MA 526 -- Fall 2014 -- Schedule

Date Section Topic File/Link
8/21 H: Ch 1, 3.1 Introduction, Ideals and Affine varieties  
8/26 H: 2.1, 2.2, 2.3 Monomial Orders, Division Procedure, Gröbner bases, Normal Forms  
8/28 H: 2.1, 2.2, 2.3 Monomial Orders, Division Procedure, Gröbner bases, Normal Forms hw1.tex hw1.pdf   Due: 9/4
9/2 H: 2.4 Noetherian Rings, Existence of Gröbner bases Macaulay 2     Singular     macaulay2.m2     Singcomp MathematicaComp.nb
9/4 H: 2.5 Buchberger's criterion, Symbolic computation software hw2.tex hw2.pdf   Due: 9/11
9/9 H: 3.1, 3.2 Ideals and varieties, the Zariski topology  
9/11 H: 3.3 Morphisms and coordinate rings hw3.tex hw3.pdf   Due: 9/18
9/16 H: 3.4, 3.5, 3.6 Rational Maps, Rational and unirational varieties  
9/18 H: 3.4, 3.5, 3.6 Rational Maps, Rational and unirational varieties hw4.tex hw4.pdf   Due: 9/25
9/23 H: 4.1, 4.2 Quiz, Elimination Theory  
9/25 H: 4.2, 4.3 Images of rational maps, Some Favorite Examples hw5.tex hw5.pdf   Due: 10/2
9/30 H: 7.1, 7.2, 7.5 Nullstellensatz  
10/2 H: 6.1, 6.2 Irreducible Varieties hw6.tex hw6.pdf   Due: 10/16
10/7   Midterm  
10/9   No Class: Fall Break  
10/14   Irreducible Varieties  
10/16 H: Ch 8 Primary Decomposition hw7.tex hw7.pdf   Due: 10/23
10/21 H: 7.3, 7.7 Dimension  
10/23 H: 9.1, 9.2 Projective space, homogeneous polynomials hw8.tex hw8.pdf   Due: 10/30
10/28 H: 9.3, 9.4, 9.5 Projective varieties, Projective Nullstellensatz  
10/30 H: 9.6, 9.7 Morphisms, rational maps hw9.tex hw9.pdf   Due: 11/6
11/4 H: 11.1, 11.2 Products, dual projective space  
11/6 H: 11.3, 11.4 The grassmannian, flag varieties hw10.tex hw10.pdf   Due: 11/13
11/11 H: 11.5 Equations for grassmannians  
11/13 H: 12.1, 12.2 Hilbert functions, series, polynomials  
11/18   Quiz, Graded modules and exact sequences  
11/20 12.3 Multiplicities of points  
11/25 12.4 Complete intersections and Bezout's theorem  
11/27   No Class: Thanksgiving  
12/2   The Hilbert scheme  
12/3   Take Home Final Due (5 PM) final.tex final.pdf