Let's discuss Mathematics

[peter grimes]

I looked on wiki for "Roche limit" and here is the first formula in that page:

Which is d = R*(2*p_M/p_m)^(1/3) if you're typing it into a computer. (I'm using p's instead of rho's.)

I don't have any mathematical proficiency (nor do I know anything about windows 7 calculator's interface) yet I was able to enter this formula into a couple different calculators on my phone with results congruent to 8 significant figures.

I used the same values for a variable in each iteration.

Maybe W7Calc has some quirks that are really strange??

 

[Lord Chambers]

For those of you who know a few quantitative methods and statistics, where did you learn? I'm curious if anyone is partially self-taught and what resources he or she used. Any websites or podcasts you use to enhance your understanding?

 

[Mise]

"Numerical Recipes" is good to have as a reference, but most of the stuff I learnt was at university or on the job.

 

[sanabas]

For those of you who know a few quantitative methods and statistics, where did you learn? I'm curious if anyone is partially self-taught and what resources he or she used. Any websites or podcasts you use to enhance your understanding?

http://mathworld.wolfram.com/ plus a few texts I have lying around, plus whatever else google might send me to. Or in some cases, housemates were struggling with their uni stuff, so I grabbed their textbooks/lecture notes, and taught myself enough of what they were doing to be able to help them. Plus there's always the fun option of deriving formulae & things yourself.

 

[Atticus]

Does anyone here know any proof other than the four colour problem, which has used computers as an aid?

 

[sanabas]

I know of proofs of why something was wrong that used computers to find a counter-example. Think it's earlier in this thread somewhere. Do they count for what you're looking for?

 

[uppi]

Does anyone here know any proof other than the four colour problem, which has used computers as an aid?

http://en.wikipedia.org/wiki/Comput...ems_proved_with_the_help_of_computer_programs

 

[Atticus]

Thanks Uppi!

And Sanabas, I'm not sure, first I thought definitely no, whereas I thought about finding simple counterexample. Then I thought to clarify that counterexamples suffice if they aren't produced by mere raw power. Then I thought everything done by computer is produced by that. Then I thought that raw power can at least in theory add up to artificial reasoning.

The thing is, I read an article by John Horgan, a science reporter, who said that computers are increasingly used in maths to prove theorems. I think that's at least misleading, since they aren't used significantly (that I would know). Horgan has also some trouble with himself because he goes at the AI too in the same article, and so he claims that maths is done more and more by computers and that there are and probably will not be AIs that are any good.

 

[PlutonianEmpire]

How do I calculate the Semi-Major Axis of an orbit from just the perihelion, and eccentricity?

 

[Petek]

Atticus,

Perhaps Horgan was referring to automated theorem proving.

 

[Leoreth]

How do I calculate the Semi-Major Axis of an orbit from just the perihelion, and eccentricity?

If a is the semi-major axis, e the eccentricity and p the perihelion, and f the distance from the center of the ellipse to one of its foci (i.e. the gravitational center of the orbit), then p = f+a.

The equation for eccentricity is e = f/a <=> f = e*a.

Plugging that into the perihelion term gives p = e*a+a <=> p = (e+1)*a <=> a = p/(e+1).

 

[del62]

Does anyone know of any web-sites that will give a good understanding of fourier theory.

 

[Atticus]

I don't know anything in the web, but found once the start of this book enlightening.

It's not probably worth of the 85 dollars they are selling it for, but if you can borrow it or something like that, read the introduction.

I didn't read the book more though. A sad thing about it was that they used Riemann integral rather than Lebesgue, which makes things a bit harder. I suppose (but am not sure) that Lebesgue integral is a must if you're going to study Fourier analysis from the maths point of view. Physics and such do probably with less.

 

[dutchfire]

I used the same book as Atticus. I think it's a useful book for a theoretical mathematician but not so much for an applied mathematician/physicist. I don't know if there are any particularly good books for physicists, most of them learn Fourier theory from their quantum mechanics courses.

 

[PlutonianEmpire]

I read a space article, although I am unsure if I got the math right:

In fact, small, terrestrial planets can form around stars nearly four times more metal-poor than our own sun, researchers said.

When I read that, I immediately thought of: 100% / 4 = 25%. Is this correct? If not, what is the correct way to visualize that in a math equation?

 

[Atticus]

The wording is in my opinion a little poor, but that's the only way to understand it, I think.

Another way could have been 100% - (4*100%)=-300%, but that won't do, since a star can't have a negative amount of metal.

"Metal poor" doesn't make it any better: they are speaking of how much metal there is, so if there's less it, the star is more metal poor. It leads to similar misunderstandings which made me spoil the food in the fridge when I tried to make it colder by turning the switch to smaller number. Yes, I'm stupid.

This is more about language than maths, although teachers and such have to struggle with these kinds of things all the time. I'm not a native English speaker, so don't take my word as authoritative.

 

[peter grimes]

I think in this case they might be using a metric like 'what fraction of the mass of the star is metal', and taking a fourth of that?

Or perhaps it's a parts-per-million?

Who know. Yet another example of terrible science writing.

 

[nc-1701]

I'm pretty it means 4 times less metal, so if for example the sun was 4% metal the star they are referring to would be 1% metal. The wording isn't great, but no other interpretations make sense.

 

[PlutonianEmpire]

That equation smack in the middle? (The one with the word "eccentricity.") How do I punch that in into Windows 7 calculator?

 

[dutchfire]

Why use windows calculator? Why not use for example Wolfram Alpha?