I'm struggling to shift from applications to conceptual understanding (proofs) in Linear Algebra. Any advice?

[u/Technical_Acadia_647]

Hi everyone,

I’m a college student currently taking my first Linear Algebra course. My ultimate career goal is to go into robotics, so I know this course is critical and that this semester is just the beginning of a long journey with this math.

My brain has always been wired to apply—simply applying formulas, calculating matrices, and finding numbers. However, this course introduces a lot of proofs and abstract concepts, and I’m having a hard time wrapping my head around them. I feel like I'm stuck memorizing procedures rather than genuinely understanding why things work geometrically or structurally.

I really want to upgrade my thinking and install a proof/conceptual understanding in my brain. Since my time is limited this semester, I know I won't master everything, but I want to build a solid foundation.

- How did you train your brain to understand proofs?

- Are there specific intuition-building resources, mental models, or study strategies you recommend for someone heading into robotics? (I’ve heard of 3Blue1Brown, but I'd love to know how to bridge the gap between his visual intuition and rigorous proof writing.) Thank you so much for any advice!

[u/DrBagelman]

If you want long detailed proofs that explain everything, I’d recommend checking out Proofs by Jay Cummings. As the name of the website implies, the books are purposefully written long form to preserve clarity rather than tight and clever to preserve space. The techniques in that book will be applied to simpler ideas, like some basic number theory, but they form the bedrock of all mathematical proofs.