Recent content by oab729

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    Schools Math Major's Chances for CS Grad Program

    wat about for masters programs
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    Algorithm for cluster finding (?)

    Hmm... perhaps I misunderstand your question? John knows Alice. Alice Knows Alex. John Doesn't know Alice. The number of connected components is 1. Or do you mean John needs to really know Alice, so could you set thresholds or something? You could also look up clustering analysis or...
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    Algorithm for cluster finding (?)

    Take each page as a vertex in a giant graph where edges indicate links between sites. Then take the laplacian matrix. The number of connected components is the multiplicity of the eigenvalue 0. http://en.wikipedia.org/wiki/Laplacian_matrix
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    Schools Math Major's Chances for CS Grad Program

    what are the chances for getting into a good computer science grad program for a math major (who's finished the first two years of graduate math courses) but who's only taken two computer science courses (software development and problem-solving using haskell).
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    Can Polynomials of Degree n be Bounded by Constants for Large |z| Values?

    Homework Statement Show that for a polynomial of degree n, P(z), that for all z with |z| sufficiently large, there are positive constants c,d, s.t. c|z|^n < |P(z)| < d|z|^n Homework Equations The Attempt at a Solution Assume it is true for n-1. p(z)=az^n+q(z) Then for z with...
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    Prove No Analytic Function F on Annulus D: 1<|z|<2

    Homework Statement Prove that there does not exist an analytic function on the annulus D: 1<|z|<2, s.t. F'(z) = 1/z for all z in D. Homework Equations The Attempt at a Solution Assume F exists, then for z in D, not a negative number, F(z) = Log z + c since Log' z = 1/z... Lost
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    In the complex field, is this function Harmonic?

    Homework Statement Without directly verifying via the laplace equations, explain why Log|z| is harmonic in the punctured complex plane. Homework Equations The Attempt at a Solution I thought it was because Log z is analytic on the complex plane except for the nonpositive real axis...
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    Analytic Function Mapping to a Line: Constant Throughout Domain?

    Homework Statement Show that if the analytic function w= f(z) maps a domain D onto a portion of a line, then f must be constant throughout D. Homework Equations The Attempt at a Solution I just have one question, can I write w = u(x,y) (a+bi) since it maps to a portion of a line...
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    Show z^2 maps the circle |z-1|=1 to a cardioid

    NVM, take z = 1+cos +isin
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    Show z^2 maps the circle |z-1|=1 to a cardioid

    Homework Statement show z^2 maps the circle |z-1|=1 to a cardioid 2(1+cos(theta))e^(i*theta) Homework Equations The Attempt at a Solution I tried using the restriction |z-1| = 1 and simply got that r^2=2x. Then I tried to apply that and got z^2=2xe^(2i*theta) I've been...
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    Is the Real Part of (z+1)^100 and (z-1)^100 Always Zero for Complex z?

    Word. I think I was just tired. I feel dumb for not seeing that.
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    Is the Real Part of (z+1)^100 and (z-1)^100 Always Zero for Complex z?

    Homework Statement (z+1)^100=(z-1)^100 z is complex Homework Equations The Attempt at a Solution (z-1)/(z+1)=e^(i2pi(k/100))
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