20 problems.
- Fourier transform of \(\operatorname{sech}^2x\)
- No surjective ring homomorphism \(M_{n+1}(F)\to M_n(F)\)
- Bounded partial derivatives allow a punctured-space function to extend continuously
- Every real sequence has a monotone subsequence
- Spectrum and determinant of the matrix with zero diagonal and ones off diagonal — Fall 1983 Problem 5; repeated exactly as Spring 1996 Problem 16
- Zeros of \(z^5+z^3+5z^2+2\) in \(1<|z|<2\)
- If \(G\times G\) has exactly four normal subgroups then \(G\) is simple nonabelian
- Symmetric orthogonal transformations of \(\RR^3\)
- Parameters yielding infinitely many critical points for a forced second-order ODE
- Uniform continuity plus convergence of an improper integral forces decay to zero
- A converse to l’Hopital’s rule need not hold
- Partial fractions for a rational function with distinct simple poles
- Scalar and vector exponential-growth inequalities
- Commuting diagonalizable matrices are simultaneously diagonalizable — Fall 1983 Problem 14; commuting diagonalizable operators are simultaneously diagonalizable
- Holomorphic functions real on the unit circle
- Derivative of \(\operatorname{tr}(F(t)^3)\)
- Finite integral domains are fields — Fall 1983 Problem 17; every finite integral domain is a field
- Implicit solution of \(f(x)=t g(x)\) near a simple zero of \(f\)
- Irreducibility of \((x^p-1)/(x-1)\) over \(\QQ\) — Fall 1983 Problem 19; prime cyclotomic polynomial is irreducible
- Full-rank rectangular matrices form an open set with a continuous left inverse