18 problems.
- Locally uniform convergence on \([a,b]\) is uniform
- A countable abelian group with \(2^{\aleph_0}\) endomorphisms
- Rational interpolation with prescribed pole-order bounds
- Every real invertible \(2\times2\) matrix is an \(n\)-th power exactly when \(n\) is odd
- Limit of \(e^{it^2}(f(t)-f(-t))\) for \(f'+2itf=e^{2it}\), \(f(0)=0\)
- Integers \(a,b\) with \(\ZZ[x]/(x^2+ax+b)\cong\ZZ\times\ZZ\)
- The Dirichlet integral \(\int_0^\infty\sin x/x\,dx\)
- A multilinear map vanishing on equal adjacent arguments is zero when \(\dim V<n\)
- \((f(x)-f(y)).(x-y)\le L|x-y|^2\) for all \(x,y\) iff \(Df(x)v.v\le L|v|^2\) for all \(x,v\)
- \(y^2+a(x)y+b(x)\) is irreducible over \(F(x)\) when \(\deg a\le g\) and \(\deg b=2g+1\)
- Maximum of \(|f'(1)|\) for \(f\) holomorphic with \(|f|\le1\) on \(|z|=2\)
- \(\|A^n\|=O(n^{d-1})\) when every eigenvalue of \(A\) has modulus \(1\)
- Unique maximum of \(\log\prod x_i\) on the simplex \(\sum a_ix_i=1\), \(x_i>0\)
- A finite group with pairwise noncommuting elements of prescribed orders
- Harmonic \(u_n\) with \(\partial_yu_n(x,0)=0\) and \(u_n(x,0)\to0\) uniformly need not tend to \(0\)
- A common eigenvector when \(AB-BA\) is a linear combination of \(A\) and \(B\)
- Limit of \(n((1+x/n)^n-e^x)\)
- Every automorphism of \(S_4\) is inner, so \(|\operatorname{Aut}(S_4)|=24\)