Winter 2009
·
Instructor: Sergi Elizalde
·
Lectures: MWF 8:45-9:50 in Haldeman 028
·
(x-hour) Th
9:00-9:50
·
Office Hours: M 11:00-12:30, W 9:50-11:00 (and
by appt.)
·
Office:
Kemeny 332
·
Email:
·
Phone:
646-8191
Announcements
Here
is the latest homework assignment.
The
final exam will be distributed on Wednesday, March 4, and due on Monday, March
9.
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.