MA 561-001, Fall 2012


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 10:00-10:50am, CB 347

Topics: Here is an outline of what I hope to include this semester:

Group Theory:
  1. Preliminaries
  2. Introduction to groups
  3. Subgroups
  4. More examples of groups
  5. Homomorphisms and isomorphisms
  6. Cyclic groups
  7. Normal subgroups and quotient subgroups
  8. The isomorphism theorems
  9. Group actions
  10. Sylow's theorems
  11. Transpositions and the alternating group
  12. Composition series and simple groups
  13. Direct products and the fundamental theorem for finitely generated abelian groups
  14. The automorphism group and inner automorphisms
Ring Theory
  1. Basic notions of ring theory
  2. Ring homomorphisms and ideals
  3. Quotient rings
  4. Polynomial rings
  5. Characteristic of a ring and prime fields
  6. Quotient fields
Grades: The final grade will be computed as follows:
Homework 25%
1st Exam 25%
2nd Exam 25%
Final Exam 25%
The date of the final exam is 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.