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[Vector]

Well... huh.

Whaddaya know about that.


I swear, mathematics is the only subject I know that can take me from "I am a genius!" to "I am an idiot!" so fast.  It's like a revolving door of self-loathing and -aggrandizement.

Same thing goes for statements of "Oh this is wonderful never stop" and "fuck my life forever."

[Christes]

By the way Vector - You made a comment about teachers in the Egypt thread that reminded me of a recent AMS article

You might be interested if you have time.  I think he makes some interesting points on how high school teachers should be taught.

[Vector]

Hmm, yeah.  That is interesting, having looked at the first couple of pages--I'll need to spend some time reading it more thoroughly later.

Thanks for the pointer

[Christes]

I swear, mathematics is the only subject I know that can take me from "I am a genius!" to "I am an idiot!" so fast.  It's like a revolving door of self-loathing and -aggrandizement.

We've all done this, by the way.  Even the greatest mathematicians have experienced this.  There was the time Lagrange read his proof of the parallel postulate to the French academy of sciences...  You can imagine how it ended.

[olemars]

Man, reading this thread reminds me how much math I've forgotten, just three years after I finished my maths/physics master. Shows that maths skills must be exercised regularly like everything else (also shows that most of the hard knowledge you learn at uni isn't that useful in work life, unless you go for an academic position).

Maybe it's time to dig out the Kreyszig again and start from chapter 1.

[ZetaX]

Yes, e+pi is an open problem (but there are much more general conjectures that would say it is irrational, and even transcendental).
One can write down suprisingly easy facts that are very very difficult. Like the inequality sigma(n) <= H_n + log(H_n)·e^H_n ; here sigma(n) is the sum of the divisors of n (e.g. sigma(12)=1+2+3+4+6+12=28) and H_n = 1/1 + 1/2 + 1/3 + ... + 1/n. I recommend not trying to prove it 

Didn't know about that mistake of Lagrange, thanks for the information on that, it gives a nice anecdote.

[ed boy]

It is known that one can express sin(nx) in a polynomial of sin(x) with order at most n. Similarly, one can express cos(nx) as a polynomial in cos(x) with order at most n.
Is there a way to express sinⁿ(x) and cosⁿ(x) in terms of sin(kx) and cos(kx) for some values of k?

[Christes]

It's unclear precisely what you mean.  Trivially, one might say that cosⁿ(x) is an expression in terms of cos(kx) where k=1. 

I think you want to write it as a linear combination of the cos(kn)'s.  In this case it should be possible using the formulas from the first theorem you mention.  Say you want to write cosⁿ(x).  Start with cos(nx).  Write this in terms of of powers of cos(x).  The first one should be cosⁿ(x).  Multiply through by a constant to make the first coefficient 1.

Now add some multiple of cos^n-1(x) to it to kill the cos((n-1)x) term, and then add a multiple of cos^n-2(x) of it to kill the cos((n-2)x) term and so on.  The later ones won't touch the cosⁿ(x).  It's essentially row-reducing a matrix, if you are familiar with that.

So that's how you do it for cosⁿ(x).  For sine, you could get some sort of an expression with sin(x) and cos(x) by repeatedly using the identity cos²(x)= 1 - sin²(x), and the previous expressions.  This wouldn't be a linear combination, though.

[Argembarger]

Hey all you maths fans

Happy Pi Day!! 

[PsyberianHusky]

Lets talk about Stem and leaf plots!
I am confused how I deal with decimals

[da dwarf lord]

Well generally the stem is the 10's and the leaf is the 1's (if you get that)  so 82,85,56,74,64,34,59,34,45 becomes:
stem:    leaf:
3          4,4     
4          5
5          6,9
6          4
7          4
8          2,5

Hope this helps

[Sowelu]

decimals

Um, I can think of two ways to do that, depending on scale.
For this number series:  13.2 14.3 14.8 16.2 22.0 22.2 22.5

1           3.2 4.3 4.8 6.2
2           2.0 2.2 2.5

or,

13         .2
14         .3 .8
16         .2
22         .0 .2 .5

I don't know which one your teacher is likely to ask for, but maybe one of them will look more obviously correct to you...

[Vector]

Happy pi day, everyone!

Go do some mathematics!  Enjoy yourselves!

[Tellemurius]

Happy pi day, everyone!

Go do some mathematics!  Enjoy yourselves!

Now thats the Vector we all remember. Aww man, all i got was cake Q_Q

[Vector]

Damn straight :I

I'm going to the student-faculty dinner in a few weeks, too~ <3