A funny artifact of complex analysis.\[\sum_{k=1}^nk=\frac{n(n+1)}2\]Which naturally goes to infinity, but via zeta function summation and Ramanujan sums, you get a value of \(-\frac1{12}\).

- anonymous

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- katieb

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- anonymous

http://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%80%A6#Summability

- anonymous

1+2+3+4+...=-1/12
So that is TRUE?

- anonymous

That's what Euler thought. :) http://en.wikipedia.org/wiki/Zeta_function_regularization#Definition

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## More answers

- anonymous

http://plato.stanford.edu/entries/goedel/#IncThe
Math is funny.

- anonymous

So, at infinity number starts to act differently?

- experimentX

pretty soon I need to work on these things.

- anonymous

My condolences, haha. Unless you enjoy particle physics. If you do, ignore me.

- experimentX

No I enjoy mathematical physics.

- experimentX

you math major @badreferences ?

- anonymous

I'm looking to do statistical physics in graduate school.

- experimentX

so you are also physics major!! didn't know that!!

- anonymous

:D

- experimentX

I was looking for solution for "Topics in Algebra" by IN Herstein.

- anonymous

Algebra is not my strong suit. I went for the analysis and stochastics route in undergraduate.

- experimentX

my undergrad was mess!! still i need to do few things in math before tackle physics. It seems i still lack strong mathematical background for tackling physics.

- anonymous

If I can recommend two introductory texts at graduate level, "All of Statistics" ( http://www.amazon.com/All-Statistics-Statistical-Inference-Springer/dp/0387402721 ) and "Mathematics: Its Content, Methods and Meaning" ( http://www.amazon.com/Mathematics-Content-Methods-Meaning-Dover/dp/0486409163/ref=sr_1_1?s=books&ie=UTF8&qid=1349543762&sr=1-1&keywords=mathematics+its+content+methods+and+meaning ). They should provide sufficient math background, I think. But I'm no expert on the subject.

- anonymous

Shhh... I have illegal electronic copies.

- anonymous

And the real things as well, so I don't feel to bad. haha.

- experimentX

haha ... no probs!! i also own illegal electronic books!! I didn't take stat seriously ...
I need to revise statistics and numerical analysis again.

- experimentX

I need to revise whole physics i read in first year. But I've math exam first.
Analysis II and Algebra II
I have Tom Aposle's Mathematical analysis for Analysis .. everytime i try to read it ... i feels like reading "War and Peace"

- experimentX

Same goes for Algebra, I have Linear Algebra by Serge Lang and Topics in algebra by IN Herstein ... but undergraduate level. But I'm doing Linear Algebra from MIT OCW.

- anonymous

Hmm, the best analysis texts are Spivak's "Calculus" and "Calculus of Manifolds".

- anonymous

I don't know about linear algebra. The best review of physics I can think of are Feynman's lectures and Dirac's books.

- experimentX

Looks like I need to hunt down those books!!

- anonymous

Wait a second. And hush, don't tell anyone. I'll post them here.

- experimentX

thanks @badreferences for goodreferences

- anonymous

Then what is:
1*2*3*4*5...

- experimentX

lol ... that diverges.
same goes from 1 + 2 + 3 + ...
but if you view it as generating function of
1/(1+x)^2 = 1 + 2x + 3x^2 + ...
it seems to converge ...
there was some Question posten my mikael on this.

- anonymous

Ya....... I remember it.

- experimentX

I haven't encountered Riemann zeta function on my studies except for finding the particular values line zeta(2), zeta(4) while integrating some functions. I think it's better to go step by step on this.

- experimentX

things aren't much intuitive ... there seems to lots of odd behaviours with this function which i don't understand. If you explain it ... probably you will be greatest mathematician of this time http://en.wikipedia.org/wiki/Millennium_Prize_Problems

- experimentX

probably long way through analysis and algebra just to understand these stuff.

- experimentX

Woops!! @mahmit2012 is here ...

- anonymous

hello everybody.

- experimentX

hello

- experimentX

where do i start with Riemann zeta function?

- anonymous

it is very simple because the series is divergence.

- anonymous

|dw:1349545376509:dw|

- anonymous

|dw:1349545461704:dw|

- anonymous

So you can play with a some young student and it is interesting for them and wondered !!

- anonymous

Okay, so the upload of the books failed haha. Are there any free file sharers?

- experimentX

looks like there are couple of file sharing sites ...
http://www.2shared.com/

- anonymous

I got it. I'll be right back, need to restart computer. I'll be using Senduit.

- experimentX

sure thank you!!

- anonymous

I think we can safely conclude that complex analysis is a funny artiact:)

- anonymous

artifact*

- experimentX

there seem to lot's of things I'm missing in complex analysis.

- anonymous

I'm sure you will get over it.....

- anonymous

Uploading the books in a zip archive... taking a while, since it's ~45MB.

- experimentX

thanks!! both for effort and books!!

- anonymous

http://ge.tt/7YAU01P/v/0

- anonymous

The file should be called AN.7z.

- anonymous

You can extract using 7-zip.

- experimentX

Thanks!! I got it!!

- anonymous

Well, I am tired of thinking........ Gud Night...... Out of my level.

- anonymous

Haha.

##### 1 Attachment

- experimentX

I was about to click Apply then OK

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