7 problems.
- \(2^{n-1}\prod_{k=1}^{n-1}\sin(k\pi/n)=n\)
- Laurent expansions of \(\frac{1}{1-z^2}+\frac{1}{z-3}\) in \(|z|<1\), \(1<|z|<3\), and \(|z|>3\)
- \(\int_0^\infty\frac{x^{a-1}}{1+x^3}\,dx\) for \(0<a<3\)
- \(|f(0)|\le|a|^2\) for holomorphic \(f:\DD\to\DD\) vanishing at \(\pm a\), and the equality case
- The Joukowski map \(f(z)=\frac{1}{2}(z+\frac{1}{z})\) on the punctured disc and its exterior
- Maximum modulus principle and zeros when \(|f|\) is constant on \(\partial U\)
- Iterates of a holomorphic self-map of the disc fixing \(0\) converge to \(0\) or the identity