I my girlfriend's numerical linear algebra textbook once, fully expecting it to be a very annoying subject dealing with implementation of floating-point numbers

I my girlfriend's numerical linear algebra textbook once, fully expecting it to be a very annoying subject dealing with implementation of floating-point numbers. It turns out, the discipline is mathematically rigorous and looks a lot like standard analysis. It was eye-opening both to me, as a mathematician, and to her, as a computer scientist, how directly the fully-abstract theorems applied to real-world floating point operations.