18 problems.
- The sequence \(\cos(nx)\) has no uniformly convergent subsequence on \(\RR\)
- Real \(a\) for which \(a^nA^n\) converges to a nonzero matrix
- A residue integral for \(\sin(n\theta)/\sin\theta\)
- Order and Sylow-\(p\) subgroups of \(GL_2(\FF_{p^n})\)
- Every solution of \(y'=f(y)\) is monotone when \(f\) is bounded and \(C^1\)
- Finite-index subrings have the same quotient modulo coprime integers
- Equal suprema force equality under a strictly increasing transform at some point
- Determinant of \(I-tL\) when the image of \(L\) lies in an invariant subspace
- A monic real polynomial avoiding the open unit disk must vanish at \(1\)
- A decreasing sequence of nonnegative continuous functions has an attained limiting supremum
- An isometry of a finite subset fixing the origin extends to a linear map
- Integral of \((1-\cos n\theta)/(1-\cos\theta)\) over \([0,2\pi]\)
- A \(2\)-group acting on an odd finite set has a fixed point
- A linear relation among initial data for decaying solutions of \(y'''-y=0\)
- A finite field not generated by its cubes must have four elements
- A strict distance contraction on a compact metric space has a unique fixed point — Problem 16
- Coprime factors of the characteristic polynomial split the vector space
- Punctured unit disk and annulus are not conformally equivalent — Problem 18