16 problems.
Algebra
- The group generated by x ↦ -x and x ↦ x+1 on R
- Normal Sylow subgroups and non-abelian group of order 105
- Conditions for a finite field to embed in another finite field
- Galois group of the splitting field of sqrt(2 + sqrt(2)) over Q
- F-isomorphic intermediate fields correspond to conjugate subgroups of the Galois group
- Classification of finitely generated modules over a local PID
- Factorization in Noetherian domains, integral closure of UFDs, and non-UFD examples
- Radical of the ideal (x^2 - y^3, x - y^2) in C[x,y]
Applied Algebra
- Schur Decomposition Theorem and characterization of normal matrices
- Discontinuity of Jordan form and Hermitian generation of real quadratic forms
- The Moore–Penrose pseudo-inverse gives the minimum-norm least-squares solution
- Schur function coefficient from trace of tensor power of a representation
- Determinant of the Jacobian of elementary symmetric functions
- Contragredient representation and character conjugation
- Gröbner basis computation and variety of an ideal generated by two polynomials
- Molien series, Hironaka decomposition, and presentation of invariant rings