7 problems.
- Jordan form of \(\begin{pmatrix}4&1&-1\\-6&-1&2\\2&1&1\end{pmatrix}\), a conjugating matrix, and the minimal polynomial
- A normal subgroup of smallest prime order lies in the center
- Groups of order \(p^2\) are abelian; the Sylow theorems; groups of order \(4225=5^2 13^2\) are abelian, with their isomorphism classes
- Splitting field, Galois group, and correspondence for \(x^4+4x^2+64\) over \(\QQ\)
- Spring 2021
- The subring of \(\ZZ[x]\) of polynomials with even non-constant coefficients is not Noetherian
- \(x^p-a\) is irreducible in characteristic \(p\) if \(a\) is not a \(p\)th power