Calculus: Is it Really That Hard?

Post Reply New Topic

I don't think you're really disagreeing with me. I never meant to say there is always a single solution. What I meant to say was math is elegant for the most part. ZFC set theory is a little weird/cludgey IMO, but when you get past that...

Must be my Asperger's.

Never struggled a lot with the Zermelo set theory. Although I disliked it for not being all inclusive.

It isn't that hard until you study advanced Calculus in the Math major. That is the study of the theory behind it. The rest is learning how to use it for other subjects...

I remember I did some calculus theory back in my multivariable days.

I always found the basic polynomial calculus to be really easy. The stuff I've been doing more recently (something about directional derivatives and vector functions) seemed a lot more challenging, but you have to keep in mind that I'm not currently in a sound state of mind and that's really impacted my learning abilities.

I am sure you got good grades though, when do you expect to graduate?

Failed actually. Didn't have the motivation to study so I forgot everything by exam time. Assuming I don't screw everything up this time around I have about two more years until graduation.

I think I got a B when I took vectoral calculus, I did take Linear Algebra which helps a lot with that stuff. I hated things like subspace and eigenvalues. Man that stuff made want to jump into a pit filled with man eating kangaroos.

I recall doing eigenvalues, eigenvectors and Gaussian elimination in a Linear Algebra unit. It was quite tedious at the time.

I've had a whole semester and a quarter of calculus.

I find it to be easier than precalculus and more fun than algebra, but I get told over and over again that I'm a math geek (and I can't argue with that.)

Linear algebra is more interesting for it's theory and it's extensive application to differential equations (and thus physics). The calculations aren't meant to be done by hand! They are supposed to be done by computers! Solving matrices by hand sucks! The important part is seeing that it CAN be done.

My problem with ZFC set theory is more philosophical. Books usually have 9 or 10 axioms that have been settled on by most mathematician. Yet, an alien race with their own mathematics might not use the same axioms we do. In other words, they are somewhat arbitrary. You can do a ton of math with only 6 or 7 of them. Also, the axioms of choice and replacement can be somewhat arbitrarily strengthened or weakened and you get a slightly different theory as a result. ZFC isn't like the Peano axioms for integers. With the Peono axioms it can be pretty easily shown that they are the ONLY set of axioms that make sense in terms of defining the integers. An alien race would likely come up with the exact same axioms. ZFC set theory just isn't so.

I think mathematics is mostly used to show consistency with the world.

There's also boolean logic though, boolean algebra is used at the electrical level. I mean you have all the higher-order languages, but at a small enough level, you can explain it in 1's and 0's.
Logic gates (or transistors) are arranged on a circuit according to boolean algebra. Boolean algebra ultimately describes how a computer will behave. That's the most truthful thing about math I can think of, at its core, it represents absolute consistency.

I passed up AP Calculus AB/BC in high school for AP Statistics becuase I thought that would be more useful for me in the short term so I can't really talk about Calculus BUT I can say that all the NT's I knew that took it thought it was the hardest crap they ever had to take in high school. To put it simply only 5 out of 32 students had A's the whole year. The grades were distributed as those 5 had A's while everyone else had D's and below. There was an insane dichotomy of Asians that did nothing but school stuff because of familial reasons and everyone else who was there because they had to be and messed around the whole time. I also did ditch my regular economics classes and stayed in those AP Calculus classes and would understand a bit about what they were doing. I could spout things off in theory but I didn't know the nitty gritty to actually pass the class had I been taking it. Most of the kids in those classes honestly didn't belong in them and complained whenever they had to write a 2 page essay (they all almost died upon getting into college and the first assignment was a 5 page essay). They pretty much just sucked and were lazy, and let the stereotype that math is insanely hard get to them. The school in itself was also pretty bad, it didn't exactly care if you understood what was going on anyway and forged ahead regardless. The students also were very narrow, thinking that a certain topic applied to only one thing that they'd been shown. They never felt inspired or saw or even tried to apply what they learned in different ways and saw everything pretty much as a chore.

All in all, I'd say with the right everything it's not that hard, especially if you enjoy math. If you don't then you're not going to want to do it and you will most likely suck at it, plain and simple.

One thing it seems to me is that you learn certain mathematical concepts long before you learn their application. Mathematics clearly holds some kind of 'truth' or else engineers wouldn't be spending so much time learning the stuff.

The way I see it is maths is designed to solve problems. Those problems aren't necessarily apparent when you're learning the basics. There's probably a lot of real-world application that would never occur to most people.

And, I hope this doesn't sound condescending because it's not supposed to, but never forget that just because something doesn't make sense to you, doesn't mean it's not true.