Fall 2008
· Instructor: Sergi Elizalde
·
Lectures: MWF 10:00-11:05 in Kemeny 201
·
(x-hour) Th
12:00-12:50
·
Office Hours: M 1:40-3:30, F 11:10-12:00
(and by appt.)
·
Office:
Kemeny 332
·
Email:
·
Phone:
646-8191
Announcements
Here
is the current homework assignment.
The
midterm exam will be handed out on Friday, Oct. 31, and due on Wednesday, Nov.
5.
The
final exam will be handed out on Monday, Nov 24, and due on Wednesday, Dec. 3.
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.
|
Lectures |
Sections in Text |
Brief Description |
|
Week 1 |
Chapter 0, 1.1-1.6, 2.1, 2.2, 2.3, 2.4 |
Groups, examples, homomorphisms,
subgroups, cyclic groups |
|
Week 2 |
Chapter 3.1, 3.2, 3.3 |
Cosets, Lagrange’s theorem, isomorphism
theorems, solvable groups |
|
Week 3 |
Chapter 3.4, 4.1, 4.2 |
Composition series, Jordan-Hölder
theorem, Group actions, permutation representations, Cayley’s theorem |
|
Week 4 |
Chapter 4.3, 4.5, 4.6, 5.1 |
Class equation, conjugacy classes in
S_n, Sylow theorems, Direct Products |
|
Week 5 |
Chapter 5.2, 5.4, 5.5 |
Semidirect Products, finitely-generated abelian
groups |
|
Week 6 |
Appendix II, Chapter 6.3, 7.1, 7.2, 7.3 |
Basic category theory (products,
coproducts, functors), free groups, introduction to rings, examples |
|
Week 7 |
7.4, 7.5, 7.6, 15.4 |
Prime and maximal ideals, localization, Chinese
Remainder Theorem |
|
Week 8 |
8.1, 8.2, 8.3, 9.1, 9.2 |
Euclidean Domains, PIDs, irreducibles
and primes in rings, UFDs, polynomial rings |
|
Week 9 |
9.3, 9.4, 9.6, 10.1 |
Polynomial rings, irreducibility criteria,
Noetherian rings, Hilbert’s Basis Theorem, group rings, modules |
Homework,
exams, and grading
The course grade will be
based on
The homework will consist of a weekly
problem set, plus studying some sections of the book. 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.
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.
Last
modified on Nov 21, 2008.