Graduate level PDE important in applied math?

[donnylee]

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.
Donny

 

[TonyG]

Dear Donny,

As a scientist with a background in both mathematics and physics, I can understand your dilemma. While it is true that many applied mathematicians may not use advanced abstract concepts like Weyl's lemma or Hopf maximum principle in their work, there are certainly cases where such knowledge can be beneficial in tackling complex problems in finance or engineering. The ability to think abstractly and deeply about mathematical concepts can help in developing new and innovative solutions to real-world problems.

However, it is also important to keep in mind that practical knowledge and experience are just as important in the field of applied mathematics. So while taking a full-blown graduate level Elliptic PDE class may expand your theoretical understanding, it is also crucial to gain hands-on experience in applying these concepts to real-world problems.

My suggestion would be to weigh the pros and cons of taking the class and consider how it fits into your overall academic and career goals. If you have a strong interest in pure mathematics and want to further develop your understanding of abstract concepts, then it may be worth taking the class. However, if your main focus is on practical applications, then perhaps your 2nd year PDE class may be enough.

Ultimately, the decision is yours and should be based on your individual interests and goals. Just remember that a well-rounded education in both theory and practice can make you a more versatile and valuable mathematician in any field.

Best of luck in your decision-making process.