Math 5031: Algebra I

FALL 2016

Time	Location	Instructor	email	Office
Tu-Th 1-2:30PM	Cupples I, Room 111	Roya Beheshti	beheshti@math.wustl.edu	Cupples I, Room 108B

Welcome to the webpage for Math 5031. This is an introductory graduate level course on the basic structures and methods of algebra.
Detailed survey of group theory, including the Sylow theorems and the structure of finitely generated abelian groups, followed by a study of rings, modules, fields, and Galois theory.
Math 5031-5032 form the basis for the Ph.D. qualifying exam in algebra.

Prerequisites: Math 430 or permission of instructor

Text book: Algebra by Serge Lang, revised third edition.

Office hour: Tuesday 2:30-3:30, Wednesday 4-5 or By appointment.

Grader: The grader for this course is Yiqian Fang (yiqianfang@wustl.edu).

Exams: There will be one in class midterm exam during the semester. There will also be a final exam. The midterm is tentatively schedule for Thursday October 27th. If you are unable to take the midterm exam for legitimate reasons, you will not be given a make up exam.

Grading Information: The midterm and the homework will each count for 30 percent of your grade. The final exam will count for 40 percent of your grade.

Additional References: Abstract Algebra (by David S. Dummit and Richard M. Foote)
An Introduction to the Theory of Groups (by Joseph J. Rotman)
Advanced Modern Algebra (by Joseph J. Rotman)
Abstract Algebra: The Basic Graduate Year (By Robert Ash). This text is posted for free download at Robert Ash's webpage .
Fields and Galois Thoery (by James Milne), available online at James Milne's webpage.


Homework: There will be weekly homework. The homework is due on Tuesdays (starting from September 13) at the beginning of class. Late homework will not be accepted.
You are encouraged to discuss the problems but the write-up must be your own.
I expect there will be 11 problem sets. The lowest homework grade will be dropped and the remaining 10 will be counted towards your final course grade.

1. Homework #1 , Due September 13, in class. Solutions
2. Homework #2 , Due September 20, in class. Solutions
3. Homework #3 , Due September 27, in class. Solutions
4. Homework #4 , Due October 6, in class. Here is a hint for Question 4. Solutions
5. Homework #5 , Due October 13, in class. Solutions
6. Homework #6 , Due October 20, in class. Solutions
7. Homework #7 , Due November 10, in class. Solutions
8. Homework #8 , Due November 17, in class. Here is a hint for Question 2. Solutions
9. Homework #9 , Due December 1, in class. Solutions
10. Homework #10 , Due December 8, in class. Solutions