1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Problem from A Beautiful Mind

  1. Aug 27, 2009 #1
    Problem from "A Beautiful Mind"

    In the movie when he first walks in to teach that ad cal class, this is the problem he wrote on the board (verbatim):

    [tex]V=\{F:\mathbb{R}^3\backslash X\rightarrow \mathbb{R}^3:\nabla\times F=0\}[/tex]

    [tex]W=\{F=\nabla g\}[/tex]

    [tex]\dim (V/W)=?[/tex]

    What's X?
     
  2. jcsd
  3. Aug 27, 2009 #2
    Re: Problem from "A Beautiful Mind"

    V/W is the first deRham cohomology group of the space R^3\X, where X is presumably some subset of R^3.
     
  4. Aug 27, 2009 #3
    Re: Problem from "A Beautiful Mind"

    Just finished reading the biog. A good read. Can't help with the above math though.
     
  5. Aug 27, 2009 #4
    Re: Problem from "A Beautiful Mind"

    Can't solve it without X.
     
  6. Dec 23, 2010 #5
    Re: Problem from "A Beautiful Mind"

    Dim(v/w) = 8 instead of question mark.

    inverse cohomology problem to find a manifold M with a 8-dimensional fundamental group.
     
  7. Dec 23, 2010 #6

    AlephZero

    User Avatar
    Science Advisor
    Homework Helper

    Re: Problem from "A Beautiful Mind"

    [tex]\times[/tex] is the vector cross-product.

    [tex]\nabla\times[/tex] is the vector calculus "curl" operator.
     
  8. Dec 23, 2010 #7

    disregardthat

    User Avatar
    Science Advisor

    Re: Problem from "A Beautiful Mind"

    In that case, what does [tex]\mathbb{R}^3 \slash \times[/tex] signify?
     
  9. Dec 23, 2010 #8
    Re: Problem from "A Beautiful Mind"

    Firstly the person is right in saying [tex]\times[/tex] is the x but that is not what the person is referring to, they are asking what the [tex]X[/tex] means in [tex]X\rightarrow \mathbb{R}^{3}[/tex]. But I believe the person is right in saying it is the first deRham cohomology group.
     
  10. Dec 24, 2010 #9
    Re: Problem from "A Beautiful Mind"

    Material on the Nash problem:

    1) http://answers.yahoo.com/question/index?qid=20080501140727AAb2Ys1", Yahoo Answers

    2) A beautiful mind http://www.math.harvard.edu/~huizenga/LECTURE35WS.PDF" [Broken].

    3) http://www.math.harvard.edu/~knill/teaching/math21a/nash.pdf" [Broken], Spring 2004

    4) "www.wfu.edu/~parslerj/math733/lecture%20notes%201-4.pdf"[/URL], Math 733: Vector Fields, Differential Forms, and Cohomology
    [PLAIN]http://www.wfu.edu/~parslerj/math733/note.html" [Broken], R. Jason Parsley
     
    Last edited by a moderator: May 5, 2017
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Problem from A Beautiful Mind
  1. Beautiful Proof (Replies: 10)

  2. Beautiful Equations (Replies: 9)

  3. Mathematical beauty (Replies: 2)

Loading...