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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.