Zeta

What, precisely, does randomness mean and what make something random?

The first thought is to consider a rigorous axiomatic definition of this term. First of all, does a definition with such precision exist? And if it does, can it be readily applied to all "random" events? I don't know the answer to this.

The second thought is the living organisms tendency to label events that it cannot find a pattern for to be "random." From this perspective, can we say that randomness doesn't exist outside of the animal's brain?

I appreciate any insights.

An inductive proof is preferred. Other methods welcomed. Thanks in advance.

A farm of growing carrots is in the shape of a 2n by 2n grid. The farmer is worried at some locations of carrots there are rabbits chewing them and he wants to get rid of both the rabbit and the chewed carrot at that location.

So he buys a tractor and wants to run them over! And he wants to go from one side of the farm to the other side in either a row or a column, hence destroying the whole row or column.

Prove that if there are 3n rabbits on the farm, he can remove them all by destroying n rows and n columns.

all are positive real numbers.

Given some complex-valued polynomial with real coefficients with all of its roots on the unit circle prove/disprove that f is a palindromic polynomial.

http://en.wikipedia.org/wiki/Palindromic_polynomia...

And also, is the other way around true? In other words, prove/disprove given a palindromic polynomial of odd degree, all of its roots are on the unit circle.

Given 7 distinct arbitrary points on the surface of a sphere, can we divide the sphere into 7 congruent and connected regions such that each region contains exactly one point?

Area = (h1 h2 h3)² sqrt(1/k)

where k = (h1 h3 + h2 h3 - h1 h2) (h1 h2 + h1 h3 - h2 h3) (h1 h2 + h2 h3 -

h1 h3) (h1 h2 + h1 h3 + h2 h3)

Given an arbitrary closed curve like this:

http://i167.photobucket.com/albums/u141/SitrONes7/...

Can we always do this?

http://i167.photobucket.com/albums/u141/SitrONes7/...

I came across this very interesting problem from IOI:

http://www.ioi2008.org/images/stories/ioi2008/task...

My first impression is that it's possible with recursion. Otherwise, one would need lots of complicated loops. Any ideas on how to code this?

http://www.imeem.com/people/i-UASz/music/LARQ4cQv/...

Anyone know what this piece is called? (and chances are this is a famous one) I'm trying to learn how to play this on a piano!

I have noticed that in certain situations when I am near some electric devices, maybe unused adapter, the monitor turned off, or sometimes in my car, my ears whistle - as though they resonate - when I move my head to specific locations. As soon as I move my head or rotate it the whistling stops. What causes this exactly?

I'm a young amateur when it comes time to talk about Laplace transform. But I am curious. What happens when Laplace transform of a function blows up to infinity, or has some other kind of discontinuity (if it ever happens)? Does that say something about the function?

Is there a plug in or add-in that can block certain elements of a webpage? (Maybe blocking by the elementID, class, or something similar).

For instance, let's say the top portion of a site has a div with id = "div1". I want Firefox to skip drawing the elements with id "div1". Is there a way to do it?

I've been wonder this for a while now, and it's hard to think of "fun" occupation for a mathematician (besides the professorship, of course). By fun occupation, I mean something that is relatively exciting and not routine, and you get to learn new things everyday.

evaluate,

1 + 1/1! + 1/2! + 1/3! - 1/4! + 1/5! + 1/6! + 1/7! + 1/8! - 1/9! + ...

Note that pattern of signs is + + + + -

This is inspired by a great question of Scythian here,

http://answers.yahoo.com/question/index;_ylt=AsTag...

Consider y = cos(x) + (1/a) cos(ax)

My observation is that this function is being bounded by the following set of envelopes,

http://sciencesoft.at/image/latexurl/image.png?src...

though I can't prove it rigorously. I would appreciate any help on how to derive this analytically.

Better yet, see if you can find the set of envelopes of form

α cos(β x + φ) for the general case

y = A cos(ax) + B cos(bx)

Yahoo's genius staff are again at their very best when it comes to innovation with the all new "cropped avatar picture" with much less image quality and bigger file size. What else happens when you are bankrupt of new ideas, and HAVE to "innovate" to survive the competition between corporations?

I really hope Yahoo gets acquired by a more legitimate company. They should have been wiped out a long time ago.

..with a calculator that has only '+','-','*','/', 'sqrt' buttons and a number pad.

det(A,B)

I know det(A) just means determinant of A. But what is det (A comma B)?

Thanks for any help!