Winter 2010
· Instructor: Sergi Elizalde
· Lectures: MWF 10:00-11:05 in Kemeny 108
· X-hour: Th 12:00-12:50
· Office Hours: MF 11:05-12:00, M 1:35-2:30
· Office: Kemeny 332
· Email:
· Phone: 646-8191
Announcements
Here is the list of homework assignments.
The final exam will be handed out on Wednesday, March 3, and due on Monday, March 8.
Textbook
Abstract Algebra by Dummit and Foote, 3rd
edition. (Available at
Wheelock Books.)
Here is their errata page.
Topics
Here is a tentative syllabus for the course. For a more up-to-date list of covered material, check the homework page.
|
Lectures |
Sections
in Text |
Brief
Description |
|
Week 1 |
Chapters 7-9, 13.1 |
Review: rings, prime and maximal ideas, quotient rings. Prime
fields, finite extensions. |
|
Week 2 |
13.2 |
Algebraic extensions |
|
Week 3 |
13.3, 13.4 |
Compass and straightedge constructions, splitting fields,
algebraic closures |
|
Week 4 |
13.5, 13.6 |
Cyclotomic polynomials, separable and inseparable extensions |
|
Week 5 |
14.1 |
Fixed fields and automorphism groups |
|
Week 6 |
14.2 |
Fundamental Theorem of Galois Theory |
|
Week 7 |
14.2, 14.3 |
Finite fields |
|
Week 8 |
14.4, 14.5 |
Composite and simple extensions, cyclotomic and abelian
extensions |
|
Week 9 |
14.6, 14.7 |
Galois groups of polynomials |
Homework, exams, and grading
The course grade will be based on
The homework will consist of weekly problem sets,
which will be collected in class on their due date. No late homework will be
accepted.
You are encouraged to collaborate on the homework, but the solutions
must be written individually. You have to mention on your problem set the names
of the students that you worked with.
Write neatly, use full sentences, and justify all the steps. Give references
for theorems that you use from the text and from class.
All homework assignments will be posted here.
No collaboration is permitted on exams.
Students with disabilities: Students with disabilities enrolled in this course that may need disability-related classroom accommodations are encouraged to make an office appointment to see me before the end of the second week of the term. All discussions will remain confidential, although the Student Accessibility Services office may be consulted to discuss appropriate implementation of any accommodation requested.