MA 561001, Fall 2012
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 10:0010:50am, CB 347
Topics: Here is an outline of what I hope to include this semester:
Group Theory:

Preliminaries

Introduction to groups

Subgroups

More examples of groups

Homomorphisms and isomorphisms

Cyclic groups

Normal subgroups and quotient subgroups

The isomorphism theorems

Group actions

Sylow's theorems

Transpositions and the alternating group

Composition series and simple groups

Direct products and the fundamental theorem for finitely
generated abelian groups

The automorphism group and inner automorphisms
Ring Theory

Basic notions of ring theory

Ring homomorphisms and ideals

Quotient rings

Polynomial rings

Characteristic of a ring and prime fields

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.