That is a very true statement, Dexter. Fortunately, I now have a calculator. If equations are more complicated than finding x, I'm still pretty much screwed though.
I did it! I did it! I really did it!
- Thread starter Andygal
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That is a very true statement, Dexter. Fortunately, I now have a calculator. If equations are more complicated than finding x, I'm still pretty much screwed though.
To some degree, I grieve for you Rev, and for every other person who thinks math sucks or who sucks at math (same thing, really). It's a fascinating and wonderful subject, one of the greatest inventions of human intelligence, but bad teachers and bad experiences poison it for too many. And it's really not that difficult if it's properly explained. It's a logical whole and the basics are readily available to anyone with a three-digit IQ. I see now that I was really fortunate in high school to be blessed with some very gifted teachers who gave me the basics, and the confidence and the techniques necessary to make sense of the harder stuff I encountered in university. Roses upon their heads...
How easy is it really? Well, here's the basics of calculus: There are two unfamiliar symbols in calculus, a lower case d and an upper case elongated S that I can't quite reproduce in the character set available here, so I'll just use S. The d means "a little bit of," and the S means "the sum of." So, the characters dx or dy mean a little bit of x or a little bit of y, whatever x or y may be, doesn't matter. Thus Sdx means the sum of all the little bits of x, which obviously must add up to x. So now we know that Sdx=x, which in essence is the fundamental theorem of calculus. How hard was that? All the little bits of something add up to all of it. Could anything be more obvious? But the teachers--and the mathematicians--surround it with jargon and formalism, none of which is really necessary to understand the heart of it. The heart of it, in fact, is intuitively obvious if it's explained clearly and stripped of its mathematician's formalism.
And by the way Andygal, congratulations on your achievement. I meant to put that in my first post in this thread, but I got distracted by the notion that math sucks. It doesn't. Some math teachers suck, which leads their unfortunate students to think math sucks, but they're wrong. They'll drill you with pointless repetition of exercises, and whoever thought that was a good way to teach anything ought to be shot and pissed on from a great height. You'll either get it with one example, or you won't get it at all, which means the teacher hasn't taught it well.
How easy is it really? Well, here's the basics of calculus: There are two unfamiliar symbols in calculus, a lower case d and an upper case elongated S that I can't quite reproduce in the character set available here, so I'll just use S. The d means "a little bit of," and the S means "the sum of." So, the characters dx or dy mean a little bit of x or a little bit of y, whatever x or y may be, doesn't matter. Thus Sdx means the sum of all the little bits of x, which obviously must add up to x. So now we know that Sdx=x, which in essence is the fundamental theorem of calculus. How hard was that? All the little bits of something add up to all of it. Could anything be more obvious? But the teachers--and the mathematicians--surround it with jargon and formalism, none of which is really necessary to understand the heart of it. The heart of it, in fact, is intuitively obvious if it's explained clearly and stripped of its mathematician's formalism.
And by the way Andygal, congratulations on your achievement. I meant to put that in my first post in this thread, but I got distracted by the notion that math sucks. It doesn't. Some math teachers suck, which leads their unfortunate students to think math sucks, but they're wrong. They'll drill you with pointless repetition of exercises, and whoever thought that was a good way to teach anything ought to be shot and pissed on from a great height. You'll either get it with one example, or you won't get it at all, which means the teacher hasn't taught it well.
Hey...maybe andygal will be the next governer general of canada 8) I wouldn't be surprised, I have read her posts 8) Now if only little ricky would get his ass back here, I think he would gouda for andygal.
Hey bevvy check your email, I sent you something so cool 8) 8) 8)
Hey bevvy check your email, I sent you something so cool 8) 8) 8)
Dexter, when I was in high school, we were lucky to have a teacher who really could teach. She introduced integral calculus by explaining that, if you want to find the area under a curve, you divide it up into little strips, and find the area of each one. Then you add them all up. And we went from there. And it was so plain, so simple, so logical, that it all made perfect sense.
That said, in my University life, my mark in every single math course was one step below the previous; they went A+, then A, A-, B+, B...then I didn't have to take any more. Multidimensional matrices got me. Or maybe it was the nights drinking.....I dunno which.
That said, in my University life, my mark in every single math course was one step below the previous; they went A+, then A, A-, B+, B...then I didn't have to take any more. Multidimensional matrices got me. Or maybe it was the nights drinking.....I dunno which.
I think what loses people in university is that math is taught by mathematicians, who like a rigorous formalism that renders it pretty much incomprehensible to anyone but another serious mathematician. There's a crucial theorem, for instance, called the Theorem of the Mean, which in formal mathematical terms is a mind bender of a statement* full of conditional clauses, but in plain English all it says is that given any two points on a wiggly but smooth line (i.e. no breaks or sharp corners in it), there's at least one other point on the line in between them where the slope of the line matches the slope of a straight line between the original two points. That's not really saying much more than that there must be a third point between any two other points, which is so blindingly obvious you might legitimately wonder why anyone would need to prove it.
*for the purists: suppose that f(x) is continuous on a closed interval [a,b] and that the first derivative of f(x), call it f'(x), exists for all x in the interval. Then there is a value of x in [a,b] such that f'(x) = (f(b) - f(a))/(b-a)
*for the purists: suppose that f(x) is continuous on a closed interval [a,b] and that the first derivative of f(x), call it f'(x), exists for all x in the interval. Then there is a value of x in [a,b] such that f'(x) = (f(b) - f(a))/(b-a)
Hm... we seem to have strayed a bit from Andygal's original and fully justifiable mood of exultation over a personal achievement. My fault, I think. One of these days I might learn not to hijack threads... 