ABSTRACT ALGEBRA II

MA 371

Catalogue Description

Abstract Algebra II is a study of groups, rings, ideals, lattices, solvable groups, can roots of polynomial equations. It is a continuation of MATH 370. 3 credits Prerequisite: MATH 370 Abstract Algebra I or equivalent

Goals

A. To develop an understanding of algebraic structure.

B. To enhance the ability of the student to construct and to appreciate proofs.

C. To relate algebraic theory to other branches of mathematics.

Procedures

A. Lecture/Discussion

B. Problem Solving/Group Problem Solving

C. Computer software supplements in Math Resource Center

Course Content

1. Review of Groups

2. The Sylow Theorems

3. The Class Equation

4. Review of Rings

5. The Euler and Fermat Theorems

6. Integral Domains

7. Fields

8. Matrix Rings and Fields

9. The Structure of Z, Q, R, and C

10. Polynomial Rings

11. Field Extensions

12. Introduction to Galois Theory

Evaluation methods at the discretion of the Instructor

Bibliography

Required Text: Hillman and Alexanderson, Abstract Algebra, 5th Ed., PWS-Kent Publishing Co., Boston, Ma. 1994.

Software

Geissinger, Ladnor, Exploring Small Groups, A Tool for Learning Abstract Algebra, Harcourt, Brace, Janovich Publishing Co., New York, 1989.