Algebra II - Math 5032

Spring 2006

Note: You can also see me outside the set office hours, if I'm in.

Subject: This is the second part of an introductory graduate level course on the basic structures and methods of algebra. We plan to cover the following topics:

• Modules
• Noncommutative algebras
• Representations of finite groups
• Valuations and p-adic numbers
• Homological algebra (if time permits.)

Grades: Grades will be based on (approximately) weekly homework assignments (approximately 9-10 assignments), a take-home mid-term and an in-class final (qualifying) exam. The due date for the mid-term exam is Friday, March 24 and the date final/qualifying exam is Friday, May 5, at 1:00 PM.

• Homeworks and mid-term - 70% (The mid-term is essentially another homework assignment, but I will try to write it in the style and level of difficulty of the final exam.)
• Final - 30%

The final exam is the same as the qualifying exam. It is three-hour long and covers the material of the whole year. If you are not enrolled in the graduate program, you have the option of taking only a final. This would be a two-hour exam about topics covered during this semester. Let me know in advance if you wish to take only the two-hour final.

Texts: Any of the following texts should serve for the course. Feel free to use your favorite.

• Algebra by Serge Lang, Springer-Verlag, 3rd edition, 2002.
• Algebra by Thomas Hungerford, Springer-Verlag, 1984.
• Algebra by Michael Artin, Prentice-Hall, 1991. (In theory, this is an undergraduate text, but it is quite nice.)
• Advanced Modern Algebra by Joseph J. Rotman, Prentice-Hall, 2002.
• Algebra by Larry C. Grove, Dover, 1983. (A nice text and inexpensive edition.)
• Abstract Algebra: The Basic Graduate Year by Robert Ash. This text is posted for free download (pdf file) at professor Ash's webpage.

Assignments will be posted below.