20 problems.
- A sparse polynomial of degree \(47\) has a zero in the unit disk — Fall 1979 Problem 1; repeated exactly as Fall 1989 Problem 16
- Sharp bound for a bounded upper-half-plane function vanishing at \(i\)
- Every finite group of order at least \(3\) has a nontrivial automorphism — Fall 1979 Problem 3; repeated exactly as Fall 1991 Problem 1
- Reduce polynomials modulo the ideal \((7,x-3)\) in \(\mathbb Z[x]\)
- A real skew-symmetric matrix has even rank
- A single Jordan-chain nilpotent has no square root
- Shift-operator eigenvectors and the Fibonacci subspace
- A harmonic-block sum converges to \(\log2\)
- Differentiate the Gaussian integral with respect to its scale parameter
- Solve an explicit two-dimensional linear ODE system
- A map of California has a unique point directly over the point it represents
- Connectedness of the graph versus continuity of a real-valued function
- Pointwise convergence of uniformly bounded-degree polynomials is uniform — Fall 1979 Problem 13; repeated exactly as Fall 1980 Problem 17
- Evenness and zeros of the solution of \(y''=-|y|\) — Fall 1979 Problem 14; repeated exactly as Summer 1981 Problem 20
- An entire function dominated by another is its scalar multiple — Fall 1979 Problem 15; entire domination implies scalar multiple
- The Euler beta integral \(\int_0^\infty x^{\alpha-1}/(1+x)\,dx\) — Fall 1979 Problem 16; Euler beta integral
- Schur triangularization by a unitary matrix
- Count symmetric matrices \(BQ\) for a diagonal matrix with distinct absolute eigenvalues
- The full matrix ring over a field has no proper nonzero two-sided ideals — Fall 1979 Problem 19; full matrix ring has no nonzero proper two-sided ideals
- Smith normal form and element orders for an abelian group on three generators