All Questions

I have always been interested in alternative definitions of mathematical objects. I wonder if one can craft an useful definition of definite integral by using the Residue Theorem from complex analysis....

This is a question about pedagogy. I want to sketch the proof of the prime number theorem or any other application of complex analysis to number theory in a single lecture, in a complex analysis ...

[Changed title as a plea to re-open the question.] If one is to motivate a course in complex variables, what specific analytic (holomorphic/meromorphic) function of one variable would you cite as an ...

I'm looking for "nice" applications of Liouville's theorem (every bounded entire map is constant) outside the area of complex analysis. An example of what I'm not looking for : a non-constant entire ...

Pedagogically speaking, I see two problems with defining $\Gamma(z)$ (at least for real $z$) by the limit $$\Gamma(z)=\lim_{m\to\infty}\frac{m! m^z}{\prod_{i=0}^m (z+i)}$$ as compared with the formula ...

At the end of this month I start teaching complex analysis to 2nd year undergraduates, mostly from engineering but some from science and maths. The main applications for them in future studies are ...