Getting past programming interview questions without a CS degree

I'm a quantitative analyst at a financial firm, but am trying to break into a developer role within finance. I use a lot of Matlab and Java in my work, so I thought I'd be able to do ok on the technical interviews after practicing with 20 or so problems on HackerRank.

At places where I've interviewed so far, I've gotten questions involving abstract syntax trees and dynamic programming. What?? I had to look these things up after the interview I obviously did not do well on.

How does someone like me, without a CS degree, get past these types of problems, or break into these types of roles?