MA 661-001, Spring 2009


Professor: Alberto Corso
Department of Mathematics
University of Kentucky

Office: 701 Patterson Office Tower (701 POT)
Telephone: (859) 257-3167

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:
  1. General aspects of divisibility and PID's
  2. Unique factorization domains
  3. Euclidean domains
  4. Irreducibility of polynomials, including polynomials in several variables
Field Theory
  1. Algebraic field extensions
  2. The Kronecker construction and splitting fields
  3. Constructions with straightedge and compass
  4. Cyclotomic fields
  5. Separable field extensions
Galois Theory
  1. Galois extensions
  2. The fundamental theorem of Galois theory
  3. Finite fields
  4. Characterizations of Galois extensions
  5. Construction of the regular n-gon
  6. Solvability by radicals
  7. 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.