20 problems.
- Real \(2\times2\) square roots of \(-I\) and of \(\operatorname{diag}(-1,-1-\varepsilon)\)
- A sine lower bound and decay of a Laplace-type integral
- Polar decomposition of a nonsingular real matrix
- A subgroup of order \(24\) in a group of order \(120\) from one matching left and right coset
- Sum of cubes of the roots of \(x^3+2x^2+7x+1\)
- The integral \(\int_0^\infty x^{a-1}/(1+x)\,dx\) and its domain of convergence
- Monotonicity and a reciprocal bound for a Gaussian-tail ratio
- Polynomial approximation with prescribed value and derivative at an endpoint
- Maximum principle and uniqueness for \(u''=e^x u\)
- The equation \(z=\lambda-e^{-z}\) has one root in the closed right half-plane
- Products of nonsquares in a cyclic group and failure outside the cyclic case
- \(A^TA\) and \(A^T\) have the same range — Problem 12
- Averaging a polynomial over the \(k\)th roots of unity
- No surjective ring homomorphism \(M_{n+1}(F)\to M_n(F)\) — Problem 14
- Boundary-growth spaces of analytic functions are shifted by differentiation
- An upper-semicontinuous function on \([0,1]\) is bounded above and attains its maximum
- Nonnegative coefficients force a singularity at the positive boundary point
- General solution of \(y_1'=-3y_1+10y_2\), \(y_2'=-3y_1+8y_2\)
- Limit of the \(n\)th root of a finite sum of \(n\)th powers
- All roots of \(x^p-x+3\) lie in the field generated by one root