"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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