14 problems.
- Schur decomposition theorem
- Vanishing Hermitian forms; normality via norms and inner products
- Pseudo-inverse gives the minimal \(2\)-norm least-squares solution
- External product of representations of a direct product of groups
- Induced trivial and Kronecker products of Specht modules in \(S_6\)
- Murnaghan–Nakayama values of \(A^{(4,1)}\) and restriction to \(S_3\times S_2\)
- Character table of the order-\(8\) group with \(a^4=1\), \(a^2=b^2\), \(b^{-1}ab=a^3\)
- Permutation representation from cosets; fixed-point character on \(S_n\)
- Character of the action on \(k\)-subsets; Frobenius image of \(\chi^{(2,4)}\)
- Frobenius reciprocity and transitivity of induced representations
- The prime ring of an integral domain is \(\mathbb{Z}\) or \(\mathbb{Z}_p\)
- Gröbner basis for the ideal cut out by \(x^2+2y^2=2\) and \(x^2-xy+y^2=1\)
- Radical identities for ideals and radical-membership computations
- Invariants of the order-four rotation; Molien series and Cohen–Macaulay generators