UCSD Math 202 covers five subjects.
Matrix analysis – Hermitian, positive definite, unitary, and normal matrices, matrix factorizations, eigenvalue location, matrix norms.
Representation theory – character tables, induced representations, and representations of the symmetric group.
Symmetric functions – the monomial, elementary, complete homogeneous, power sum, and Schur bases, and the characteristic map.
Gröbner bases and varieties – Buchberger’s algorithm, elimination, the Nullstellensatz.
Invariant theory – the finiteness theorems of Noether and Hilbert, Molien’s formula, the Reynolds operator.
Past exams are listed in the Sources listing; each exam page lists its problems in exam order.