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badreferences

  • 2 years ago

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 \(-\frac1{12}\).

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

  2. sauravshakya
    • 2 years ago
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    1+2+3+4+...=-1/12 So that is TRUE?

  3. badreferences
    • 2 years ago
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    That's what Euler thought. :) http://en.wikipedia.org/wiki/Zeta_function_regularization#Definition

  4. badreferences
    • 2 years ago
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    http://plato.stanford.edu/entries/goedel/#IncThe Math is funny.

  5. sauravshakya
    • 2 years ago
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    So, at infinity number starts to act differently?

  6. experimentX
    • 2 years ago
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    pretty soon I need to work on these things.

  7. badreferences
    • 2 years ago
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    My condolences, haha. Unless you enjoy particle physics. If you do, ignore me.

  8. experimentX
    • 2 years ago
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    No I enjoy mathematical physics.

  9. experimentX
    • 2 years ago
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    you math major @badreferences ?

  10. badreferences
    • 2 years ago
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    I'm looking to do statistical physics in graduate school.

  11. experimentX
    • 2 years ago
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    so you are also physics major!! didn't know that!!

  12. badreferences
    • 2 years ago
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    :D

  13. experimentX
    • 2 years ago
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    I was looking for solution for "Topics in Algebra" by IN Herstein.

  14. badreferences
    • 2 years ago
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    Algebra is not my strong suit. I went for the analysis and stochastics route in undergraduate.

  15. experimentX
    • 2 years ago
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    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.

  16. badreferences
    • 2 years ago
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    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.

  17. badreferences
    • 2 years ago
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    Shhh... I have illegal electronic copies.

  18. badreferences
    • 2 years ago
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    And the real things as well, so I don't feel to bad. haha.

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

  20. experimentX
    • 2 years ago
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    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"

  21. experimentX
    • 2 years ago
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    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.

  22. badreferences
    • 2 years ago
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    Hmm, the best analysis texts are Spivak's "Calculus" and "Calculus of Manifolds".

  23. badreferences
    • 2 years ago
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    I don't know about linear algebra. The best review of physics I can think of are Feynman's lectures and Dirac's books.

  24. experimentX
    • 2 years ago
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    Looks like I need to hunt down those books!!

  25. badreferences
    • 2 years ago
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    Wait a second. And hush, don't tell anyone. I'll post them here.

  26. experimentX
    • 2 years ago
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    thanks @badreferences for goodreferences

  27. sauravshakya
    • 2 years ago
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    Then what is: 1*2*3*4*5...

  28. experimentX
    • 2 years ago
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    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.

  29. sauravshakya
    • 2 years ago
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    Ya....... I remember it.

  30. experimentX
    • 2 years ago
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    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.

  31. experimentX
    • 2 years ago
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    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

  32. experimentX
    • 2 years ago
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    probably long way through analysis and algebra just to understand these stuff.

  33. experimentX
    • 2 years ago
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    Woops!! @mahmit2012 is here ...

  34. mahmit2012
    • 2 years ago
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    hello everybody.

  35. experimentX
    • 2 years ago
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    hello

  36. experimentX
    • 2 years ago
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    where do i start with Riemann zeta function?

  37. mahmit2012
    • 2 years ago
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    it is very simple because the series is divergence.

  38. mahmit2012
    • 2 years ago
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    |dw:1349545376509:dw|

  39. mahmit2012
    • 2 years ago
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    |dw:1349545461704:dw|

  40. mahmit2012
    • 2 years ago
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    So you can play with a some young student and it is interesting for them and wondered !!

  41. badreferences
    • 2 years ago
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    Okay, so the upload of the books failed haha. Are there any free file sharers?

  42. experimentX
    • 2 years ago
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    looks like there are couple of file sharing sites ... http://www.2shared.com/

  43. badreferences
    • 2 years ago
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    I got it. I'll be right back, need to restart computer. I'll be using Senduit.

  44. experimentX
    • 2 years ago
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    sure thank you!!

  45. estudier
    • 2 years ago
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    I think we can safely conclude that complex analysis is a funny artiact:)

  46. estudier
    • 2 years ago
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    artifact*

  47. experimentX
    • 2 years ago
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    there seem to lot's of things I'm missing in complex analysis.

  48. estudier
    • 2 years ago
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    I'm sure you will get over it.....

  49. badreferences
    • 2 years ago
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    Uploading the books in a zip archive... taking a while, since it's ~45MB.

  50. experimentX
    • 2 years ago
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    thanks!! both for effort and books!!

  51. badreferences
    • 2 years ago
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    http://ge.tt/7YAU01P/v/0

  52. badreferences
    • 2 years ago
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    The file should be called AN.7z.

  53. badreferences
    • 2 years ago
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    You can extract using 7-zip.

  54. experimentX
    • 2 years ago
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    Thanks!! I got it!!

  55. sauravshakya
    • 2 years ago
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    Well, I am tired of thinking........ Gud Night...... Out of my level.

  56. badreferences
    • 2 years ago
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    Haha.

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  57. experimentX
    • 2 years ago
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    I was about to click Apply then OK

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