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Invisible wrote:
> Fredrik Eriksson wrote:
>
>> Basic high-school level math. I am slightly surprised that you did not
>> know it,
>
> What, you mean given that I've never been tought mathematics?
Don't feel bad; my math skills aren't too great either. I just found
this link: http://math.com/
Evidently you can work your way up from basic skills to more advanced
topics. I plan to do so, hopefully achieving the ability to decipher
many of the incomprehensible formulae found at wolfram.com.
Sam
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On 11/16/09 10:12, Darren New wrote:
> Which just goes to show the problem I have with 90% of all matehmatical
> notation. It's so utterly inconsistent that even something like
> (f(f(x))) is ambiguous.
I'm not a mathematician. But I took enough courses that I almost
qualified for an MS in Math (which may well be a BSc in some European
countries, but never mind...).
I can sympathize with them. There simply aren't enough symbols floating
around to accommodate all possible uses. Heck, it's painful enough when
you're typing to be able to type all the standard symbols.
--
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On 11/16/09 10:21, Darren New wrote:
> Invisible wrote:
>> Just for giggles: how many meanings can you find for "normal"?
>
> Sure. But even differences between things like
>
> sin x^-1 vs sin^-1 x
>
> where the two "^-1" mean entirely different operations. Similarly with
>
> lg^2 X vs lg X^2
Actually, the 2 means the same thing. In both cases, you're squaring.
You're just squaring different quantities.
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On 11/16/09 10:33, Invisible wrote:
>> sin x^-1 vs sin^-1 x
>>
>> where the two "^-1" mean entirely different operations.
>
> The first one, at least, is unambiguous. But the second one? Now do you
> suppose that's the arcsine of x? Or the reciprocol of the sine of x?
I think you'd be hard pressed to find someone who has used it to mean
the reciprocal of the sine. Perhaps that's why they defined the cosecant?
> And then of course, people will write "log x". Wanna take a guess which
> base that is? Now, sometimes it actually doesn't matter which base. And
> if it does, it *probably* means the natural logarithm. Probably...
Go back far enough, and it always meant base e. I wonder when ln(x)
notation cropped up.
If it doesn't matter what base it is, then it'd be "obvious" from the
context.
> Speaking of which, the base of natural logarithms is "e". And sometimes
> "e" means 1 + 1/1 + 1/2 + 1/3 + 1/4... And sometimes "e" is just another
> variable.
You're missing some exclamation symbols.
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On 11/16/09 16:22, andrel wrote:
>> I've also seen pi used more than once as a general variable, rather
>> than a function name or a mathematical constant. This is why you see
>> phrases like "e^(i x) where e is the base of natural logarithms and i
>> is the imaginary unit". Because otherwise it's horrifyingly ambiguous.
>
> I am working in an environment where the imaginary unit is j (because i
> is for current). I have trouble adapting.
Damn them electrical engineers.<G>
When I was an undergrad, I worked at a math tutoring institute. A
number of tutors were EE majors. I once caught one of them trying to
help a student, and he kept writing stuff with j. It was really
confusing her till I pointed out to the tutor that just about everyone
else uses "i". I've met a bunch of guys who didn't know that.
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On 11/16/09 08:59, scott wrote:
> You'd be surprised how many industries require specialist knowledge :-)
> For example, I suspect the structural engineer that designed your
> building did plenty of calculations using calculus to estimate stresses
> based on the loading (simple cases can be looked up in tables, but
> anything unusual needs to be worked out manually). Ditto for an
> electrical engineer who designed the power supply for your computer, the
> DCDC converter in your mobile phone and numerous other circuits -
> without an understanding of calculus you're going to be totally lost.
I somewhat doubt it.
Often, calculus is used in developing the theory. Then the rest is
simply approximations or computers.
When I was taking a statics course, the professor taught us how to
calculate the center of mass by taking the shape, splitting up into
triangles, calculating the center of mass of each (formula for
triangles), and taking the weighted average.
He never once mentioned the generic integral formulation. I asked him
why. He said, "That's good stuff to know if you're going to grad
school/academia, but in the real world, you almost never have the actual
function to integrate."
Which is mostly true. Of course, it's a stretch to say no one in
industry uses calculus, but it's a tiny tiny minority.
> Of course computers can simulate and calculate stuff for you, but you're
> going to look a right idiot if you need to run ten 12 hour simulations
> to decide the correct structure or capacitor size when your colleague
> can work it out exactly in a few minutes with a piece of paper.
If your colleague can work it out quickly on paper, it shouldn't take
long to do it on a computer (Maple, Mathematica, etc). Just because it's
computers doesn't mean it has to be a finite element or Monte Carlo
calculation. Additionally, if it's routine enough, there are handbooks...
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On 11/16/09 16:36, andrel wrote:
>> None of these seem to require knowledge of calculus. In fact, jobs
>> that *do* require such knowledge are seemingly so absurdly rare that I
>> almost find it difficult to believe they exist.
>
> So I don't exist? Nor do many of my collegues?
> I think I disagree.
I think your job _is_ fairly rare. Even among people in technical fields.
Does it require a PhD?
There you go.
Perhaps he exaggerated a bit, but to be honest, it *is* fairly hard to
get a job outside of academia that requires calculus knowledge, and
doesn't require a graduate degree (at least in the US).
It's kind of like people who know advanced CS, and are depressed to
find almost all jobs for programmers are for code monkeys. Although I'm
sure there are some good jobs that don't require a graduate degree in CS...
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On 11/16/09 10:09, Darren New wrote:
> Invisible wrote:
>> What the hell is the derivative of f(f(x))?
>
> LMATFY
You really shouldn't start any acronym with LMA... It was quite
anticlimactic.
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Neeum Zawan <m.n### [at] ieee org> wrote:
> On 11/16/09 10:21, Darren New wrote:
> > Invisible wrote:
> >> Just for giggles: how many meanings can you find for "normal"?
> >
> > Sure. But even differences between things like
> >
> > sin x^-1 vs sin^-1 x
> >
> > where the two "^-1" mean entirely different operations. [/snip]
It's actually the same operation, you are just inverting different objects with
respect to different operations. In the first case you are inverting a number
(x) with respect to multiplication, in the second case you are inverting a
function (sin) with respect to composition.
It's similar to how sin and sin(x) are not the same thing. sin is a function and
sin(x) is the value of said function at the number x.
Mindblow anyone? :)
Regards Roman
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>> I've also seen pi used more than once as a general variable, rather
>> than a function name or a mathematical constant. This is why you see
>> phrases like "e^(i x) where e is the base of natural logarithms and i
>> is the imaginary unit". Because otherwise it's horrifyingly ambiguous.
>
> I am working in an environment where the imaginary unit is j (because i
> is for current). I have trouble adapting.
Hahaha.
Arbitrary conventions FTW!
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