ABSTRACT ALGEBRA I

MA 370

Catalogue Description

This is the first course in abstract algebra. Topics include study of groups, permutations, cyclic groups, subgroups, isomorphism, cosets, rings, fields, and integral domains. 3 credits Prerequisites: MATH 295 Survey of Modern Math and MATH 191 Calculus II 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 structures 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

A. Fundamentals

1. Mathematical Induction

2. Euclid's Algorithm

3. Unique Factorization

B. Groups

1. Definition and Examples

2. Permutations

3. Subgroups

4. Cyclic Groups

5. Quotient Groups

6. Isomorphisms

7. Homomorphisms

8. Cayley's Theorem

C. Rings

1. Definition and Examples

2. Elementary Properties

3. Ideals

4. Ring Homomorphisms

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.