10 problems.
- Uniform limits of Riemann integrable functions are Riemann integrable — Problem 1
- Radius of convergence of a power series — Problem 2
- Continuous differentiability of \(\sum\frac{\sin nx}{n^{5/2}}\) — Problem 3
- Implicit function theorem for \(x^2y^3+x^3z+2yz^4=4\) at \((1,1,1)\) — Problem 4
- Uniform continuity of \(x^\alpha\) on \([0,\infty)\) — Problem 5
- Compactness of a set of Lipschitz functions with unit \(L^2\) norm in \(C[0,1]\) — Problem 6
- Non-diagonalizable \(3\times3\) upper triangular matrix with a repeated eigenvalue — Problem 7
- Orthogonal maps of \(\mathbb R^{2n+1}\) have an eigenvalue \(\pm1\) — Problem 8
- Spectral theorem for real symmetric matrices — Problem 9
- Commuting complex matrices have a common eigenvector — Problem 10