Math 649 SPRING 2007, List of lectures

  • On this page I will post content of all lectures with reference to the book. All handouts also will be posted here.
  • Monday, April 2: Jordan canonical form. Section 9.3. Here is homework!
  • Wednesday, April 4: Smith normal forms. Section 9.4.
  • Friday, April 6: More on Smith normal forms. Section 9.4.
  • Monday, April 9: Generalities on bilinear forms. Section 9.5.
  • Wednesday, April 11: Classification of alternating bilinear forms. Section 9.5.
  • Friday, April 13: Classification of symmetric bilinear forms: real numbers and finite fields. Section 9.5. New homework!
  • Monday, April 16: Orthogonal and symplectic groups. Graded algebras. Sections 9.5-9.6.
  • Wednesday, April 18: Hilbert series of graded algebras. Exterior algebra. Sections 9.6, 9.8.
  • Friday, April 20: Exterior algebras and determinants. Pfaffian. Section 9.9. New homework!
  • Monday, April 23: Hilbert basis theorem. Section 6.3.
  • Wednesday, April 25: Varieties and ideals; operations Var and Id. Section 6.5.
  • Friday, April 27: Radical of ideal and radical ideals. Weak Nullstellensatz. Section 6.5. New homework!
  • Monday, April 30: Hibert's Nullstellensatz. Section 6.5.
  • Wednesday, May 2: Decomposition into irreducible components. Prime decomposition. Section 6.5.
  • Friday, May 4: Primary decomposition. Varieties and finitely generated algebras with no nilpotents. Section 6.5. We will have MIDTERM on Thursday, May 10, 11am-1pm, Deady 210. New homework!
  • Monday, May 7: Groebner basis. Section 6.6.
  • Wednesday, May 9: Existence of Groebner basis; Buchberger algorithm. Section 6.6.
  • Thursday, May 10: We had Midterm today; here are the solutions.
  • Monday, May 14: Categories: definition, examples. Coproducts. Section 7.2. New homework!
  • Wednesday, May 16: Constructions in categories: coproducts, products, pullbacks, pushouts. Section 7.2.
  • Friday, May 18: Functors. Additive categories and additive functors. Section 7.3.
  • Monday, May 21: Exactness of functors. Projective/injective objects. Sections 7.3-7.4. New homework!
  • Wednesday, May 23: Natural transformations of functors. Equivalences of categories. Section 7.6.
  • Friday, May 25: Adjoint functors. Section 7.6.
  • Wednesday, May 30: Morita theory. Section 7.6. Last homework!
  • Friday, June 1: Grothendieck groups. Section 7.5.
  • Monday, June 4: More on Grothendieck groups. Section 7.5.
  • Wednesday, June 6: Nullstellensatz for countable fields. Section 11.2.
  • We will have FINAL EXAM on Thursday, June 14, 10-12am, Deady 104.
  • THE END.