18 problems.
- The integral \(\int_0^1 x^4(1-x)^4/(1+x^2)\,dx = 22/7-\pi\) and the bound \(0<22/7-\pi<1/256\)
- Cousin’s lemma for a positive gauge on \([a,b]\)
- Images of polynomial maps \(\RR\to\RR\) and \(\RR^2\to\RR\)
- Laurent series for \(1/(z(1+z^2))\) — Problem 4A
- Difference of contour integrals for \(e^{\pi/z}/(z^2+4)\)
- Lagrange interpolation in Cauchy-matrix form
- Determinant of the Pascal matrix \(\left[\binom{i+j}{i}\right]\)
- Factorization of \(11x^5-11x^4+14x^2-21x+7\) over \(\QQ\)
- Cyclic decomposition of \((\ZZ_{12}\times\ZZ_{12})/\langle(2,6)\rangle\)
- Integral bounds for \(n!\)
- Maximum-area triangle inscribed in an ellipse
- A summable sequence eventually dominating countably many summable sequences
- Punctured unit disk and annulus are not conformally equivalent — Problem 4B
- Polynomial growth forces a meromorphic function to be rational — Problem 5B
- Maximal positive-definite subspace for a quadratic form on \(\RR^4\)
- Low-rank approximation of the exponential kernel matrix
- Groups of exponent \(2\) are abelian; groups of odd prime exponent need not be
- Legendre’s formula and the base-\(p\) digit sum of \(n\)