Tentative Lecture Schedule

Tuesday

Thursday

Jan 11 Tuesday, January 11

Introduction

Jan 13 Thursday, January 13

Affine Varieties
§1.1, §1.2

Jan 18 Tuesday, January 18

Parametrization
§1.3

Jan 20 Thursday, January 20

Ideals
§1.4

Jan 25 Tuesday, January 25

Univariate Polynomials
§1.5

Assignment 1

Jan 27 Thursday, January 27

Univariate Polynomials
§1.5, §2.1

Feb 1 Tuesday, February 1

Monomial Orderings
§2.2

Feb 3 Thursday, February 3

Division Algorithm
§2.3

Assignment 2

Feb 8 Tuesday, February 8

Monomial Ideals
§2.4

Feb 10 Thursday, February 10

Midterm 1

Feb 15 Tuesday, February 15

Gröbner Bases
§2.5

Feb 17 Thursday, February 17

Buchberger’s Criterion
§2.6

Feb 22 Tuesday, February 22

Buchberger’s Algorithm
§2.7

Feb 24 Thursday, February 24

First Applications
§2.8

Assignment 3

Mar 1 Tuesday, March 1

Elimination Theory
§3.1

Mar 3 Thursday, March 3

Elimination Theory
§3.1

Mar 8 Tuesday, March 8

Spring Break

Mar 10 Thursday, March 10

Spring Break

Mar 15 Tuesday, March 15

Geometry of Elimination
§3.2

Mar 17 Thursday, March 17

Implicitization
§3.3

Assignment 4

Mar 22 Tuesday, March 22

Proofs and Singularities
§3.4, §3.5

Mar 24 Thursday, March 24

Midterm 2

Mar 29 Tuesday, March 29

Nullstellensatz
§4.1

Mar 31 Thursday, March 31

Radical Ideals
§4.2

Apr 5 Tuesday, April 5

Sums, Products, Intersections
§4.3

Apr 7 Thursday, April 7

Closures, Quotients, Saturations
§4.4

Assignment 5

Apr 12 Tuesday, April 12