I have a very general question about people's experiences with learning math. I can think of a couple of times where I had the following situation. I was seeking to learning about topic A. However, topic B is a prerequisite for learning about topic A, and I don't know enough about topic B to continue. The interesting point of these learning experiences is that I found a resource on topic A, and I found that the resource explained topic B to me better than any resource I found which is devoted to topic B.
For example, I got a lot better intuition on measure theory by reading a couple of books on probability theory. I also got a good grounding on functional analysis from a book on theoretical numerical analysis. I was wondering if others have had similar experiences, where they have learned more about a topic from a resource which was really meant to be on a different topic. Anyone here have other examples of this?
Although my recollection is hazy, I think I once learned something interesting about determinants from an appendix in Artin's Galois Theory, and also something quite neat about finite-dimensional linear algebra in general from an appendix in Dieudonné's Foundations of Modern Analysis.
(Perhaps someone who's actually studied Kelley's General Topology properly will mention having learned set theory from its famous appendix; but I didn't; and indeed, I'm still hoping to learn set theory properly, by studying something it's a prerequisite for. That covers a lot of ground! Perhaps set theory is the canonical example of a "topic B", for every "topic A"?)