Back in college I stopped doing maths in second year as a major because of the way it was taught. I just hated it. Numerical methodds in particular broke me. My main problem was we never really got told how things fit together. Resources like 3blue1brown just didn't exist at that time, sadly. We just had dusty and expensive and very dry textbooks to rely on. For example, we just got through into ODEs and were told "just use e^at". We started doing contour integrals without really telling us what was going on. Honestly, things like linearity were never really taught for basic stuff like derivatives and integrals.
But I had always loved maths and went back to it much later. After having done some computer science, some concepts just made it click more for me. Like sets were a big one. Seeing functions as just a mapping between sets. Seeing functions as set elements. Seeing derivatives and integrals as simply the mapping between sets of functions.
What fascinates me is that differentiation is solved, basically. Don't come at me about known closed form expressions. But integration is not. Now this makes a certain amount of sense. Differentiation is non-injective after all. But what's more fascinating (and possibly really good evidence of my own neurodivergence) is that integration isn't just an algorithm. It requires some techniques to find, of which the Feynman technique is just one. I think I was introduced to it with the Basel problem. I have to confess I end up watching daily Tiktok integration problems. It scratches an itch.
I kinda wish I'd made it to complex analysis at least in college. I mean I kinda did. I do remember doing something with contour integrals. But it just wasn't structured well. By that I mean Laplace transforms, poles of a function in the S-plane and analytic continuations.
I'm not particularly proficient at the Feynman technique. Like I can't generally spot the alpha substitution that should be made. Maybe one day.
But I had always loved maths and went back to it much later. After having done some computer science, some concepts just made it click more for me. Like sets were a big one. Seeing functions as just a mapping between sets. Seeing functions as set elements. Seeing derivatives and integrals as simply the mapping between sets of functions.
What fascinates me is that differentiation is solved, basically. Don't come at me about known closed form expressions. But integration is not. Now this makes a certain amount of sense. Differentiation is non-injective after all. But what's more fascinating (and possibly really good evidence of my own neurodivergence) is that integration isn't just an algorithm. It requires some techniques to find, of which the Feynman technique is just one. I think I was introduced to it with the Basel problem. I have to confess I end up watching daily Tiktok integration problems. It scratches an itch.
I kinda wish I'd made it to complex analysis at least in college. I mean I kinda did. I do remember doing something with contour integrals. But it just wasn't structured well. By that I mean Laplace transforms, poles of a function in the S-plane and analytic continuations.
I'm not particularly proficient at the Feynman technique. Like I can't generally spot the alpha substitution that should be made. Maybe one day.