Back To The Course Mod-01 Lec-01 What is Algebraic Geometry? Free Video Tutorials and Notes Lectures Mod-01 Lec-02 The Zariski Topology and Affine Space Free Video Tutorials and Notes Lectures Mod-01 Lec-03 Going back and forth between subsets and ideals Free Video Tutorials and Notes Lectures Mod-02 Lec-04 Irreducibility in the Zariski Topology Free Video Tutorials and Notes Lectures Mod-02 Lec-05 Irreducible Closed Subsets Correspond to Ideals Whose Radicals are Prime Free Video Tutorials and Notes Lectures Mod-03 Lec-06 Understanding the Zariski Topology on the Affine Line Free Video Tutorials and Notes Lectures Mod-04 Lec-08 Topological Dimension, Krull Dimension and Heights of Prime Ideals Free Video Tutorials and Notes Lectures Mod-04 Lec-09 The Ring of Polynomial Functions on an Affine Variety Free Video Tutorials and Notes Lectures Mod-04 Lec-10 Geometric Hypersurfaces are Precisely Algebraic Hypersurfaces Free Video Tutorials and Notes Lectures Mod-05 Lec-11 Why Should We Study Affine Coordinate Rings of Functions on Affine Varieties ? Free Video Tutorials and Notes Lectures Mod-03 Lec-07 The Noetherian Decomposition of Affine Algebraic Subsets Into Affine Varieties Free Video Tutorials and Notes Lectures Mod-05 Lec-12 Capturing an Affine Variety Topologically Free Video Tutorials and Notes Lectures Mod-06 Lec-13 Analyzing Open Sets and Basic Open Sets for the Zariski Topology Free Video Tutorials and Notes Lectures Mod-06 Lec-14 The Ring of Functions on a Basic Open Set in the Zariski Topology Free Video Tutorials and Notes Lectures Mod-07 Lec-15 Quasi-Compactness in the Zariski Topology Free Video Tutorials and Notes Lectures Mod-07 Lec-16 What is a Global Regular Function on a Quasi-Affine Variety? Free Video Tutorials and Notes Lectures Mod-08 Lec-17 Characterizing Affine Varieties Free Video Tutorials and Notes Lectures Mod-08 Lec-18 Translating Morphisms into Affines as k-Algebra maps Free Video Tutorials and Notes Lectures Mod-08 Lec-19 Morphisms into an Affine Correspond to k-Algebra Homomorphisms Free Video Tutorials and Notes Lectures Mod-08 Lec-20 The Coordinate Ring of an Affine Variety Free Video Tutorials and Notes Lectures Mod-08 Lec-21 Automorphisms of Affine Spaces and of Polynomial Rings - The Jacobian Conjecture Free Video Tutorials and Notes Lectures Mod-09 Lec-22 The Various Avatars of Projective n-space Free Video Tutorials and Notes Lectures Mod-09 Lec-23 Gluing (n+1) copies of Affine n-Space to Produce Projective n-space in Topology Free Video Tutorials and Notes Lectures Mod-10 Lec-24 Translating Projective Geometry into Graded Rings and Homogeneous Ideals Free Video Tutorials and Notes Lectures Mod-10 Lec-25 Expanding the Category of Varieties Free Video Tutorials and Notes Lectures Mathematics - Basic Algebraic Geometry : Varieties, Morphisms, Local Rings, Function Fields and Nonsingularity Free Video Tutorials and Notes LecturesMod-06 Lec-14 The Ring of Functions on a Basic Open Set in the Zariski Topology Free Video Tutorials and Notes Lectures