MA 661001, Spring 2009
Professor: Alberto Corso
Department of Mathematics
University of Kentucky
Office: 701 Patterson Office Tower (701 POT)
Telephone: (859) 2573167
Email: corso@ms.uky.edu
URL: www.ms.uky.edu/~corso
Office Hours:
stop by my office whenever you see me.
Lecture: MWF 9:00  9:50 am CB 338
Topics: Here is an outline of what I hope to include this semester:
Ring Theory:

General aspects of divisibility and PID's

Unique factorization domains

Euclidean domains

Irreducibility of polynomials, including polynomials in several variables
Field Theory

Algebraic field extensions

The Kronecker construction and splitting fields

Constructions with straightedge and compass

Cyclotomic fields

Separable field extensions
Galois Theory

Galois extensions

The fundamental theorem of Galois theory

Finite fields

Characterizations of Galois extensions

Construction of the regular ngon

Solvability by radicals

Galois group of polynomials
Grades:
The final grade will be computed as follows:
Homework 33.3%
Midterm Exam 33.3%
Final Exam 33.3%
The dates of the exams are TBA.
Homework: I will assign homework regularly throughout the semester.
I strongly encourage students to discuss material together, but the
homework assignments that are turned in have to be individual efforts.
Discussing problems with other students is useful, but it is in your best
interest to not copy other students' answers. You must develop your own
ability to solve problems and to write them up clearly and correctly.
Text:
Abstract Algebra (3rd edition) by D.S. Dummit and R.M. Foote.
Reference:
I suggest that you learn to use the Mathematics Library by consulting other
books on Abstract Algebra. There are many choices. If you find a particularly
good reference, tell others in the class about it. I can also suggest
some references.