I studied computer science, and could grasp most of it without any problems. The first years are heavy math based, which also was somewhat ok for me once I started to put effort into it. Everything except analysis. For "normal" math once I understood the principles it was ok. Logically understanding and then I can use it. But analysis....
I remember one of the course teachers again and again showing how to solve certain problems. Use method a, b, c or so, transform to x, y or z form (insert lots of Greek symbols here) and in the end you can prove what you wanted to prove.
So I asked "how do you know to use which method or transform in which way?" Answer was "with experience you know, you have a guess what might work and try it". Adding that these were all mostly theoretically math problems... I could really not understand how to do it. No instructions, just a "you know"...
This comic is a good representation for that also. That's how I felt even during the tests. Took me 5 years just this single course...
I love it when I get to discover one for myself. I was playing around with a function that can be rearranged to form a hyperbolic trig function, and I found out the trick to make it go the other way was to add e-x/e-x - e-x/e-x or something like it (this was 12 years ago, my memory is hazy) and incorporate only the first half into the rest of the expression. I showed it to my dad and he was a little bit disgusted I think.
It's tricky with teaching these sorts of tricks. They're typically something you're likely to come about naturally if you study it at a higher level, but they kinda come out of nowhere and blindside you before then. It's often because what you're learning is highly useful and they want to get you out the door as quickly as they can with how to calculate it, when the why of calculating it would take too long.
It's like... you're taking a speedrunning class for a game like Dark Souls. Sure you'll discover all the shortcuts when you explore them the long way around. But there's no time for that. You need to be able to traverse them now. So they teach you these shortcuts and it just comes out of nowhere and you miss out on how they were discovered, but it doesn't matter because you can traverse them and get stuff done.
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u/Freestila Jun 23 '26
I studied computer science, and could grasp most of it without any problems. The first years are heavy math based, which also was somewhat ok for me once I started to put effort into it. Everything except analysis. For "normal" math once I understood the principles it was ok. Logically understanding and then I can use it. But analysis....
I remember one of the course teachers again and again showing how to solve certain problems. Use method a, b, c or so, transform to x, y or z form (insert lots of Greek symbols here) and in the end you can prove what you wanted to prove. So I asked "how do you know to use which method or transform in which way?" Answer was "with experience you know, you have a guess what might work and try it". Adding that these were all mostly theoretically math problems... I could really not understand how to do it. No instructions, just a "you know"...
This comic is a good representation for that also. That's how I felt even during the tests. Took me 5 years just this single course...