Question

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 \(-\frac1{12}\).

Answer 1

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

Answer 2

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

Answer 3

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

Answer 4

http://plato.stanford.edu/entries/goedel/#IncThe

Math is funny.

Answer 5

So, at infinity number starts to act differently?

Answer 6

pretty soon I need to work on these things.

Answer 7

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

Answer 8

No I enjoy mathematical physics.

Answer 9

you math major @badreferences ?

Answer 10

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

Answer 11

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

Answer 12

:D

Answer 13

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

Answer 14

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

Answer 15

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.

Answer 16

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.

Answer 17

Shhh... I have illegal electronic copies.

Answer 18

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

Answer 19

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

Answer 20

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"

Answer 21

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.

Answer 22

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

Answer 23

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

Answer 24

Looks like I need to hunt down those books!!

Answer 25

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

Answer 26

thanks @badreferences for goodreferences

Answer 27

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

Answer 28

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.

Answer 29

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

Answer 30

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.

Answer 31

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

Answer 32

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

Answer 33

Woops!! @mahmit2012 is here ...

Answer 34

hello everybody.

Answer 35

hello

Answer 36

where do i start with Riemann zeta function?

Answer 37

it is very simple because the series is divergence.