V63.0344-001: ALGEBRA
| Term: | Spring 2011 |
| Meeting times: | 11:00 a.m. -12:15 p.m. MW in WWH 201 |
| Recitation: |
8:00 - 9:15 a.m. M |
| Instructor: | Prof. Joel Spencer |
| Office: | 729 WWH |
| Office hours: | TBD and by appointment |
| Phone: | 212-998-3219 |
| Email: | spencer@cims.nyu.edu |
| Website: |
Algebra
II |
Prerequisites
Students who wish to enroll in Algebra II must meet the following prerequisites:
- Prerequisite: V63.0343 Algebra I with a grade of C or better.
Goals and Topics
A continuation of Algebra I but on a more conceptual level.
- Topics
include:
Rings, Fields. Finite Fields. Polynomials over Fields.
Extension Fields.
Elements of Galois Theory.
Course Details
Textbook and Materials
Herstein, Topics in Algebra (as used in Algebra I)Stewart, Galois Theory
Homework
Assigned weekly (during the Wednesday class) and collected at the beginning of next Monday class (5-6 problems / week)Exams
There will be a midterm exam date to be determined.
The final exam will be May 16, 10a.m. - 11:50 a.m.
Grading policy
The results of homework, quizzes, midterm, and final will be combined
Calendar
| Week | Topic |
|---|---|
| 1 | Fields (Chapter H5) |
| 2 | Finite Fields (Chapter H7) |
| 3 | Linear Algebra over Fields (Chapter H6) |
| 4 | Magic Squares (Chapter L) |
| 5 | Ruler-Compass (Chapter H5) |
| 6 | Field Extensions (Chapter H5-L) |
| 7 | More Field Extensions (Chapter H5-L) |
| 8 | |
| 9 | Galois Theory - start (Chapter S) |
| 10 | Galois Theory - more (Chapter S) |
| 11 | Galois Correspondence Theorem (Chapter S) |
| 12 | Galois Theory - Finite Fields (Chapter S) |
| 13 |
The Moment Problems (Chapter L) |
| 14 |
Potpourri-Review |