Set theory is, probably, the most fundamental. Everything could be defined as a set or as a function.
Lambda calculus, obviously.
Some combinators. Basics of linear algebra.
No category theory and other bullshit is needed. Sets will do.
It is actually very important skill to avoid wasting time in disconnected from reality obscure academic bullshit, be it philosophy, physics or math. Do not follow other people's hallucinations. Have your own.)
As a rule of thumb - you need just enough math to understand The Wizards Lectures and SICP.
Again, the substitution model, sets (for notion of types and basic collecttions) and high order functions (the "domain and range" mantra) is enough.
For algorithms the notion of being bound by some function and orders of growth.