Covers the fundamentals of algebraic geometry, including algebraic numbers and irreducible polynomials.
Explores minimal annihilating polynomials and cyclic invariant subspaces, showcasing their practical applications through matrix computations.
Covers the dimension theory of rings, including additivity of dimension and height, Krull's Hauptidealsatz, and the height of general complete intersections.
Covers polynomial identity testing using oracles and random point evaluation, with applications in graph theory and algorithmic aspects.
