What I never liked much in books that should provide knowledge.

[ttw]

Based on some years teaching math (and some music and chemistry) and computer science, I find such an approach unhelpful. It somewhat reminds one of the "Moore Method" of teaching (topology of course) where the teacher provides a few axioms and expects the students to come up with the theorems. I did drop a (topology of course) course because that was the method being used; I was interested in concepts of convergence, boundedness, and other such things of use to numerical analysis.

I assume that students took my courses because they wanted to learn something that the didn't already know (or that the courses were required but that wasn't my problem.) Give the beginner (or a genius who hasn't seen the material) a chance to get started. Different people have hang ups on different parts of mathematics; all of the subject should be presented at the level required.