9 problems.
- Character table of \(S_4\) via Murnaghan–Nakayama; restriction of \(A^{(2,2)}\)
- Character table of the nonabelian group of order \(21\)
- Inductions and Kronecker product of Specht modules of \(S_5\), \(S_7\), \(S_8\)
- Permutation representation from cosets; fixed-point character on \(S_n\)
- Irreducible representations of a direct product \(G\times H\)
- Ordered commutative ring is an integral domain; positive cone
- Gröbner basis for the ideal cut out by \(x^2+y=-2\) and \(2xy=y^2-2y\)
- Intersections of ideals: elimination, varieties, radicals, and a Gröbner computation
- Nullstellensatz: statement, radical membership, and radicals of principal ideals