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Invisible <voi### [at] dev null> wrote:
> I'm not sure they teach calculus *currently* in schools. Then again, I'm
> not sure because I didn't attend a normal school... I think in this
> country, if you want to learn about mathematics (not just arithmetic),
> you have to take a special course. I think it's outside the normal
> school curriculum.
Depends what you mean by 'school'. Derivatives (including the chain rule!),
integrals, and even differential equations were all on the maths A-level
syllabus that I did (I would hope that they still are!). I did my A-levels at
school, but I think many people go to college to study A-levels if their school
does not offer them.
Note that an A-level college is usually *not* the same thing as a university
(cue lengthy debate on schooling ages/terminology in different countries!).
> (Or you're an academic, which nobody is.)
I believe there are many regular posters here who might disagree with that! :-)
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> Depends what you mean by 'school'. Derivatives (including the chain
> rule!),
> integrals, and even differential equations were all on the maths A-level
> syllabus that I did (I would hope that they still are!).
They were when I did my maths A levels (1999).
> Note that an A-level college is usually *not* the same thing as a
> university
> (cue lengthy debate on schooling ages/terminology in different
> countries!).
Hehe yes, I went to a sixth form college to do my A levels because schools
in my area tended to finish at 16 and not offer A levels at all. Then I
left this college at 18 to go to another college, which was part of a
university - grande confusione!
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Invisible wrote:
> Suppose that the first derivative of f(x) is g(x).
>
> What the hell is the derivative of f(f(x))?
Unrelated to your question, but when I read the topic I first thought
you were after the n-th derivative of some function...
For example, deriving n times f(x)*g(x) has a fun formula :-)
--
Vincent
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>> Depends what you mean by 'school'. Derivatives (including the chain
>> rule!),
>> integrals, and even differential equations were all on the maths A-level
>> syllabus that I did (I would hope that they still are!).
>
> They were when I did my maths A levels (1999).
I don't *have* any A-levels, so I wouldn't know what is or isn't
included there.
(You get to choose which ones you want to do though, right?)
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Invisible <voi### [at] devnull> wrote:
> >> Depends what you mean by 'school'. Derivatives (including the chain
> >> rule!),
> >> integrals, and even differential equations were all on the maths A-level
> >> syllabus that I did (I would hope that they still are!).
> >
> > They were when I did my maths A levels (1999).
>
> I don't *have* any A-levels, so I wouldn't know what is or isn't
> included there.
>
> (You get to choose which ones you want to do though, right?)
Yep. As scott said, any education beyond 16 is optional in the UK. If you were
so inclined, there'd be nothing to stop you doing a maths A-level now - many
people do. I suspect you'd find much of it relatively easy, and you'd definitely
find the calculus interesting and useful! No idea what it might cost tho.
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"scott" <sco### [at] scottcom> wrote:
> > Depends what you mean by 'school'. Derivatives (including the chain
> > rule!),
> > integrals, and even differential equations were all on the maths A-level
> > syllabus that I did (I would hope that they still are!).
>
> They were when I did my maths A levels (1999).
I think the structure of A-levels changed in 2000 (more continuous assessment
instead of oodles of exams after 2 years), but I expect it's broadly the same.
> Hehe yes, I went to a sixth form college to do my A levels because schools
> in my area tended to finish at 16 and not offer A levels at all. Then I
> left this college at 18 to go to another college, which was part of a
> university - grande confusione!
Indeed. And of course many universities have the word 'college' in their names,
especially the younger ex-polytechnics, confusing the issue still further!
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>>>> Depends what you mean by 'school'. Derivatives (including the chain
>>>> rule!),
>>>> integrals, and even differential equations were all on the maths A-level
>>>> syllabus that I did (I would hope that they still are!).
>>> They were when I did my maths A levels (1999).
>> I don't *have* any A-levels, so I wouldn't know what is or isn't
>> included there.
>>
>> (You get to choose which ones you want to do though, right?)
>
> Yep. As scott said, any education beyond 16 is optional in the UK. If you were
> so inclined, there'd be nothing to stop you doing a maths A-level now - many
> people do. I suspect you'd find much of it relatively easy, and you'd definitely
> find the calculus interesting and useful! No idea what it might cost tho.
...all of which seems to support my assessment of "calculus is no longer
part of standard school education".
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Invisible wrote:
> What the hell is the derivative of f(f(x))?
LMATFY
http://www.wolframalpha.com/input/?i=derivative+of+f(f(x))
--
Darren New, San Diego CA, USA (PST)
I ordered stamps from Zazzle that read "Place Stamp Here".
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Fredrik Eriksson wrote:
> Except that it is the wrong answer, or rather the wrong question.
> Wolfram thought you meant (f <dot> f)(x), when what you actually meant
> was (f <circle> f)(x).
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.
--
Darren New, San Diego CA, USA (PST)
I ordered stamps from Zazzle that read "Place Stamp Here".
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Darren New wrote:
> Invisible wrote:
>> What the hell is the derivative of f(f(x))?
>
> LMATFY
>
> http://www.wolframalpha.com/input/?i=derivative+of+f(f(x))
FAIL.
The correct query is of course
http://www.wolframalpha.com/input/?i=derivative+of+f[f[x]]
Nice try tho. :-P
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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.
Several millennia of mathematical discoveries, all made by different
people in different places, and apparently several of them discovered
the same or similar things, but gave them different names - or gave them
names which clash with existing but inrelated things they didn't know about.
Just for giggles: how many meanings can you find for "normal"?
There's the normal distribution, normal vectors, a normed space...
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Invisible wrote:
> Darren New wrote:
>> Invisible wrote:
>>> What the hell is the derivative of f(f(x))?
>>
>> LMATFY
>>
>> http://www.wolframalpha.com/input/?i=derivative+of+f(f(x))
>
> FAIL.
Yes. I didn't see there were 50 responses before I posted that. :-)
> http://www.wolframalpha.com/input/?i=derivative+of+f[f[x]]
Apparently so. One of the reasons I hate mathematical notation.
--
Darren New, San Diego CA, USA (PST)
I ordered stamps from Zazzle that read "Place Stamp Here".
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>> FAIL.
>
> Yes. I didn't see there were 50 responses before I posted that. :-)
>
>> http://www.wolframalpha.com/input/?i=derivative+of+f[f[x]]
>
> Apparently so. One of the reasons I hate mathematical notation.
Wolfram at least have come up with a consistent, non-ambiguous notation.
In their notation, a(b)c unambiguously means the product a*b*c, and
a[b]c unambiguously means that b is the argument of function a,
multiplied by c. This is partly how Mathematica is able to determine
precisely what you meant.
Of course, nobody else uses this notation. And while *Mathematica*
rigorously follows it, *Alpha* attempts to "guess" what you mean. So in
the case above, it takes "f(f(x))" and guessees that you maybe mean "f *
f[x]", which isn't quite right. (This is what happens when computers try
to guess things...)
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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
Drove me nuts, as I learned computers before I learned all this higher-level
math.
--
Darren New, San Diego CA, USA (PST)
I ordered stamps from Zazzle that read "Place Stamp Here".
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>> Just for giggles: how many meanings can you find for "normal"?
>
> Sure.
Because it's not just the notations that are ambiguous - it's the
language as well!
> But even differences between things like
>
> 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?
Good luck with that one.
> Similarly with
>
> lg^2 X vs lg X^2
>
> Drove me nuts, as I learned computers before I learned all this
> higher-level math.
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...
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.
Hell, I've seen formulas where pi does *not* refer to the well-known
transcendental number!
Doomed, DOOMED, WE'RE ALL DOOMED! >_<
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Invisible wrote:
> But the second one? Now do you
> suppose that's the arcsine of x? Or the reciprocol of the sine of x?
That's exactly my point.
> if it does, it *probably* means the natural logarithm.
Well, that makes sense, yes.
> Doomed, DOOMED, WE'RE ALL DOOMED! >_<
I asked an exchange professor from Greece once, and he said they use the
same capital-sigma notation for summation and delta-for-change and such that
we use in America, except all their variables are also greek letters. *That*
must suck. :-)
--
Darren New, San Diego CA, USA (PST)
I ordered stamps from Zazzle that read "Place Stamp Here".
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Darren New wrote:
> I asked an exchange professor from Greece once, and he said they use the
> same capital-sigma notation for summation and delta-for-change and such
> that we use in America, except all their variables are also greek
> letters. *That* must suck. :-)
Heh. Mathematics, not content with featuring a zoo of custom symbols
ranging from "+" and "/" right up to those weird curly arrows, *also*
uses letters from at least the Latin, Greek and Hebrew alphabets. All at
once!
Sqrt(-1) = i [So that's Latin.]
Exp(1) = e [Latin again - except when people use Epsilon instead...]
Asin(1) = pi [Definitely Greek.]
|Z| = Alpha0 [So Hebrew then - with Arabic subscripts just for good
measure.]
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Invisible wrote:
> |Z| = Alpha0 [So Hebrew then - with Arabic subscripts just for good
> measure.]
...assuming you can SPELL. >_<
The cardinality of the set of integers is of course Aleph-null.
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Invisible <voi### [at] devnull> wrote:
> 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...
IIRC, 'log x' with no base usually means base 10, and 'ln x' is the natural log.
But, as you say, depends what the local conventions are.
> Hell, I've seen formulas where pi does *not* refer to the well-known
> transcendental number!
Now that's just careless.
> Doomed, DOOMED, WE'RE ALL DOOMED! >_<
Eat more pi.
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On Mon, 16 Nov 2009 17:12:29 +0100, Darren New <dne### [at] sanrrcom> 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.
Although I understand (and to some extent agree with) the point you are
trying to make, (f(f(x))) is not ambiguous in mathematical notation. The
problems come when you remove parentheses or interpret them in a
non-standard manner. Wolfram Alpha does those things because mathematical
notation does not translate easily into ASCII.
--
FE
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"Fredrik Eriksson" <fe79}--at--{yahoo}--dot--{com> wrote:
> Basic high-school level math. I am slightly surprised that you did not
> know it, though I am not in the least surprised that you did not bother to
> google for it.
They teach derivatives at high school?
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On Mon, 16 Nov 2009 18:22:34 +0100, Nicolas Alvarez
<nic### [at] gmailcom> wrote:
>
> They teach derivatives at high school?
They did at my high school, though possibly not to all students. I do not
recall which course introduced derivatives, but there were 5 math courses
in total, and only those studying natural sciences or technology took all
five. Most only took the first two.
--
FE
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On 16-11-2009 17:15, Invisible wrote:
> 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.
>
> Several millennia of mathematical discoveries, all made by different
> people in different places, and apparently several of them discovered
> the same or similar things, but gave them different names - or gave them
> names which clash with existing but inrelated things they didn't know
> about.
>
> Just for giggles: how many meanings can you find for "normal"?
>
> There's the normal distribution, normal vectors, a normed space...
Wednesday I have again an opportunity to give my talk on deriving
programs from specifications. One of the things I mention is that the
humble '=' has at least five and possibly more meanings depending on
context, interpretation, and the type op the object that it is applied
to*. And I will not even mention that the general use is inconsistent in
the context of A=B+C where A,B,and C are matrices. Here '+' is
pointwise, while '=' has an implicit summation**. As far as I know there
is not even an generally accepted symbol to express pointwise equality.
I know of people that try the opposite and make the summation explicit,
but that breaks most of other mathematical uses.
* equivalence, equality, definition, EXNOR, assignment and perhaps one
or more that don't have names. The type plays a role in A=B=C which is
OK if they are all booleans (or A or C is) but not if they are all
integers. In A=5 it can be an expression of equality, if A was undefined
it can be a binding/assignment, but it can also be a boolean that is
false everywhere except at 5.
** See also the concept of '=' in OO languages. Are two objects the same
if all fields are the same?
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On 16-11-2009 18:00, Bill Pragnell wrote:
> Invisible <voi### [at] devnull> wrote:
>> 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...
>
> IIRC, 'log x' with no base usually means base 10, and 'ln x' is the natural log.
> But, as you say, depends what the local conventions are.
>
>> Hell, I've seen formulas where pi does *not* refer to the well-known
>> transcendental number!
>
> Now that's just careless.
Not really, if you have a scheme where s->sigma t->tau then p->pi.
The one I remember (though I forgot the exact formula) is for the energy
per particle in an electric field. Energy is 'E', per particle it is 'e'
the expression contained an exponential function that depended on the
charge of an electron.
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>> 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...
>
> IIRC, 'log x' with no base usually means base 10, and 'ln x' is the natural log.
> But, as you say, depends what the local conventions are.
Some people use log to mean base-10. Some use it to mean an unspecified
base. But (arguably) *most* geniune maths sources use it to mean the
natural logarithm.
>> Hell, I've seen formulas where pi does *not* refer to the well-known
>> transcendental number!
>
> Now that's just careless.
It's a standard convention.
http://en.wikipedia.org/wiki/Prime-counting_function
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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>> If you can't add, you're going to have a bit of a problem doing your
>> weekly shopping, but there's not much need for higher math unless
>> you're working in some specialist industry somewhere.
>
> 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. Ditto for an
> electrical engineer who designed the power supply for your computer.
I'm going to go out on a limb and say that the number of people who
actually do that kind of things are a tiny minority.
As far as I can tell, the majority of people in the world have jobs
like... Telemarketing. Driving trucks. Working in an office doing
filing. Fitting central heating systems. Hotel receptionists.
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.
I mean, doing a job that requires mathematics is like being an olympic
athlete. Hypothetically, anybody can become an olympian. But seriously
guys, how many olympians have you personally met?
Exactly.
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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Orchid XP v8 <voi### [at] devnull> wrote:
> >> 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...
> >
> > IIRC, 'log x' with no base usually means base 10, and 'ln x' is the natural log.
> > But, as you say, depends what the local conventions are.
>
> Some people use log to mean base-10. Some use it to mean an unspecified
> base. But (arguably) *most* geniune maths sources use it to mean the
> natural logarithm.
Just looked at wikipedia - it seems you can tell a person's primary field by the
base they expect log x to be in!
http://en.wikipedia.org/wiki/Logarithm#Notations_of_bases_and_implicit_bases
> It's a standard convention.
>
> http://en.wikipedia.org/wiki/Prime-counting_function
I did not know that :-)
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>> Some people use log to mean base-10. Some use it to mean an unspecified
>> base. But (arguably) *most* geniune maths sources use it to mean the
>> natural logarithm.
>
> Just looked at wikipedia - it seems you can tell a person's primary field by the
> base they expect log x to be in!
>
> http://en.wikipedia.org/wiki/Logarithm#Notations_of_bases_and_implicit_bases
Crazy stuff, eh?
>> It's a standard convention.
>>
>> http://en.wikipedia.org/wiki/Prime-counting_function
>
> I did not know that :-)
I'm going to go out on a limb and guess that the people working on
number theory and investigating the properties of prime numbers didn't
need to know about the circumference of a circle. ;-)
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.
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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On 16-11-2009 22:22, Orchid XP v8 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.
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On 16-11-2009 21:40, Orchid XP v8 wrote:
>>> If you can't add, you're going to have a bit of a problem doing your
>>> weekly shopping, but there's not much need for higher math unless
>>> you're working in some specialist industry somewhere.
>>
>> 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. Ditto for an
>> electrical engineer who designed the power supply for your computer.
>
> I'm going to go out on a limb and say that the number of people who
> actually do that kind of things are a tiny minority.
>
> As far as I can tell, the majority of people in the world have jobs
> like... Telemarketing. Driving trucks. Working in an office doing
> filing. Fitting central heating systems. Hotel receptionists.
But for those who do there is a window in their development during which
they are most capable of learning maths. So you try to teach them in
that period. Besides it is part of our culture. OTOH I know there are
those cultural barbarians that think that it is cool not to know maths,
like politicians and most other public figures.
> 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 mean, doing a job that requires mathematics is like being an olympic
> athlete. Hypothetically, anybody can become an olympian. But seriously
> guys, how many olympians have you personally met?
none, but I can name a few who know a lot of them.
You could also have asked for e.g. opera singers. Most people also know
none of those. OTOH I think I have met more than 10.
So it is all just a matter of who you know and who they know.
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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.
--
Friends help you move. Real friends help you move bodies.
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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.
--
Friends help you move. Real friends help you move bodies.
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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.
--
Friends help you move. Real friends help you move bodies.
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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.
--
Friends help you move. Real friends help you move bodies.
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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...
--
Friends help you move. Real friends help you move bodies.
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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...
--
Friends help you move. Real friends help you move bodies.
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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.
--
Friends help you move. Real friends help you move bodies.
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Neeum Zawan <m.n### [at] ieeeorg> 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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>> 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.
Oh, so it's actually 1/n! then? I didn't actually know that...
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> * equivalence, equality, definition, EXNOR, assignment and perhaps one
> or more that don't have names.
I'm failing to see how equivalence and definition are different. (I know
some people use the triple-line symbol for this though.)
The main confusion is between assignment and equality, generally. Or, in
mathematics, between a test for equality and a statement of equality.
> ** See also the concept of '=' in OO languages. Are two objects the same
> if all fields are the same?
You would first have to define the concept of fields being "the same". ;-)
Fortunately, in a pure functional language, the question becomes a lot
simpler.
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stbenge wrote:
> hopefully achieving the ability to decipher
> many of the incomprehensible formulae found at wolfram.com.
Yeah, good luck with that. ;-)
Wolfram plays with some pretty advanced stuff. Between the Euler gamma
function, the Riemann zeta function, spherical harmonics, elliptic
integrals, Pochammer symbols, Godel numbers, hypergeometric functions,
the Airy functions and so forth... it could take a lifetime to learn all
this stuff.
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>> 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.
Logically, I know such people must exist somewhere. They're just so rare
it sometimes seems difficult to really *believe* they exist.
>> I mean, doing a job that requires mathematics is like being an olympic
>> athlete. Hypothetically, anybody can become an olympian. But seriously
>> guys, how many olympians have you personally met?
>
> none, but I can name a few who know a lot of them.
>
> You could also have asked for e.g. opera singers. Most people also know
> none of those. OTOH I think I have met more than 10.
>
> So it is all just a matter of who you know and who they know.
Professional singers, actors, athletes, musicians, dancers... I don't
know any of these people. Admittedly I don't know a huge number of
people, but my point is just that people who do specialised stuff like
that are very rare.
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Neeum Zawan wrote:
> 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?
>
Neither is unambiguous, really. The first one I might read as either
(sin x)^-1 or sin(x^-1). The second I have seen used to represent both
cosecant and arcsin. All depending on which professor was scribbling the
function.
>> 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.
>
My high school and college professors learned from a different book.
ln(x) was always natural log, while log(x) was either base 10 for the
normal math courses or base 2 for the computer courses. Most of the
time, people were expected to place a subscript noting the base.
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> As far as I can tell, the majority of people in the world have jobs
> like... Telemarketing. Driving trucks. Working in an office doing filing.
> Fitting central heating systems. Hotel receptionists.
Yes, the majority of people do a wide variety of jobs :-)
> 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.
I'd say most Chartered Engineers would have used calculus in their job at
some point or another, there's 180000 of them in the UK. Call that absurdly
rare if you want.
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>> As far as I can tell, the majority of people in the world have jobs
>> like... Telemarketing. Driving trucks. Working in an office doing
>> filing. Fitting central heating systems. Hotel receptionists.
>
> Yes, the majority of people do a wide variety of jobs :-)
More precisely: The majority of people are in service jobs. (At least,
in the UK.) Used to be manufacturing, now it's service.
As far as I can tell, higher math is more relevant to design and
engineering, which is quite rare.
>> 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.
>
> I'd say most Chartered Engineers would have used calculus in their job
> at some point or another, there's 180000 of them in the UK. Call that
> absurdly rare if you want.
What's a chartered engineer? And how do you know how many there are?
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> 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.
I guess it depends exactly what you're doing in the real world, but in the
situations where I've used calculus I've known exactly the function to
integrate (eg force applied at an exact point during a test). If I didn't
know the exact function I wouldn't be able to ask a finite element solver to
do it either!
> If your colleague can work it out quickly on paper, it shouldn't take long
> to do it on a computer (Maple, Mathematica, etc).
Sure, but the point is you need to have a good knowledge of calculus to even
ask Maple of Mathematica to do such things. If you have never been taught
calculus at university then good luck trying to solve the problem with a
computer math tool like Mathematica!
> Just because it's computers doesn't mean it has to be a finite element or
> Monte Carlo calculation.
It does for people who don't know calculus.
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On 11/17/09 03:17, Invisible wrote:
>>> 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.
>
> Oh, so it's actually 1/n! then? I didn't actually know that...
Yep. What you listed diverges to infinity.
--
Be independent! No, not that way! This way!
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On 11/17/09 08:09, scott wrote:
>> If your colleague can work it out quickly on paper, it shouldn't take
>> long to do it on a computer (Maple, Mathematica, etc).
>
> Sure, but the point is you need to have a good knowledge of calculus to
> even ask Maple of Mathematica to do such things. If you have never been
> taught calculus at university then good luck trying to solve the problem
> with a computer math tool like Mathematica!
Sure, but not that much. I know people who've correctly used computers
to do this while they thought that the integral of a product is the
product of the integrals.
--
Be independent! No, not that way! This way!
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