I am studying "Singularity theory of differentiable maps".
If we divide MATHEMATICS simply into ALGEBRA, GEOMETRY,
ANALYSIS and others, then we can say that "Singularity theory
of differentiable maps" belongs to GEOMETRY.
However, singularity theory needs many notions of
ALGEBRA and GEOMETRY. Since "Singularity theory of
differentiable maps" has many applications, in one sense
we can view it as
a modern equivalent of the differential calculus.