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