Personally, my problem was always that math concepts were never presented in a way that actually made sense in the “real world.”
I was taught that complex numbers were real numbers with imaginary parts that had something to do with the square root of -1. Yeah, I get it, but… why?
Fast forward a few decades and I’m writing code that processes a digitized waveform. Now it makes sense. Math isn’t hard when you have a frame of reference. Learning math concepts solely for the sake of learning them is very hard.
I can’t give a satisfying explanation, but I can really recommend 3Blue1Brown on YT for great motivations for such things. He presents these topics in ways that make you want to understand them. I’m not sure which videos approach imaginary numbers - there might be standalone ones, but it definitely comes up in his explanation of the Fourier transformation.
I think people also quit before they can play the game. Calculus was the first time I felt it was all coming together and was really fun. Up until then it can seem like you are learning rules to a complicated game, and then people chose to just not play.
I work in maintenance …I’ll go to some jobs, fix the issue and walk away, I’ll go to some jobs and there will be some troubleshooting and I’ll walk away, other jobs I’ll have to leave and won’t be able to resolve the issue. The first two I’ll look back on and I might have learned something and I’ll be really happy. The third makes me feel like shit. I remember being the same about linear equations.
This was always my experience as well. The deeper you go into mathematics, the more abstract / theoretical things seem to become.
Funny you should mention digitized waveforms, a class on signals and transforms was by far the hardest part of my degree. I really struggled with both the math and the visualization. Probably the thing that ended up helping me grasp some of the course’s concepts most was messing around with convolution reverb effects for audio processing.
Personally, my problem was always that math concepts were never presented in a way that actually made sense in the “real world.”
I was taught that complex numbers were real numbers with imaginary parts that had something to do with the square root of -1. Yeah, I get it, but… why?
Fast forward a few decades and I’m writing code that processes a digitized waveform. Now it makes sense. Math isn’t hard when you have a frame of reference. Learning math concepts solely for the sake of learning them is very hard.
Can you explain them? Not having worked with them, I’m still in the “but why?” phase of complex numbers.
(different person here)
I can’t give a satisfying explanation, but I can really recommend 3Blue1Brown on YT for great motivations for such things. He presents these topics in ways that make you want to understand them. I’m not sure which videos approach imaginary numbers - there might be standalone ones, but it definitely comes up in his explanation of the Fourier transformation.
I think people also quit before they can play the game. Calculus was the first time I felt it was all coming together and was really fun. Up until then it can seem like you are learning rules to a complicated game, and then people chose to just not play.
I work in maintenance …I’ll go to some jobs, fix the issue and walk away, I’ll go to some jobs and there will be some troubleshooting and I’ll walk away, other jobs I’ll have to leave and won’t be able to resolve the issue. The first two I’ll look back on and I might have learned something and I’ll be really happy. The third makes me feel like shit. I remember being the same about linear equations.
Yeah - wasn’t until later when I did some work with camera orientation in 3D that Linear Algebra and Matrix Transformations clicked a bit more for me.
This was always my experience as well. The deeper you go into mathematics, the more abstract / theoretical things seem to become.
Funny you should mention digitized waveforms, a class on signals and transforms was by far the hardest part of my degree. I really struggled with both the math and the visualization. Probably the thing that ended up helping me grasp some of the course’s concepts most was messing around with convolution reverb effects for audio processing.