20 problems.
- Evaluate \(\int_{-\infty}^{\infty}\cos x/(1+x^4)\,dx\)
- Contractive autonomous systems
- A \(p\)-subgroup action has a fixed point
- Cayley transform between orthogonal and skew-symmetric matrices
- Ratio limit for Fibonacci numbers
- Averaging a periodic function against rapid oscillations
- A polynomial for \(\sqrt2+\sqrt[3]{3}\)
- Zeros of \(3z^{100}-e^z\) in the unit disk
- Trace and determinant of \(X\mapsto AXB\)
- Jacobi formula for the derivative of a determinant
- Eigenvalues of circulant matrices
- Harmonic function \(\frac{a^2+b^2-x^2-y^2}{(a-x)^2+(b-y)^2}\) as the real part of \(\frac{c+z}{c-z}\)
- Nondegenerate critical points are isolated
- Energy conservation for a potential system
- A nonidentity holomorphic self-map of the disk has at most one fixed point
- Three complementary normal subgroups force an abelian group
- Limits involving \(n\int_0^1x^nf(x)\,dx\)
- Real matrices similar over \(\mathbb C\) are similar over \(\mathbb R\)
- Limits of composites, images of open sets, and analyticity from bounded derivatives
- A group of order \(10\) with a normal subgroup of order \(2\) is abelian