The schedule for topics covered in lecture is as follows. Please do
the assigned reading prior to lecture. This will make the lectures
more effective for you.
January 26th UNIT 1. MODULES AND HOMOLOGICAL ALGEBRA
Appendix II: Category Theory
January 28th
Section 10.4 Tensor Products of Modules
February 2nd
Section 10.5 Exact Sequences — Projective, Injective and Flat Modules
February 4th
Section 17.1 Introduction to Homological Algebra — Ext and Tor
Problem Set 1
due in lecture.
April 6th UNIT 4. GALOIS THEORY. COMPUTATIONS AND APPLICATIONS
Section 14.4, Composite Fields
April 8th
Section 14.4 continued, Primitive Element Theorem, Separable and
Algebraic Closures.
April 13th
Section 13.6 Cyclotomic Polynomials and Extensions, and Section 14.5
Cyclotomic Extensions and Abelian Extensions over Q
April 15th
Section 14.6 Galois Groups of Polynomials, and
Section 13.1 Classical Straightedge and Compass Constructions
Problem Set 4
due in lecture.
Oral Presentation Topics
must be approved by this date.
April 20th
Section 14.7 Solvable and Radical Extensions: Insolvability of the
Quintic, and
Section 14.8 Compuation of Galois Groups over Q
April 27th UNIT 5. REPRESENTATIONS OF FINITE GROUPS
Section 18.1 Linear Actions and Modules over Group Rings and
Section 18.2 Wedderburn's Theorem and Some Consequences
April 29th
Section 18.3 Character Theory and the Orthogonality Relations
May 4th
Section 19.1 Characters of Groups of Small Order and
Section 19.2 Theorems of Burnside and Hall
May 6th
Section 19.3 Introduction to the Theory of Induced Characters
Problem Set 5
due in lecture.
Oral Presentations
should be delivered on or before this date.
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