(505)
277-2214
Text : Abstract Algebra 3rd Edition by Dummit and Foote
Course Requirements:1) Homework
(200 points): Homework will be assigned weekly on Wednesdays
and will
be collected the following Thursday by 8 am under my office
door.
Homework
will not be graded unless it is written in order
and labeled
appropriately. The definitions and theorems
in the
text and
given in class are your tools for the homework proofs. If
the theorem has a name, use it. Otherwise, I
would prefer that you fully
describe the theorem in words, than state by Theorem
3. Each week around 4 or 5 of the assigned problems will be
graded. The
weekly assignments will each be worth 20 points. I will
drop your lowest two homework scores
and the remaining homework will be averaged to get a score out of 200.
2) Exams
(400
points): I will give two midterms (100 points each) and a final
(200
points). There are no make up exams. If a test is
missed,
notify me as soon as possible on the day of the
exam.
For the midterms only, if you have a legitimate and documented
excuse, your grade will be recalculated without that test using the
percentage that you receive on the final exam. The
Midterms
are tentatively scheduled for Monday February 24 and Monday, April 13.
The Final is on Friday, May 15, from 12:30-2:30 pm.
| Date | Section | Topic | Homework |
| 1/22 | 10.1-10.3 | Modules, Module homomorphisms and Free Modules | 10.1 5, 7, 13 10.2 1, 4, 6, 7 10.3 7 Due January 30. |
| 1/24 | 10.4 | Tensor Products | |
| 1/27 | 10.4 | More on Tensor Products | |
| 1/29 | 10.5 | Exact Sequences | |
| 1/31 | 10.5 | Projective Modules | 10.4 3, 4, 6, 16 Due February 7 by the end of the day. |
| 2/3 | 10.5 | Injective Modules | |
| 2/5 | 10.5 | Flat Modules | 10.5 2, 3, 6, 7, 28 Due February 13. |
| 2/7 | 11.3 | Dual Vector Spaces | |
| 2/10 | 11.5 | Tensor Algebras | 10.5 5, 20, 21, 25 11.3 3, 4 11.5 1, 13 Due February 20 |
| 2/12 | 11.5 | The Symmetric Algebra of a module | |
| 2/14 | 11.5 | The Exterior Algebra of a module | |
| 2/17 | 12.1 | The fundamental theorem of finitely generated modules over PIDs | |
| 2/19 | 12.1 | Finite F[x]-modules | 11.5 12, 14 12.1 5, 8, 13, 14, 15 Due February 28 by the end of the day. |
| 2/21 | Review | ||
| 2/24 | Midterm 1 | ||
| 2/26 | 12.2 | Rational Canonical Form | 12.2 4, 8, 10, 11, 12 Due March 5 |
| 2/28 | 12.2 | Rational Canonical Form continued | |
| 3/2 | 12.3 | Jordan Canonical Form | |
| 3/4 | 12.3 | Jordan Canonical Form continued | 12.2 9 (1st 2 matrices) 12.3 1, 2, 5, 10, 18, 24 Due March 12 |
| 3/6 | 13.1 | Field Extensions | Class Notes typed by Galen |
| 3/9 | 13.2 | Algebraic Extensions | |
| 3/11 | 13.2 | Algebraic Extensions continued | 13.1 2, 6, 7 13.2 4, 7, 9, 14 Due March 26 |
| 3/13 | 13.4 | Splitting Fields | Class Notes typed by Galen |
| 3/23 | 13.4 | The algebraic closure of a field | |
| 3/25 | 13.5 | Separable Extensions | |
| 3/27 | 13.5 | Inseparable Extensions | |
| 3/30 | 13.6 | Cyclotomic Extensions | |
| 4/1 | 14.1 | Automorphisms fixing a field and the fixed field of an automorphism | |
| 4/3 | 14.2 | Fundamental Theorem of Galois Theory | |
| 4/6 | 14.2 | Fundamental Theorem of Galois Theory Continued | |
| 4/8 | 14.3 | Finite Fields | |
| 4/10 |
Review |
||
| 4/13 |
Midterm 2 |
||
| 4/15 |
14.4 |
Composite Extensions |
|
| 4/17 |
14.4 |
Simple Extensions |
|
| 4/20 |
14.5 |
Abelian Extensions |
|
| 4/22 |
14.6 |
Galois Groups of Polynomials |
|
| 4/24 |
14.6 |
Galois Groups of Polynomials continued |
|
| 4/27 |
14.7 |
Solvable and Radical Extensions; Insolvability of the quintic |
|
| 4/29 |
14.8 |
Galois groups over the rationals |
|
| 5/1 |
14.9 |
Transcendental Extensions |
|
| 5/4 |
Review |
||
| 5/6 |
Review |
||
| 5/8 |
Review |
||
| 5/15 |
Final Exam 12:30-2:30 pm |