Commutative Algebra and Algebraic Geometry MATH 741 (3)
A study of ideals and varieties. Topics include affine varieties, ideals, the Hilbert basis theorem, resultants and elimination, Hilbert's Nullstellensatz, irreducible varieties and prime ideals, decomposition of varieties, polynomial mappings, quotient rings, projective space and projective varieties. Additional topics depending on the instructor. Groebner bases and automatic theorem proving in geometry, Bezout's theorem, dimension, and elliptic curves.