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Columbian College of Arts and Sciences

Mathematics (MATH)

MATH

6102

Algebra II

Algebra II

Fall 2015

3

Course Type

Lecture

Default Grading Method

Letter Grade

No

No

Corequisites

20

Frequency of Offering

Term(s) Offered

Are there Course Equivalents?

No

No

Fee Type

No

Continuation of MATH 6101. Theory of modules, including modules over a principal idea domain and tensor product of modules. Theory of fields, including finite fields and Galois theory.

Learning Outcomes:

As a result of successfully completing this course, students will be able to:

1. Recall all basic definitions, theorems, proofs and examples relating to the topics of groups, rings, fields, and modules;

2. Perform analyses of the logic and structure of various kinds of proofs in abstract algebra.

3. Synthesize material from different subfields of abstract algebra in order to construct conceptual frameworks of increasing abstraction;

4. Apply their knowledge of the facts of abstract algebra and their comprehension of the conceptual structure of that field in the creation of arguments and examples relating to facts and concepts of groups, rings, fields and modules with which they do not have prior experience.

As a result of successfully completing this course, students will be able to:

1. Recall all basic definitions, theorems, proofs and examples relating to the topics of groups, rings, fields, and modules;

2. Perform analyses of the logic and structure of various kinds of proofs in abstract algebra.

3. Synthesize material from different subfields of abstract algebra in order to construct conceptual frameworks of increasing abstraction;

4. Apply their knowledge of the facts of abstract algebra and their comprehension of the conceptual structure of that field in the creation of arguments and examples relating to facts and concepts of groups, rings, fields and modules with which they do not have prior experience.

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Course Attribute

Key: 5623