Math 5031: Algebra I

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 basic ring theory, fields and Galois theory.
Math 5031-5032 form the basis for the Ph.D. qualifying exam in algebra.

Prerequisites: Math 430.

Text book: Algebra by Serge Lang, the 3rd revised edition.

Office hour: Tuesday 4:30-5:30, Wedensday 1-3pm, and by appointment

Homework: There will be weekly homework. The homework is due on Tuesdays (starting from Tuesday September 8th) 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 12 problem sets. The lowest two homework grade will be dropped and the remaining 10 will be counted towards your final course grade.

Grader: Your grader is Qingyun Wang.

Exams: There will be one in class midterm exam during the semester. There will also be a final exam.
The midterm is schedule for Tuesday October 20th. 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: Here is a list of texts you may find useful:
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 .

Problem Sets:
1. Problem Set 1 , Due September 8. Solutions
2. Problem Set 2 , Due September 15. Solutions
3. Problem Set 3 , Due September 22. Solutions
4. Problem Set 4 , Due September 29. Solutions
5. Problem Set 5 , Due October 6. Solutions
6. Problem Set 6 , Due October 22.
7. Problem Set 7 , Due November 3.
8. Problem Set 8 , Due November 10.
9. Problem Set 9 , Due November 17.
10. Problem set 10: will be due Tuesday December 1.
11. Problem set 11: will be due Tuesday December 8.