Take the process of Riemann integration, for example. How many times are you actually going to draw tiny rectangles under your function and let their widths go to zero?
In this case, numerical integration is almost that (it's rectangles but it can be trapezes). Well, I guess you could do a numerical limit using e-d definition
Should we not teach students this process then, and just show a shaded area under a function, teach simple formulas for integrating polynomials, and tell them to look up all other antiderivatives in a table, as that is what they will use in real jobs anyway?
Interesting, because then you're defining (mathematically) the integral as an antiderivative.
I wouldn't say skip this definition. But a lot of other things in calculus yes.
I think knowing how vague concepts such as the area under a function, smoothness, continuity, "close enough," are properly defined give you a deeper insight, and teach you to go beyond practical issues of how to compute and to not ignore a little voice in your head that says "how do we know that these fuzzy concepts work?"
Computers can compute, but humans can and should understand.
I agree. But interestingly, the concepts in derivatives and integrals, (except with maybe continuity) are present in a lot more places than the limit definitions.
And think about this: digital signal processing. You have 'derivatives', 'integrals', but not limits!
I have, and I stand by my statement. But it brings me to another criticism:
You say 'skip limits' because it's 'self-indulgence.' One of the critical functions of a math education is it teaches people to reason and think in a rigorous way.
Well, true.
Introductory calculus is already on shaky enough ground as it is,
In university, you mean?!
if you start throwing away limits you get rid of what little rigor is there already, and you've undermined one of the most important functions of a mathematical education...
I meant slashing limits (or better, simplifying it) for HS, not university level studies.
Still, limits are not "most important functions". Derivatives and integrals are. So study the concept of limits but for all practical purposes use L'Hospital
The problem is spending time with limits, or how to calculate the integral of arcsin(x^2) and then missing the important stuff afterwards.
I don't need to know by heart the integral of cosh(x) (even though it's simple)
Instead, explain how to turn a partial differential equation in an equation system to be solved on the computer. For that, you can't look in a table. Of course you need the definition of derivative (and limit) for that
Still, the definition of limits smells bad for me, it's like "it's the value of the equation at the point, except when it isn't. Then it is the value that it would be except it isn't" (by the epsilon-delta definition I don't see how it's different from that, of course, simplifying things like one-sided limit, ->infinite, etc)
They spend too much time teaching crap and instead skip over the important stuff
Why the f... did I learn trigonometric equations ins high school?! Really... Polynomial equation solving?!
Derivatives would be much more useful. And don't beat around the bush on limits, etc, that's math "self-indulgence", go directly to derivatives, simple, done
If they cut the crap and stick with the essentials, then maybe people will learn better. Maybe can they shave a year from the school curriculum so that students can go and study what interests them.
A heat pump cannot approach 100% efficiency. Indeed, a heat pump does work, which makes it subject to the laws of thermodynamics, whereas a resistive heater does no work at all. It merely increases the average energy in a region.
On the contrary. A Heat Pump can be, according to its definition, MORE than 100% efficient. Where efficiency is defined as (heat pumped)/(energy spent). So you can pump 500W of heat with 100W of electricity (non real values)
So you can have more heating for the same electricity then with an electrical heater.
Look up the tech data for an air conditioning unit.
Oh, but we do need "entire new technology" for these in terms of human passengers. The summary says that the purpose of the trip is to discuss human spaceflight, and it seems only prudent to discuss alternates to Russia.
As you said, for LEO, etc, they could try and create a human rated Atlas V or Delta rocket
However getting to, landing on, and leaving the moon or mars isn't plug-and-play. The Apollo program can't be duplicated because the schematics and records are lost.
Yes, you're right. Going to the moon again is a big challenge and to Mars is an an order of magnitude more complex.
With the way things are going I don't see anyone matching the capability of the shuttle for decades, much less sending people to the moon or mars.
They were ordered by Clinton and then Bush to work on a program to replace the aging Space Shuttle fleet, which needed retiring.
I'm with you so far...
That program is Constellation. They didn't "blow" the money, they were told to come up with a bullshit cost estimate by bean counters when they were trying to create entirely new technology
you don't need "entire new technology" for LEO, MEO, GEO, get to the moon or mars. If it was needed, nobody would have done these things.
that involved all sorts of problems that we hadn't had to solve previously.
Problems created by reinventing the wheel for the nth time...
It's idiots like you that have made scientific exploration in the US fall so far behind.
Because I want to reinvent the wheel and spend money on solving already solved problems?!
It's ok to 'refresh' the technology, my money is on Falcon launchers, and NASA should have gone DIRECT.
Then there's money to spare for the real important things: new experiments, space probes, space telescopes, etc
Hello (wait 40 years) Hi (wait 40 years) Well Hi there (wait 40 years) How are you doing ?! (wait 40 years) Fine how are you (wait 40 years) Sorry what did you say!?! we lost it
If there hadn't been the shuttle but instead a proper heavy lift rocket, those would have still been able to go up. The shuttle's design was just never optimal for anything related to launch. Note that I'm not saying that great things were not done with the shuttle, but rather that they were not specifically enabled by the shuttle. Versions of those great missions would have probably happened anyway.
Yes, of course. They use what they have. I don't think Galileo was able to be launched by a rocket, but Cassini was, for a similar payload and mission...
Slashdot Mirror
It's not always a matter of incidents.
Sometimes you only need help. Sometimes it's a config issue. Sometimes there's nothing wrong but you need it changed.
I'm not sure how deep the basic support goes, but I've seen people at RH doing very deep, very specific work for a customer.
I am interested in what a good sentence is for a malicious DDOS attack,
5 years... of using only Windows Vista
Exactly
Some people can only function with a pile of paper apparently.
if waterfall has delivered?!
It seems most projects work in spite of waterfall, not because of it.
I'm not saying it doesn't work. That is for small/medium projects with a very tight scope it does.
What's the name of that FBI project again?! Virtual case file?! Oh well...
Take the process of Riemann integration, for example. How many times are you actually going to draw tiny rectangles under your function and let their widths go to zero?
In this case, numerical integration is almost that (it's rectangles but it can be trapezes). Well, I guess you could do a numerical limit using e-d definition
Should we not teach students this process then, and just show a shaded area under a function, teach simple formulas for integrating polynomials, and tell them to look up all other antiderivatives in a table, as that is what they will use in real jobs anyway?
Interesting, because then you're defining (mathematically) the integral as an antiderivative.
I wouldn't say skip this definition. But a lot of other things in calculus yes.
I think knowing how vague concepts such as the area under a function, smoothness, continuity, "close enough," are properly defined give you a deeper insight, and teach you to go beyond practical issues of how to compute and to not ignore a little voice in your head that says "how do we know that these fuzzy concepts work?"
Computers can compute, but humans can and should understand.
I agree. But interestingly, the concepts in derivatives and integrals, (except with maybe continuity) are present in a lot more places than the limit definitions.
And think about this: digital signal processing. You have 'derivatives', 'integrals', but not limits!
You got it. Almost 100%. Except for the "you must be joking" part
The problem with e-d is that it's too obvious. Good for the math definition, but it doesn't say anything!
The definition doesn't help you in calculating (sin x)/x for example (beyond the definition, of course).
I have, and I stand by my statement. But it brings me to another criticism:
You say 'skip limits' because it's 'self-indulgence.' One of the critical functions of a math education is it teaches people to reason and think in a rigorous way.
Well, true.
Introductory calculus is already on shaky enough ground as it is,
In university, you mean?!
if you start throwing away limits you get rid of what little rigor is there already, and you've undermined one of the most important functions of a mathematical education...
I meant slashing limits (or better, simplifying it) for HS, not university level studies.
Still, limits are not "most important functions". Derivatives and integrals are. So study the concept of limits but for all practical purposes use L'Hospital
The problem is spending time with limits, or how to calculate the integral of arcsin(x^2) and then missing the important stuff afterwards.
I don't need to know by heart the integral of cosh(x) (even though it's simple)
Instead, explain how to turn a partial differential equation in an equation system to be solved on the computer. For that, you can't look in a table. Of course you need the definition of derivative (and limit) for that
Still, the definition of limits smells bad for me, it's like "it's the value of the equation at the point, except when it isn't. Then it is the value that it would be except it isn't" (by the epsilon-delta definition I don't see how it's different from that, of course, simplifying things like one-sided limit, ->infinite, etc)
What I'm saying is that they should learn less, but more importantly, something else in math.
calculus -> derivative -> newton-raphson + computer = both problems solved if you ever see them
Read again, I'm not talking about 'general trig' and 'general polynomials'
They spend too much time teaching crap and instead skip over the important stuff
Why the f... did I learn trigonometric equations ins high school?! Really... Polynomial equation solving?!
Derivatives would be much more useful. And don't beat around the bush on limits, etc, that's math "self-indulgence", go directly to derivatives, simple, done
If they cut the crap and stick with the essentials, then maybe people will learn better. Maybe can they shave a year from the school curriculum so that students can go and study what interests them.
Hey, you're right. But you don't need to be so obtuse, with such an acute error...
I really want to know who messed this up...
They have an alternative to Symbian, it's called Maemo
Someone came up with this MeeGo thing, which is great, but it shouldn't be against Maemo
They have a cell phone with Maemo, the N900
The should begin getting Maemo to run on other platforms (maybe even the X8 one) and instantly fire anyone who starts whining about it
Now, I wonder what would happen when putting electrons in a C60 buckyball...
A heat pump cannot approach 100% efficiency. Indeed, a heat pump does work, which makes it subject to the laws of thermodynamics, whereas a resistive heater does no work at all. It merely increases the average energy in a region.
On the contrary. A Heat Pump can be, according to its definition, MORE than 100% efficient. Where efficiency is defined as (heat pumped)/(energy spent). So you can pump 500W of heat with 100W of electricity (non real values)
So you can have more heating for the same electricity then with an electrical heater.
Look up the tech data for an air conditioning unit.
The keep splitting themselves into even fractionally dimensioned smaller pieces
AMEN TO THAT
C++ is like barbecue sauce. Too much and it will ruin everything.
One of the most important things in a C++ project is setting coding style and clear rules of what's ok/not ok.
So you don't have 10 levels of inheritance, 'creative use' of STL, etc, etc
And then came Java, which is C++ minus C
Hence, Java == Cancer
Well, the thing with Concorde is, when flying fast, the atmosphere is a burden
The longest commercial flight on schedule today is Newark->Singapore at 9500Mi, almost a 19h flight (see wikipedia Non-stop_flight)
I'm sure some will shell the money to get there faster.
Oh, but we do need "entire new technology" for these in terms of human passengers. The summary says that the purpose of the trip is to discuss human spaceflight, and it seems only prudent to discuss alternates to Russia.
As you said, for LEO, etc, they could try and create a human rated Atlas V or Delta rocket
However getting to, landing on, and leaving the moon or mars isn't plug-and-play. The Apollo program can't be duplicated because the schematics and records are lost.
Yes, you're right. Going to the moon again is a big challenge and to Mars is an an order of magnitude more complex.
With the way things are going I don't see anyone matching the capability of the shuttle for decades, much less sending people to the moon or mars.
True, me neither. Very sad.
They were ordered by Clinton and then Bush to work on a program to replace the aging Space Shuttle fleet, which needed retiring.
I'm with you so far...
That program is Constellation. They didn't "blow" the money, they were told to come up with a bullshit cost estimate by bean counters when they were trying to create entirely new technology
you don't need "entire new technology" for LEO, MEO, GEO, get to the moon or mars. If it was needed, nobody would have done these things.
that involved all sorts of problems that we hadn't had to solve previously.
Problems created by reinventing the wheel for the nth time...
It's idiots like you that have made scientific exploration in the US fall so far behind.
Because I want to reinvent the wheel and spend money on solving already solved problems?!
It's ok to 'refresh' the technology, my money is on Falcon launchers, and NASA should have gone DIRECT.
Then there's money to spare for the real important things: new experiments, space probes, space telescopes, etc
They had the money and they chose to blow it on Constellation
So, Tough.
Well, but in real animal beings 'bad signals' (pain, pressure, heat, etc) are that... signals
Hello
(wait 40 years)
Hi
(wait 40 years)
Well Hi there
(wait 40 years)
How are you doing ?!
(wait 40 years)
Fine how are you
(wait 40 years)
Sorry what did you say!?! we lost it
Yes, it would not be very entertaining :P
Of course no one knows what's the reaction of people (even consenting ones) when stuck in a computer 'body' for ever...
If there hadn't been the shuttle but instead a proper heavy lift rocket, those would have still been able to go up. The shuttle's design was just never optimal for anything related to launch. Note that I'm not saying that great things were not done with the shuttle, but rather that they were not specifically enabled by the shuttle. Versions of those great missions would have probably happened anyway.
Yes, of course. They use what they have. I don't think Galileo was able to be launched by a rocket, but Cassini was, for a similar payload and mission...
One of the things that the Space Shuttle helped are things like AMS-1 http://en.wikipedia.org/wiki/Alpha_Magnetic_Spectrometer (and it will deliver AMS-2 later)