This is why I'm a big fan of Axler's Linear Algebra Done Right. The book's emphasis is on the concepts behind the calculations rather than the calculations. I

This is why I'm a big fan of Axler's Linear Algebra Done Right. The book's emphasis is on the concepts behind the calculations rather than the calculations. I could never learn mathematics that way, and goodness knows, school systems in both Europe and America have tried to teach it to me that way. What I understand of mathematics today has mostly been achieved through autodidaction. Some of us cannot, repeat can not go from the abstract to the empirical; I'm one of those people, who have to go from the empirical to the abstract instead. I need to see the mechanics of it, because I learn by observing the pattern. If I cannot make out the pattern, I cannot comprehend the abstraction. Take UNIX manual pages for example: the first thing I go to after reading the SYNOPSIS is the EXAMPLES section (and since most GNU/Linux manual pages have no EXAMPLES sections, it's a product which is useless to me, unlike UNIX). The more examples the EXAMPLES section entails, the faster I'm able to grasp the concept. Same with http://matrixmultiplication.xyz/ http://matrixmultiplication.xyz/, if I could have learned matrix multiplication that way, visually, instead of having to do it in my head, it would have been far easier. The other way around, it was a slow, painful torture, and to this present day, I cannot multiply the matrices in my head, or without these visualisations to remind me of the rules: they're too complicated for me to keep in my head. The point I'm trying to make is that not everyone learns the same way, and our brains do not process the information in the same way, even if the final result, understanding of the concept, is identical. A lot of abstract concepts which are difficult to reliably repeat, or whose outcome is either non-deterministic or unclear, we do not even understand the same way, hence opinions often differ by a small or large margin. Don't assume that the learning technique which works for you would work for someone else. That's a major failure of most pedagogical approaches, with the exception of perhaps Montessori and Fröbel. Unlike Montessori and Fröbel, most pedagogical approaches force a uniform way of learning, except that a human brain does not learn in a uniform manner, differing from individual to individual instead. Teaching should be a highly individualized approach.