  This is a kind of introduction to some basic topics in analysis, some of
which would be covered in standard graduate courses, and some not. However, an
important difference is that not much in the way of prerequisites are needed,
beyond linear algebra and beginning analysis. In particular, this should be
accessible to undergraduates or readers whose main focus is not necessarily
pure mathematics. One could easily accommodate Lebesgue integrals and so forth
if one wanted to, but they are not really needed.
