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- 3/9/11
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Hi, I was curious whether people here have encountered interview questions on these two topics, as I am familiar with both subjects on some level and questions about them seem to appear in at least one quant interview.
For example, Crack includes proving Liouville's theorem as a (***) exercise (meaning 'very hard'), but this rating seems only partly justified if the interviewee is a math major (who has not necessarily hinted at having studied complex analysis before). Anyone who claims to have studied complex analysis should find this a rather simple exercise, as it is one of the most well-known and perhaps easiest results in basic complex analysis, which is full of short and elegant proofs. According to Joshi, an interviewer might (actually did?) ask whether an interviewee who claims to have studied complex analysis wants a theory question or a computational question. In the latter case, a definite integral is usually given (presumably to solve via residue calculus, though ironically the integral Joshi gives in his book can be done much more elegantly by real analysis).
Also, I've only seen a few examples of straight up PDE problems. I guess by "straight up", I mean something like converting the BS equation to Heat equation, since this is making a change of variables, which in itself is just a mathematical technique often used in PDE theory. Solving one of the well-known equations such as the heat equation or the Laplace equation is another example. Other examples include solving some actual PDEs using the method of characteristics or the Fourier transform. My impression is that these questions are rather rare, and probably depends on whether you put "PDE" on your resume. But has anyone here encountered such questions in interviews?
Thanks.
For example, Crack includes proving Liouville's theorem as a (***) exercise (meaning 'very hard'), but this rating seems only partly justified if the interviewee is a math major (who has not necessarily hinted at having studied complex analysis before). Anyone who claims to have studied complex analysis should find this a rather simple exercise, as it is one of the most well-known and perhaps easiest results in basic complex analysis, which is full of short and elegant proofs. According to Joshi, an interviewer might (actually did?) ask whether an interviewee who claims to have studied complex analysis wants a theory question or a computational question. In the latter case, a definite integral is usually given (presumably to solve via residue calculus, though ironically the integral Joshi gives in his book can be done much more elegantly by real analysis).
Also, I've only seen a few examples of straight up PDE problems. I guess by "straight up", I mean something like converting the BS equation to Heat equation, since this is making a change of variables, which in itself is just a mathematical technique often used in PDE theory. Solving one of the well-known equations such as the heat equation or the Laplace equation is another example. Other examples include solving some actual PDEs using the method of characteristics or the Fourier transform. My impression is that these questions are rather rare, and probably depends on whether you put "PDE" on your resume. But has anyone here encountered such questions in interviews?
Thanks.