I am NOTa strong mathematician unfortunately but I am blessed with a good memory,
From what I can recall, these were covered in analysis. Definitions such as bijection means "one to one and onto" whatever that means!
Algebra contained defns such as isomorphism, congruence, etc.
Alg courses included groups, group rep, rings, alg number theory, lin alg and geom.
Analysis had complex analysis, functional analysis, real analysis, prob from a pure perspective, analytical geometry (as oppsed to differential geom) and analytical number theory.
Most people at school would not have come across pure, so really chooses between applied and stats.
Why are you so interested in pure?