Algebra is the study of sets and their operations.
In OOP you spend a lot of time defining sets (classes) and coming up with operations on those sets (methods).
In FP you're not so concerned about coming up with sets and operations but rather breaking things up into ever smaller pieces. I mentioned elsewhere that analysis is about starting with big circles and making them arbitrarily small. This is pretty much what recursion is.
In OOP you spend a lot of time defining sets (classes) and coming up with operations on those sets (methods).
In FP you're not so concerned about coming up with sets and operations but rather breaking things up into ever smaller pieces. I mentioned elsewhere that analysis is about starting with big circles and making them arbitrarily small. This is pretty much what recursion is.