MATH 8000, Algebra I, Fall 2009
Dr. Mitchell Rothstein
Room 404, Boyd Graduate Studies Building
(706) 542-2567
rothstei@math.uga.edu
Office Hours: MWF
Noon-1PM
Text: Abstract Algebra,
3rd edition, Dummit and Foote
Course Description from the
bulletin: Groups and rings, including Sylow
theorems, classifying small groups, finitely generated abelian groups,
Jordan-Holder theorem, solvable groups, simplicity of the alternating
group, euclidean domains, principal ideal domains, unique factorization
domains, noetherian rings, Hilbert basis theorem, Zorn's lemma, and
existence of maximal ideals and vector space bases.
Prerequisite:
MATH 4010/6010 or permission of department
Topical Outline: groups, rings,
fields, modules and Galois theory
Course Objective: to provide
the foundation in algebra necessary to pursue a Ph.D. in
mathematics. The course is designed largely but not exclusively
as preparation for the Ph. D. algebra qualifying exam.
Grading: Homework will be assigned
and collected weekly, usually on Fridays.
Your grade will be determined on the following basis:
Homework 50%
Midterm exam 25%
Final exam 25%
Exam Dates:
Midterm exam: Friday, October 9
Final exam: Wednesday, December 16, 8am
Homework
Assignments
Notes
on Galois Theory
Newton's
Theorem on Symmetric Polynomials
Cyclotomic
Extensions
Academic Honesty: As a
University of Georgia student, you have agreed to abide by the
University’s academic honesty policy, “A Culture of Honesty,” and the
Student Honor Code. All academic work must meet the standards described
in “A Culture of Honesty” found at:
www.uga.edu/honesty. Lack of knowledge of the academic honesty
policy is not a reasonable explanation for a violation. Questions
related to course assignments and the academic honesty policy should be
directed to the instructor.
Disclaimer: The course syllabus is a general plan for the
course; deviations announced to the class by the instructor may be
necessary.