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badreferences
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 \(-\frac1{12}\).
http://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E2%80%A6#Summability
1+2+3+4+...=-1/12 So that is TRUE?
That's what Euler thought. :) http://en.wikipedia.org/wiki/Zeta_function_regularization#Definition
http://plato.stanford.edu/entries/goedel/#IncThe Math is funny.
So, at infinity number starts to act differently?
pretty soon I need to work on these things.
My condolences, haha. Unless you enjoy particle physics. If you do, ignore me.
No I enjoy mathematical physics.
you math major @badreferences ?
I'm looking to do statistical physics in graduate school.
so you are also physics major!! didn't know that!!
I was looking for solution for "Topics in Algebra" by IN Herstein.
Algebra is not my strong suit. I went for the analysis and stochastics route in undergraduate.
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.
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.
Shhh... I have illegal electronic copies.
And the real things as well, so I don't feel to bad. haha.
haha ... no probs!! i also own illegal electronic books!! I didn't take stat seriously ... I need to revise statistics and numerical analysis again.
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"
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.
Hmm, the best analysis texts are Spivak's "Calculus" and "Calculus of Manifolds".
I don't know about linear algebra. The best review of physics I can think of are Feynman's lectures and Dirac's books.
Looks like I need to hunt down those books!!
Wait a second. And hush, don't tell anyone. I'll post them here.
thanks @badreferences for goodreferences
Then what is: 1*2*3*4*5...
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.
Ya....... I remember it.
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.
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
probably long way through analysis and algebra just to understand these stuff.
Woops!! @mahmit2012 is here ...
where do i start with Riemann zeta function?
it is very simple because the series is divergence.
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So you can play with a some young student and it is interesting for them and wondered !!
Okay, so the upload of the books failed haha. Are there any free file sharers?
looks like there are couple of file sharing sites ... http://www.2shared.com/
I got it. I'll be right back, need to restart computer. I'll be using Senduit.
I think we can safely conclude that complex analysis is a funny artiact:)
there seem to lot's of things I'm missing in complex analysis.
I'm sure you will get over it.....
Uploading the books in a zip archive... taking a while, since it's ~45MB.
thanks!! both for effort and books!!
The file should be called AN.7z.
You can extract using 7-zip.
Thanks!! I got it!!
Well, I am tired of thinking........ Gud Night...... Out of my level.
I was about to click Apply then OK