MATH 423:424
ABSTRACT ALGEBRA I, II

Catalog Entry

MATH 423. Abstract Algebra I, II
Three hours lecture (3:3).

Prerequisites: MATH 300.

A study of the structure of algebraic systems with emphasis on groups, rings, integral domains and fields.

Detailed Description of Content of Course

The major topics covered in these two courses are those which represent the foundation of the field of modern algebra. It is, for most students, an introduction to the axiomatic method. Topics included in MATH 423 are:

a. Equivalence relations
b. Binary operations
c. Groups
d. Subgroups
e. Cyclic Groups
f. Rings
g. Integral domains
h. Polynomial rings
i. Fields
j. Finite Fields

The history of the main results covered in the course will also be discussed.

Topics included in MATH 424 are:

a. Cosets
b. Homomorphisms
c. Factor groups
d. Ideals
e. Quotient rings
f. Factorization of polynomials over a field
g. Extension fields
h. Vector spaces
i. Automorphisms of fields
j. Construction of finite fields
k. Galois Theory (Optional)

Detailed Description of Conduct of Course

Most instructors will present the course material in a lecture format. Students may be required to prepare and present problems for class discussion.

Goals and Objectives of the Course

In the twentieth century abstract algebra has become one of the three main divisions of mathematics.  This course offers an introduction to that area as well as an introduction to the axiomatic method so improtant to modern mathematics.

Assessment Measures

Graded instruments may include in-class tests, homework assignments, pop quizzes, presentation of problem assignments and class participation.

Other Course Information

This course may require library research in recent developments in the field. This course is intended for students who will teach or pursue graduate studies.

Review and Approval

DATE ACTION APPROVED BY
Sept. 2001 Review Stephen Corwin, Chair