy-grade proof of concept is yet another. And writing (again, non-toy-grade) databases. And formal verification of programs, this is hard to learn on one's own, too.