Here's what I've covered, excluding advanced statistics & econometrics courses. I just have a hard time believing that most admitted candidates have gone further. What do you think?
BSc in Physics, year I – Differential and integral calculus
Real and complex numbers, sequences and series, single variable real functions, differential equations, R^n Euclidean space, multivariable real functions, implicit and inverse functions, curves, surfaces and vectorial analysis.
BSc in Physics, year I – Linear algebra and geometry
Structured sets, isomorphisms, automorphism groups, orbits, stabilizers, lateral classes, normal subgroups, vectorial spaces and fields, linear systems and transformations, matrices, eigenvalue, determinants, diagonalization and triangulation of linear operators, dual spaces, Euclidean spaces, quadratic forms, conic and quadratic sections.
BSc in Business Engineering, year I – Mathematics I
Radix, real series, single variable real functions (limits, continuity, derivative, extrema, concavity), integration, complex numbers, vectorial spaces, matrix calculus, linear systems.
BSc in Business Engineering, year II – Mathematics II
Linear algebra, multivariate functions, differential equations and applications. (can't find the detail of this course but it was extensive)