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Graduate level PDE important in applied math?

  1. Apr 2, 2010 #1
    Dear Mathematicians and Physicists,

    In light of the coming fall semester, I am having a decision to take a full blown graduate level Elliptic PDE class. The prerequisites is of course Graduate level analysis and perhaps a undergrad class in PDE, both of which I already have. The class will be following Folland's text, signifying the advance level of math in the class.

    Thus my question? Would taking such an abstract class be of any use for someone who wishes to stay in the realm of applied mathematics, namely, an aspiring quantitative analyst who seeks to model finance systems (and possibly any sort of complex system - could also include problems in engineering).

    I have sort of fallen in love with the idea that only pure mathematicians, who knows the ins-and-outs of the abstract theory of math can dwell deeper into the equations used in the real world and discover some hidden solutions to provide a better answer to the problem at hand. I thought to believe that this ability is hard to find in applied mathematicians because they are simply using the already present ideas and thus lack the intuition to think deeper, think original, think out-of-the-box.

    Then again, most people I talk to say that the highest math anyone uses in Wall Street is standard solving 2nd order linear ODEs. So really, would there really be a time where I can take the spotlight and use the idea of Weyl's lemma, Hopf maximum principle, and harmonic functions to bring light to various problems.

    If no, then maybe my 2nd year PDE class is enough. If yes, then I'll have to recap my Rudin and enter graduate level PDE next year.

    Thanks for your opinions.
  2. jcsd
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