20 problems.
- If every continuous real-valued function on \(K\subset\mathbb R^n\) is bounded, then \(K\) is compact
- Local and global injectivity of \((u,v)\mapsto(u+v,u^2+v^2)\) on \(u>v\)
- If \(f^2\) and \(f^3\) are analytic, then \(f\) is analytic
- Polynomial representation of every function on a finite field
- Periodization of a decaying continuous function and integration against periodic functions
- Derivative bound from \(|f(z)|\le C/(1-|z|)\) on the unit disk
- Self-adjoint form of a second-order linear ODE
- Derivatives preserve a strict half-plane containing all polynomial roots
- Rational linear systems solvable over \(\mathbb C\) are solvable over \(\mathbb Q\)
- Embedding of a finite group of order \(n\) in the real orthogonal group \(O(n)\)
- The equation \(ae^x=1+x+x^2/2\) has exactly one real root
- Approximation of \(\int_0^{1/2}\sin x/x\,dx\) within \(0.005\)
- Bounded first partial derivatives force a removable puncture for a \(C^1\) real function
- The unique noncyclic group of order four has automorphism group \(S_3\)
- Entire functions sending unbounded sequences to unbounded sequences need not be polynomials — Problem 15
- The pointwise supremum of a uniformly bounded equicontinuous family is continuous
- A finite-dimensional differentiation-invariant function space is the kernel of a constant-coefficient ODE
- Commuting diagonalizable matrices are simultaneously diagonalizable — Problem 18
- Every finite subgroup of the multiplicative group of a field is cyclic
- The integral \(\int_0^\pi \cos(4\theta)/(1+\cos^2\theta)\,d\theta\)