I probably should've thrown in combinatorics, which certainly existed before calculus or linear algebra, and certainly plays a role in applied math.
I would say graph theory is part of combinatorics, and set theory is part of logic.
Category theory was born out of trying to abstract the relationships between different objects in abstract algebra, so is kind of the child of abstract algebra and logic. I think it's fair to say the parents of abstract algebra are combinatorics and linear algebra.
Number theory at an elementary level is combinatorics, but at higher levels branches into analytic number theory (Calculus) and algebraic number theory ((Linear) Algebra).
I would say graph theory is part of combinatorics, and set theory is part of logic.
Category theory was born out of trying to abstract the relationships between different objects in abstract algebra, so is kind of the child of abstract algebra and logic. I think it's fair to say the parents of abstract algebra are combinatorics and linear algebra.
Number theory at an elementary level is combinatorics, but at higher levels branches into analytic number theory (Calculus) and algebraic number theory ((Linear) Algebra).