18 problems.
- Every finite group of order at least \(3\) has a nontrivial automorphism
- A continuous distance-expanding map \(\mathbb R\to\mathbb R\) is surjective
- The contour integral \(\frac1{2\pi i}\oint_{\abs z=1}\frac{z^{n-1}}{3z^n-1}\,dz\)
- Decomposition of a real matrix into antisymmetric, traceless symmetric, and scalar parts
- \(f(1)=f(0)=\cdots=f^{(n)}(0)=0\) forces a zero of \(f^{(n+1)}\) in \((0,1)\)
- An \(L^1\) bound on radial values of \(f'\) controls \(f\) on a radius
- Exponential norm bound for a time-dependent linear system
- Convergence of \(\sum\sqrt{a_na_{n+1}}\) from convergence of \(\sum a_n\)
- A group of order \(2p\) with a normal subgroup of order \(2\) is cyclic
- Order of \(SL_3(\FF_p)\)
- Images commute with intersections of nested compact sets
- Logarithmic derivative of a polynomial whose zeros lie in the upper half-plane
- Eigenvalues of a row-stochastic nonnegative matrix lie in the unit disk
- Integral identities for a compactly supported divergence-free vector field
- \(\ZZ[x]/(x-7,15)\cong\ZZ/15\ZZ\)
- The set of nilpotent real matrices is closed
- \(\norm{f(t)}\) is increasing near \(0^+\) for a \(C^1\) curve with \(f(0)=0\) and \(f'(0)\neq0\)
- An entire function bounded by \(|\operatorname{Re}z|^{-1/2}\) off the imaginary axis is constant