The Math Thread

[Vortex]

Protip: use the "Simple English" language for complicated stuff. That removes all of the theories and such that you really don't need, and just explains the formula or whatever it is.

I.e.
http://en.wikipedia.org/wiki/Riemann_zeta_function

vs.

http://simple.wikipedia.org/wiki/Riemann_zeta_function

Ok, I know what that function is used for now (and I know what functions overall are about, we had that at school). But still, I have no idea what that big sigma sign represents, or what does that weird R mean, for that matter.

I think the weird R is just the symbol for the function. Not sure on this one though. And also nobody would probably use it, because it looks shit hard to draw

The big sigma just means evaluate the following [the number above it] times, starting at [the number below it] and use the number of times you did it instead of n. (or whatever variable it says in the bottom) Then add it all together.

I think it is called summation or something in English?

What is this easy stuff you're talking about? I'm curious.

Lately we've been talking about really really basic probability and what I suppose is number theory.
Before that we had Euclidan geometry - the volumes and fields of cones, cylinders, balls and stuff.

I feel you. We have just started basic trigonometry...

The R means the real part of a complex number. For example, R(5+6i)=5. And the big sigma is a repeated summation (Σummation?). For example, Σ(i=1 to 3) 2*i = 2*1 + 2*2 + 2*3. Az explained it well.
The zeta function would be, for example, for s=2:
zeta(2) = 1/1 + 1/4 + 1/9 + 1/16 + 1/25 + 1/36 + etc. = 1.64493...

[Anteroinen]

Protip: use the "Simple English" language for complicated stuff. That removes all of the theories and such that you really don't need, and just explains the formula or whatever it is.

I.e.
http://en.wikipedia.org/wiki/Riemann_zeta_function

vs.

http://simple.wikipedia.org/wiki/Riemann_zeta_function

Ok, I know what that function is used for now (and I know what functions overall are about, we had that at school). But still, I have no idea what that big sigma sign represents, or what does that weird R mean, for that matter.

I think the weird R is just the symbol for the function. Not sure on this one though. And also nobody would probably use it, because it looks shit hard to draw

The big sigma just means evaluate the following [the number above it] times, starting at [the number below it] and use the number of times you did it instead of n. (or whatever variable it says in the bottom) Then add it all together.

I think it is called summation or something in English?

The weird R is most likely refers to the Real number line, although a different looking, neater R is more commonly used. I say probably because I am not any sort of expert on this but I don't really doubt that judgment either.

The big sigma is a glorified plus sign, as explained above, like the big pi denotes multiplication. And the word you're looking for is addition.

EDIT: Ninja'd, I believe is the proper term?

[Vortex]

Yeah, sorry XD

If you want an explanation of why the real part has to be greater than 1, here's one:

When you raise a number to a real power, if it's greater than 1 the number becomes bigger, and if it's less the number becomes smaller. For example 2^16=65536, 2^(-4)=0.0625

When you divide 1 by a big number, it becomes small, for example 1/100000=0.00001, and viceversa. So the fraction 1/2^16 is small and 1/2^(-4) is big, hence we need a big exponent (>1) to make a small fraction. Now here comes the violent part:

If you sum infinite big fractions the result is infinity, so the function explodes at that point and is useless, while if you sum infinite small fractions the result often converges and gives you a normal result.

The imaginary part of the exponent can be whatever you want, because rather than growing or shrinking numbers, what it does is rotate (literally) the number in the complex plane, leaving the magnitude unchanged.

So that's why the real part of the exponent has to be bigger than 1 I hope it was understandab...

hey... HEY WAKE UP!! proof is finished! XD


EDIT: moral of this fable: everytime a mathematical expression returns an infinity, a random Sublevel explodes

[sundayfever]

Lately we've been talking about really really basic probability and what I suppose is number theory.
Before that we had Euclidan geometry - the volumes and fields of cones, cylinders, balls and stuff.

Oh we did that in 8th grade if I remember well.

I feel you. We have just started basic trigonometry...

WHAT?!?! Aren't you 15 like me?? Here, we are learning that in 3rd grade of high school! That's 2 more years to go!!

[azareus]

Lately we've been talking about really really basic probability and what I suppose is number theory.
Before that we had Euclidan geometry - the volumes and fields of cones, cylinders, balls and stuff.

Oh we did that in 8th grade if I remember well.

I feel you. We have just started basic trigonometry...

WHAT?!?! Aren't you 15 like me?? Here, we are learning that in 3th grade of high school! That's 2 more years to go!!

I am indeed. And I believe our 9th grade (10th actually, but it starts at 0 for some reason) of elementary is supposed to be something like 2th grade of American high school. I don't know about Croatian ones though...

[Anteroinen]

Yeah, sorry XD

If you want an explanation of why the real part has to be greater than 1, here's one:

When you raise a number to a real power, if it's greater than 1 the number becomes bigger, and if it's less the number becomes smaller. For example 2^16=65536, 2^(-4)=0.0625

When you divide 1 by a big number, it becomes small, for example 1/100000=0.00001, and viceversa. So the fraction 1/2^16 is small and 1/2^(-4) is big, hence we need a big exponent (>1) to make a small fraction. Now here comes the violent part:

If you sum infinite big fractions the result is infinity, so the function explodes at that point and is useless, while if you sum infinite small fractions the result often converges and gives you a normal result.

The imaginary part of the exponent can be whatever you want, because rather than growing or shrinking numbers, what it does is rotate (literally) the number in the complex plane, leaving the magnitude unchanged.

So that's why the real part of the exponent has to be bigger than 1 I hope it was understandab...

hey... HEY WAKE UP!! proof is finished! XD


EDIT: moral of this fable: everytime a mathematical expression returns an infinity, a random Sublevel explodes

I did professor. Thank you.

[sundayfever]

I am indeed. And I believe our 9th grade (10th actually, but it starts at 0 for some reason) of elementary is supposed to be something like 2th grade of American high school. I don't know about Croatian ones though...

I'm now in 9th grade, so to speak. That's 1st grade of high school here, in Croatia.

But if you're 15 like me, how are you going to SECOND grade? You started going to school at the age of 5 or 6? Cause I first went to school when I was 6-7.

[Vortex]

Yeah, sorry XD

If you want an explanation of why the real part has to be greater than 1, here's one:

When you raise a number to a real power, if it's greater than 1 the number becomes bigger, and if it's less the number becomes smaller. For example 2^16=65536, 2^(-4)=0.0625

When you divide 1 by a big number, it becomes small, for example 1/100000=0.00001, and viceversa. So the fraction 1/2^16 is small and 1/2^(-4) is big, hence we need a big exponent (>1) to make a small fraction. Now here comes the violent part:

If you sum infinite big fractions the result is infinity, so the function explodes at that point and is useless, while if you sum infinite small fractions the result often converges and gives you a normal result.

The imaginary part of the exponent can be whatever you want, because rather than growing or shrinking numbers, what it does is rotate (literally) the number in the complex plane, leaving the magnitude unchanged.

So that's why the real part of the exponent has to be bigger than 1 I hope it was understandab...

hey... HEY WAKE UP!! proof is finished! XD


EDIT: moral of this fable: everytime a mathematical expression returns an infinity, a random Sublevel explodes

I did professor. Thank you.

Me? A professor?
*jumps through the window*

[azareus]

I am indeed. And I believe our 9th grade (10th actually, but it starts at 0 for some reason) of elementary is supposed to be something like 2th grade of American high school. I don't know about Croatian ones though...

I'm now in 9th grade, so to speak. That's 1st grade of high school here, in Croatia.

But if you're 15 like me, how are you going to SECOND grade? You started going to school at the age of 5 or 6? Cause I first went to school when I was 6-7.

Most people start at 6, yes.

[Vortex]

I am indeed. And I believe our 9th grade (10th actually, but it starts at 0 for some reason) of elementary is supposed to be something like 2th grade of American high school. I don't know about Croatian ones though...

I'm now in 9th grade, so to speak. That's 1st grade of high school here, in Croatia.

But if you're 15 like me, how are you going to SECOND grade? You started going to school at the age of 5 or 6? Cause I first went to school when I was 6-7.

Most people start at 6, yes.

I don't see a problem... in Northern Ireland people start going to school at 4, not?