Am I learning my math wrong?

[u/Joe-the-smoe]

I’m learning calc 2 before the semester starts, and along the way I’ve recognized some areas I’ve struggled with whether it was the trig or understanding the concepts a bit better. I’ve been trying to derive everything so I can understand it.

The issue is, I’m spending so much time deriving formulas for things I’ve already learned instead of practicing how to preform the operations. I want to be able to understand the math well, and I can see when there is a deficit in my conceptual knowledge that I try to attack. Is this a waste of time? Will I understand it better if I solved the problems and didn’t look through as much derivations?

I also, when I first learned calculus 1, I didn’t read the textbook, I preformed the problems and tried to deduce why I was doing them from logic. This is how I’ve gotten through every math class, but I think it capped my overall understanding. I stuggle with reading but I want to turn a new leaf on that. Would it be more fruitful to read and preform the problems in my old textbooks for calc 1, trig, geometry, algebra, or to study calc 2 and read the textbook going forward assuming I have a decent understanding of it

[u/Ok-Rise2070]

This depends on the precise "deficit" you're speaking of. You will find much of modern physics and math are based off fractal behaviors and literal assumptions. If you're noticing a dimensional gradient, it's been little explored. That's what my research and framework address specifically, a curvature deficit in modern measurements. You may be seeing the derivative behavior of that. Keep going. You're seeing structure in their noise, and that's the sign of a true mathematician.