How could you possibly write a program that "approximates nearly any integral" without having learned calculus in the first place. I by that I don't mean to "spend half a year memorizing" any tricks. (If that's what they taught you, I am sorry to say you had a pretty awful teacher and you should seek to educate yourself elsewhere).

Oh yes, I forgot about the 3 minute part. You didn't write anything from scratch. You just at best googled for a math library and hooked it up to your hello world program... if not downloaded the whole damned thing from easy-Aplus.com!!!

Nevermind, rest assured that grownups never had to learn anything in order to build the infrastructure you happen to enjoy today.

First, these are all exaggerated cases, inspired by experience. I appreciate the infrastructure a great deal, but I'm saying that there's a tremendous amount you can do if you focus on learning concepts and have a computer. School doesn't even care if you understand concepts; memorization is usually sufficient. And anyone who understands basic conceptual 1-var calculus and programming can indeed easily write functions in plain C that perform numerical integration and derivation because the hard part about calculus is putting up with the countless algebra tricks that are not obvious to mortals. Don't know how to manipulate that monstrous algebraic expression to take the limit? Good thing your computer can use some tiny floats. People who are not going to be math/physics professors or NASA physicists who need to plan a Mars voyage to the nearest nanometer would really benefit from focusing on the concepts instead of algebra. And my calculus teachers were pretty superb, by the way.

Why am i not able to downvote this. You are wrong on so many levels I don't even know where to start.

I'll just say that a good general knowledge of various topics will greatly help in life in a variety of situations. What you get taught in high school after all is the basics of the basics. If you don't know what a gerund is... sorry, you're an ignorant, and I don't care how many stars your JavaScript library has on github.

I don't know what a gerund is, and I've never needed to except in 8th grade grammar tests, which I failed. Yet I got a 79/80 on the writing section of the SAT because my grammar is pretty solid. I've been in a remedial English class, actually, with ESL kids. Like yourself and most other rational people, I am a big proponent of acquiring knowledge on diverse topics. I just think people should be able to pursue the topics they're interested in instead of dealing with distracting busywork that old people decided was a good fundamental curriculum. Do you fail to see the problem with schools forcing kids to memorize things about Native Americans and Greek columns and long division (etc.) when 1) most do not care about such things and 2) even more will never need to know such things? It's one problem to have an outdated curriculum and another to force a set curriculum, even a great one that works really well for the average student, on kids.

I understand and completely agree with your issue about memorization. In my experience good teachers don't force you to simply memorize formulas/details but make you appreciate the meaning of the concepts behind those. After understanding the concepts the formulas come out by themselves and look obvious.

E.g.: It's important to know that Greek history is divided in 3 pretty different big main periods and each of them had different column designs but after that knowing the details of those designs is pretty unimportant.

A gerund is a pretty easy and obvious notion. Personally I just know it without even thinking about it probably because I was taught about it at a pretty young age. To me someone not knowing what gerund is is like someone e not knowing what multiplication is.

Honestly anything before college is a pretty young age and 99% of people aren't sure (or shouldn't be sure) about what they're going to do with their life because they don't know enough about it yet. Even that 1% will benefit out of basic knowledge in the long run because that's what makes you a man with basic culture that can discuss on a range of topics.

We humans are not computer programs specialized on solving a single task. High school makes us more like an OS, providing the features to solve (hopefully) any kind of problem we encounter in life.

Those "integration tricks" are introducing you to some of the most basic fundamentals of mathematical thought. Pay attention, kid, you'll have a lot harder time picking up maths in the future if you let it slip now.

Actually, most algebraic tricks in calculus, which are what make it challenging, are pretty unnecessary to know if you can program a computer or use existing math software. Conceptual tricks, on the other hand, which might be more aptly called "conceptual applications," should be understood and derived. The unfortunate thing is that many students get so accustomed to memorizing tricks that would indeed require really advanced math abilities and lots of time to derive that they gloss over valuable concepts that they should actually understand very well.

No, not actually.

I only used the word "trick" because you did. There are NO TRICKS in math. If a practitioner uses the word "trick" its because he's being facetious or joking. The algebraic manipulations which you find challenging are absolutely essential to master inside-out to be able to follow more advanced mathematical reasoning. You'll see these "tricks" again in a profoundly more generalized form if you study Algebra again (abstract algebra, that is).

There is utility in doing algebra on your computer when you're dealing with literally pages for one expression. That is done to save time and reduce the probability of errors-- and NOT because you "can't" otherwise do it. Even then, you'll need to manually sanity-check the work using skills you learned doing all those tedious problem sets.

Memorizing culture is a social issue and an issue about teachers, not about curriculum. Or you think a teacher can't tell the difference between a student that memorized a few formulas and the student that understood the concepts behind those?

EDIT: When I was in high school there were a few teachers that frowned upon memorizing things. They would give low grades to such students. Then halfway my education I went to live in another country where memorization was the accepted learning method and I've felt the difference greatly so I know what you're talking about.

I guaran-fuckin-tee you that Earnest Hemingway knew what a gerund is.