MATH 620 Fall 2012 Section 1

The documents contained herein are all pdf files and require Adobe Acrobat (or something similar) to view them. Go back to the math department's course information page here for more information on how to obtain (for free!) Adobe Acrobat.

Basic Information

Note about Email

Barring some sort of catastrophy, I read my email several times a day. Thus, this is an excellent way to communicate with me outside of the classroom. Please note, however, that I use text-only mail readers, so sending me email encoded in HTML is inconvenient for me to read and sending me stuff like Word documents as attachments is futile. Most email programs will prompt you whether to send mail in HTML or not. If you don't understand this stuff, don't worry about it.

Text and Syllabus

The textbook for the course is Algebra by Hungerford (Springer GTM 73). We will be covering material for the comprehensive exam in algebra: group theory through the Sylow theorems, some ring theory, and field theory through Galois theory. The prerequisite for this course is MATH 420/520.

Course Objectives

The student is expected to acquire a thorough understanding of the basic theory of groups, rings and fields at the graduate level. In addition, the student will hone his or her skills at constructing and writing mathematical proofs and presenting mathematics orally.

Grading Scale

Grades will be based on homework, a midterm exam and the final exam. The weights for these are 40%, 20% and 40%, respectively.


Homework will be collected once a week on Mondays. It will be turned in at the beginning of class. You are free to work with other students on the homework; in fact, this is encouraged. Sloppy and/or illegible work will be returned back with no credit! Your homework is something of which you should be proud (notice how I didn't end with a preposition there). Expect to spend lots of time on it. The specific assignment for each week will be available on this webpage. Class time will also be set aside each Friday to discuss/present homework and other assigned presentations.


The midterm exam will be during class on Friday, October 19. The final exam is from 10 to 11:50 a.m. on Wednesday, December 12. The final exam will be comprehensive.

Homework Assignments/Weekly Syllabus


If you go to one of my old 420 webpages, you'll find lots of goodies on polynomial rings which you may find useful. (Go down to "Daily Log" and the handouts from August 24 through September 2.) Also, I've prepared some notes on fields and Galois theory and subnormal series and Abel's theorem. Finally, as a nice application of some of the big results this semester, here is a proof that the complex numbers are an algebraically closed field.

Homer does math!

Yes indeed, there's plenty of math humor to be found in the Simpsons. Just look and see!

Last update: December 10, 2012