you're probably a victim of rote learning math classes. learning math for real (getting it) is not a linear process.
lots of aha moments where lots of concepts fall into place suddenly and then you move on to more advanced things.
that said, I would consider everything below calculus to be merely clever ways of tallying stones. algebra can be tricky at times (abstract algebra sucks) but it is really not that interesting in of itself (yes you can solve a lot of practical problems with it but the questions aren't generally interesting, so the answers aren't that interesting). you do need to have it down pat in order to "get" calculus however. And if you "get" at least the basic concept of calculus down a lot of things fall in to place.
OTOH I could be totally biased and/or wrong, but I personally didn't really see how math could describe complex systems in a way that let me get those complex systems until calc. Some really mind blowing aha moments.
I did understand a lot of maths, I just mean that I think the way we do maths often is not really understanding. If we have proved something with a hundred step proof, I might be able to verify every single step of the proof and conclude that it is correct. But we might not really have a feel for why it is correct. Can't really think of a good example right now :-/ I mean usually we jump through quite a few hoops to prove something - maybe there are other ways of looking at it that would make more sense.
One example might be the autistic people who just know if a number is prime or not. Not sure if they are really doing anything special, or just calculating really fast, though.
funny, I always thought it was the other way around, calculus was just a clever calculating trick, but give me a good algebra, then we can really do something :-)
yeah, i can empathize with that stance from an engineering perspective. but to me calculus feels like looking under the hood of the universe though. algebra is static, calculus is dynamic.
that said, I would consider everything below calculus to be merely clever ways of tallying stones. algebra can be tricky at times (abstract algebra sucks) but it is really not that interesting in of itself (yes you can solve a lot of practical problems with it but the questions aren't generally interesting, so the answers aren't that interesting). you do need to have it down pat in order to "get" calculus however. And if you "get" at least the basic concept of calculus down a lot of things fall in to place.
OTOH I could be totally biased and/or wrong, but I personally didn't really see how math could describe complex systems in a way that let me get those complex systems until calc. Some really mind blowing aha moments.