Aula #1 - Mod-01 Lec-01 What is Algebraic Geometry?
Aula #2 - Mod-01 Lec-02 The Zariski Topology and Affine Space
Aula #3 - Mod-01 Lec-03 Going back and forth between subsets and ideals
Aula #4 - Mod-02 Lec-04 Irreducibility in the Zariski Topology
Aula #5 - Mod-02 Lec-05 Irreducible Closed Subsets Correspond to Ideals Whose Radicals are Prime
Aula #6 - Mod-03 Lec-06 Understanding the Zariski Topology on the Affine Line
Aula #7 - Mod-03 Lec-07 The Noetherian Decomposition of Affine Algebraic Subsets Into Affine Varieties
Aula #8 - Mod-04 Lec-08 Topological Dimension, Krull Dimension and Heights of Prime Ideals
Aula #9 - Mod-04 Lec-09 The Ring of Polynomial Functions on an Affine Variety
Aula #10 - Mod-04 Lec-10 Geometric Hypersurfaces are Precisely Algebraic Hypersurfaces
Aula #11 - Mod-05 Lec-11 Why Should We Study Affine Coordinate Rings of Functions on Affine Varieties ?
Aula #12 - Mod-05 Lec-12 Capturing an Affine Variety Topologically
Aula #13 - Mod-06 Lec-13 Analyzing Open Sets and Basic Open Sets for the Zariski Topology
Aula #14 - Mod-06 Lec-14 The Ring of Functions on a Basic Open Set in the Zariski Topology
Aula #15 - Mod-07 Lec-15 Quasi-Compactness in the Zariski Topology
Aula #16 - Mod-07 Lec-16 What is a Global Regular Function on a Quasi-Affine Variety?
Aula #17 - Mod-08 Lec-17 Characterizing Affine Varieties
Aula #18 - Mod-08 Lec-18 Translating Morphisms into Affines as k-Algebra maps
Aula #19 - Mod-08 Lec-19 Morphisms into an Affine Correspond to k-Algebra Homomorphisms
Aula #20 - Mod-08 Lec-20 The Coordinate Ring of an Affine Variety
Aula #21 - Mod-08 Lec-21 Automorphisms of Affine Spaces and of Polynomial Rings - The Jacobian Conjecture
Aula #22 - Mod-09 Lec-22 The Various Avatars of Projective n-space
Aula #23 - Mod-09 Lec-23 Gluing (n+1) copies of Affine n-Space to Produce Projective n-space in Topology
Aula #24 - Mod-10 Lec-24 Translating Projective Geometry into Graded Rings and Homogeneous Ideals
Aula #25 - Mod-10 Lec-25 Expanding the Category of Varieties
Aula #26 - Mod-10 Lec-26 Translating Homogeneous Localisation into Geometry and Back
Aula #27 - Mod-10 Lec-27 Adding a Variable is Undone by Homogenous Localization
Aula #28 - Mod-11 Lec-28 Doing Calculus Without Limits in Geometry
Aula #29 - Mod-11 Lec-29 The Birth of Local Rings in Geometry and in Algebra
Aula #30 - Mod-11 Lec-30 The Formula for the Local Ring at a Point of a Projective Variety
Aula #31 - Mod-12 Lec 31 The Field of Rational Functions or Function Field of a Variety
Aula #32 - Mod-12 Lec 32 Fields of Rational Functions or Function Fields of Affine and Projective Varieties
Aula #33 - Mod-13 Lec 33 Global Regular Functions on Projective Varieties are Simply the Constants
Aula #34 - Mod-13 Lec 34 The d-Uple Embedding and the Non-Intrinsic Nature of the Homogeneous Coordinate Ring
Aula #35 - Mod-14 Lec 35 The Importance of Local Rings - A Morphism is an Isomorphism
Aula #36 - Mod-14 Lec 36 The Importance of Local Rings
Aula #37 - Mod-14 Lec 37 Geometric Meaning of Isomorphism of Local Rings
Aula #38 - Mod-14 Lec 38 Local Ring Isomorphism, Equals Function Field Isomorphism, Equals Birationality
Aula #39 - Mod-15 Lec 39 Why Local Rings Provide Calculus Without Limits for Algebraic Geometry Pun Intended!
Aula #40 - Mod-15 Lec 40 How Local Rings Detect Smoothness or Nonsingularity in Algebraic Geometry
Aula #41 - Mod-15 Lec 41 Any Variety is a Smooth Manifold with or without Non-Smooth Boundary
Aula #42 - Mod-15 Lec 42 Any Variety is a Smooth Hypersurface On an Open Dense Subset