Algebra I - Math 5031

Fall 2005

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

Subject: 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.

Grades: Grades will be based on (approximately) weekly homework assignments (approximately 9-10 assignments), and take-home mid-term and final exams. The exams due dates are: October 28 and December 19.

• Homeworks - 50%
• Mid-term - 20%
• Final - 30%

Texts: The main recommended text for the course is Lang's. However, all of what we will cover can be found in most other graduate level books in algebra. You should feel free to use your favorite. Here is a list of texts you may find useful.

• 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.