Complexity theory: If you can't tell the difference between an exponential and polynomial algorithm, you'll be waiting for the job to finish while someone else codes up a faster program and goes home early.

Basic statistics and number theory come up sometimes.

Recursion -- lots of definitions involve recursion, or are more simply stated recursively. Functional programming fits in here, though most languages have some form of recursion available.

There are many nuggets in TAOCP, but it seems you have to know where to look, or guess that your topic has been mentioned. I often find pointers there from other searches.