This page is a very brief outline of the material we expect to cover the first semester.

  • Definition of a ring and examples
  • Homomorphisms and subrings
  • Ideals and quotient rings
  • Algebras and polynomials
  • Noetherian rings
  • Algebraic subsets
  • Statement of Hilbert’s Nullstellensatz
  • Affine varieties
  • Regular maps
  • Localization