Huh, interesting. What did they cover? I guess I thought you were talking about stuff like sparse iterative solvers (Krylov subspace, that sort of stuff). But those are computational tools mostly, I guess, right?
The math department at my college had three linear algebra courses.
“Intro to linear algebra.” 200-level. Vectors are (x,y,z), more or less. Class includes math, engineering, science, and business majors. 200-level makes it nominally a second-year course but lots of first-year students will take it. Required course for many different majors.
“Applied linear algebra.” 300-level. Vectors are finite. Eigenvalues, linear transformations, determinants, matrix algebra, factorization. Touches on numerical methods but doesn’t spend much time on them. Students were mostly math, with some physics and electrical engineers mixed in.
“Advanced linear algebra.” Series of two 400-level / 500-level courses. Almost exclusively math majors and math grad students. Algebraic topology, tensor spaces, exterior algebra, spectral theory, differential forms.
There were also numerical methods courses—one in the math department and one in the CS department.
