20 problems.
- \((\cos\theta)^p\le\cos(p\theta)\) for \(0<p<1\)
- Pointwise convergence of monotone functions to a continuous limit is uniform
- Existence of \(\lim_{t\to0^+}\left(\int_0^1(x^4+t^4)^{-1/4}\,dx+\log t\right)\)
- Local functional dependence from parallel gradients
- Powers \(A^{100}\) and \(A^{-7}\) of a unipotent \(2\times2\) matrix
- Automorphisms of a direct product of finite groups of coprime order
- Maximum of the generalized Rayleigh quotient \(\langle Ax,x\rangle/\langle Bx,x\rangle\)
- When the complex-number matrix ring over a field is a field
- The integral \(\int_0^{2\pi}\frac{\cos^2(3\theta)}{5-4\cos(2\theta)}\,d\theta\)
- Coefficient bounds from \(|f(z)|\le(1-|z|)^{-1}\)
- Restricting a diagonalizable operator to an invariant subspace preserves diagonalizability
- Complex similarity of real matrices implies real similarity
- Homomorphisms from \((\mathbb Q,+)\) to the positive rationals under multiplication — Fall 1987 Problem 13; repeated exactly as Fall 1993 Problem 2
- The full matrix ring over a field has no proper nonzero two-sided ideals
- Reality on the unit circle forces reality on the nonzero real axis
- Zeros of \(2z^5-6z^3+z+1\) in the annulus \(1\le|z|\le2\)
- A positive harmonic function on the plane is constant
- A plane curve whose points bisect their first-quadrant tangent segments
- Convergence of the iteration \(x_{n+1}=1/(1+x_n)\) — Fall 1987 Problem 19; repeated exactly as Spring 2019 Problem 3B
- Maximum of \(\int_0^1f\) over \(f(0)=0\), \(\int_0^1(f')^2\le1\)