MAT 544 — Fall 2016 Homepage
MAT 544 — Fall 2016 Problem Sets
MAT 544 Syllabus
Algebra III: Commutative Algebra, Homological Algebra, Representation Theory.
Fall 2016
The tentative schedule for topics covered in lecture is as follows.
Tuesday, August 30
Chapter 1 Atiyah-MacDonald. Rings and Ideals.
Thursday, September 1
Chapter 2 Atiyah-MacDonald. Module.
In-class Diagnostic Quiz.
Tuesday, September 6
LABOR DAY. NO CLASS.
Thursday, September 8
Chapters 3 and 4 Atiyah-MacDonald. Fractions and Primary Decomposition.
Problem Set 1
due in lecture.
Tuesday, September 13
Chapter 5 Atiyah-MacDonald. Integral Dependence and Valuations.
Thursday, September 15
Chapters 6 and 7 Atiyah-MacDonald. Chain Conditions and Noetherian Rings.
Problem Set 2
due in lecture.
Tuesday, September 20
Chapters 8 and 9 Atiyah-MacDonald. Artin Rings and Dedekind Domains.
Thursday, September 22
Chapter 10 Atiyah-MacDonald. Completions.
Problem Set 3
due in lecture.
Tuesday, September 27
Chapter 11 Atiyah-MacDonald. Dimension Theory.
Thursday, September 29
Chapter 1 Weibel. Chain Complexes.
Problem Set 4
due in lecture.
Tuesday, October 4
Chapter 2 Weibel. Derived Functors.
Thursday, October 6
Chapter 5 Weibel. Spectral Sequences.
Problem Set 5
due in lecture.
Tuesday, October 11
Chapter 5 Weibel. Spectral Sequences.
Thursday, October 13
Chapter 10 Weibel. The Derived Category.
Problem Set 6
due in lecture.
Tuesday, October 18
Chapter 10 Weibel. The Derived Category.
Thursday, October 20
Lectures 1 to 3 Fulton and Harris. Representations of Finite Groups.
Problem Set 7
due in lecture.
Tuesday, October 25
Lecture 4 Fulton and Harris. Representations of Symmetric Groups.
Thursday, October 27
Lectures 7 and 8 Fulton and Harris. Lie Groups and Lie Algebras.
Problem Set 8
due in lecture.
Tuesday, November 1
Lecture 9 Fulton and Harris. Initial Classification of Lie Algebras.
Thursday, November 3
Lectures 11 Fulton and Harris. Representations of sl2.
Problem Set 9
due in lecture.
Tuesday, November 8
Lectures 12 and 13 Fulton and Harris. Representations of sl3.
Thursday, November 10
Lecture 21 Fulton and Harris. Classification of Semisimple Lie Algebras.
Problem Set 10
due in lecture.
Tuesday, November 15
Lecture 22 Fulton and Harris. Exceptional Lie Algebras.
Thursday, November 17
Lectures 23 and 24 Fulton and Harris. The Weyl Character Formula.
Problem Set 11
due in lecture.
Tuesday, November 22
Lectures 14 and 15 Fulton and Harris. sl n.
Thursday, November 24
THANKSGIVING. NO CLASS.
Tuesday, November 29
Lectures 16 and 17 Fulton and Harris. sp 2n.
Thursday, December 1
Lectures 18 and 19 Fulton and Harris. so n.
Problem Set 12
due in lecture.
Tuesday, December 6
Local Cohomology
Thursday, December 8
Group Cohomology
Problem Set 13
due in lecture.
Back to my home page.
Jason Starr
4-108 Math Tower
Department of Mathematics
Stony Brook University
Stony Brook, NY 11794-3651
Phone: 631-632-8270
Fax: 631-632-7631
Jason Starr