but X? How is concept X to linear algebra? And so on. Sure, if I looked a bit more, I could tell you how linear combinations might be connected to concept X. Why was it invented? When I open up a book of Linear Algebra, I can't concretely/literally connect the first chapter on linear combinations (for example). All I can ascertain is that many problems in many fields of life and the sciences are discretely solved (broken-up, or simplified) by using linear algebra. I tried searching for a sane introductory description of Linear Algebra. I can look at a problem type and tell you it's familiar and look up how to 'solve' this problem type, but I'm completely oblivious of any real mathematics.

I can't tell you what a unit circle is for (other than passing corresponding set of problem types). I'm not able to keep anything this way because I don't understand its context, its relation to other concepts that I've learned (that I will most likely soon forget anyhow), and the bigger picture in math of why this specific concept's invention was necessary. I've always been so frustrated that the way I've been taught - I argue the way most students have been taught - is from the bottom up: teaching one section at a time, with each concept seemingly isolated from each other, with each concept not fitting into a larger big picture, and then saying we 'learned'. I too often interpret concepts visually and desire concrete and literal visualizations, and I demand learning from the top-down. The second reason is because of the way I learn.

I've done the bare minimum (memorize the steps to solve a problem type) to pass tests, I forget the steps right after the test, and I have never ever understood the reasons for the concepts I've learned in mathematics.

The first reason I'm confused in the course is because I've never studied math correctly.

I'm extremely confused, for a couple of reasons. I'm a second-year college student having just previously finished calculus (derivatives and integrals, we never really got too far into multivariable calculus though we briefly went over some Taylor Series stuff) and I'm taking Linear Algebra right now.

Khan linear algebra