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spankie
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 Posted: Sat, 4th Feb 2012 19:16 Post subject: |
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spankie
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| Posted: Sat, 4th Feb 2012 20:16 Post subject: |
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Weird, my Mathematica @ home cannot calculate the sum :\
"Quantum mechanics is actually, contrary to it's reputation, unbeliveably simple, once you take the physics out."
Scott Aaronson | chiv wrote: | | thats true you know. newton didnt discover gravity. the apple told him about it, and then he killed it. the core was never found. |
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b0se
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Location: Rapture
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| Posted: Sat, 4th Feb 2012 20:38 Post subject: |
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What the fuck is that ?
[spoiler][quote="SteamDRM"]i've bought mohw :derp: / FPS of the year! [/quote]
[quote="SteamDRM"][quote="b0se"]BLACK OPS GOTY[/quote]
No.[/quote][/spoiler]
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Przepraszam
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Location: Poland. New York.
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| Posted: Sat, 4th Feb 2012 21:18 Post subject: |
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| b0se wrote: | | What the fuck is that ? |
Don't worry about it. |
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spankie
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| Posted: Mon, 6th Feb 2012 17:54 Post subject: |
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Yeah, I can still remember the days, only 10 years ago, when I was doing mathematics in high school as a 17-18yo. (Still wondering when I will actually will use most of that stuff. I finished engineering in university and now doing mathematical economics (nice hobby project to keep up to date with the technical skills) and still only used 10-20% of the misery they put me through in high school...)
I had to make complex integrals, differential equations, series expansions, continuity analysis, limits of sums etc etc. We were with 15 in the class and we all had different results, ALWAYS.
And now you just put it in the webside and you get everything you can imagine. Really amazing.
There is stuff you need 2 or 3 pages of fancy mathematics to calculate, and wolphram alpha/mathematica calculates it analytically (!) in 5 seconds. I never understood why so many of the teachers/old dinosaur profs focus on the 'elegance' of the mathematics, especially in applied sciences such as engineering or economics. 90% of the 'elegance' are little mathematical tricks that you have to memorize and have been discovered by accident. I am quite sure a computer is better at trying the whole repertoire of tricks than a human, so why put all those students through it.
I am really happy that there are a bunch of intelligent and modern people that are running science/engineering/economics departments here. No more stupid paper and pencil mathematics that is so complex that eventually you will make mistakes on exams because of the stress/time/whatever. A lot of exams I am doing (in economics) or putting students through (in my own engineering dep) are open book, using formulas/computers/computerized output. People should focus on the application of the methods, rather than the method itself.
Tools like wolphram alpha really really really speed up R & D and general development. Instead of doing tedious/semi-retarded mathematics, you can cut the crap and immediately go to the results and use your brain to analyse the results etc. And even with the help of computers to calculate the tedious calculation, there is still plenty of room for brains and mathematical elegance.
Btw, I am not saying people should do everything with a calculator, especially in lower educational levels. Because i know some people that cannot multiply 6 * 16 by head  That's not really ideal. And you need a more than basic level of algebra and analytical skills to be able to understand theoretical frameworks etc. But the actual calculation of 90% of those 'problems' are really useless.
Btw Reklis, print this and give it to your supervisor. Kind greetings from a local PhD dude @ the math and statistics department.
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spankie
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| Posted: Mon, 6th Feb 2012 20:27 Post subject: |
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I think I got that one.
let's see, another problem. I understand the how just not the why. (This time: antiderivaties!)
Couldn't find out the solution so I asked wolfram alpha and took a look at the steps and my first reaction was seriously WTF!?
because the first thing it does it substitute x = sin(u) , dx = cos(u)du for the integrand and sqrt(1-sin^2(u)) = cos(u) and u = sin^-1(x)
And I completely don't get it. How would you even think of those substitutions if you don't know the result already? O.o
Seeing as this is from a homework paper that, as a whole, was worth 40 points and that particular problem is worth 3 I suspect that there's a WAY easier method to solve this but I couldn't come up with anything useful, even after consulting every piece of literature I have available.
| sabin1981 wrote: | | Now you're just arguing semantics. Getting fucked in the ass with a broom stale is an "improvement" over getting stabbed in the eye with a fork |
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| Posted: Mon, 6th Feb 2012 21:23 Post subject: |
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| Reklis wrote: | I think I got that one.
let's see, another problem. I understand the how just not the why. (This time: antiderivaties!)
Couldn't find out the solution so I asked wolfram alpha and took a look at the steps and my first reaction was seriously WTF!?
because the first thing it does it substitute x = sin(u) , dx = cos(u)du for the integrand and sqrt(1-sin^2(u)) = cos(u) and u = sin^-1(x)
And I completely don't get it. How would you even think of those substitutions if you don't know the result already? O.o
Seeing as this is from a homework paper that, as a whole, was worth 40 points and that particular problem is worth 3 I suspect that there's a WAY easier method to solve this but I couldn't come up with anything useful, even after consulting every piece of literature I have available. |
Actually a pretty common substitution tho.
When you have things like scattering problems, or some kind of distribution in some region of space, you usually go to spherical coordinates, because things are much more intuitive and simpler there.
So, say you have something you need to integrate in the whole space (volume). The volume element in spherical coordinates is given by:
r^2 sin\theta dr d\theta d\phi
And the limits of theta are from 0 to pi, and for phi are from 0 to 2pi. So when you have trigonometric functions it's kinda hard to work with them. So you make a simple substitution:
x=\cos\theta
You derive the both sides and get:
dx=-\sin\theta d\theta
And the limits become from 1 to -1, now you see that the integral for theta simplifies greatly -> no \sin\theta, and a simple elementary integral.
Plus this substitution makes sense if you remember that
\sin^2\theta+\cos^2\theta=1 => 1-\cos^2\theta=\sin^2\theta and you can see that the square will cancel out the root, which again leaves you with a simple integral...
"Quantum mechanics is actually, contrary to it's reputation, unbeliveably simple, once you take the physics out."
Scott Aaronson | chiv wrote: | | thats true you know. newton didnt discover gravity. the apple told him about it, and then he killed it. the core was never found. |
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HubU
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