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MTH 301 - Abstract Algebra


Course credit:  Three semester hours                   

 

Text:  

Hillman, A. and Alexanderson, G.  Abstract Algebra, 5th Edition; Waveland Press, Prospect Heights, Illinois; 1994 

 

Prerequisite: MTH 237, Linear Algebra

 

Course Description:                   290-3-3-.13  (1) (a) 1

 

This first course in abstract algebra covers concepts of algebraic theory, including sets, relations and functions, equivalence classes, inductive and deductive arguments, the structure of the integers, groups, and group homomorphisms.

 

 Behavioral Objectives:              290-3-3-.13  (1) (a) 1

 

The Abstract Algebra I course provides experiences in the study of abstract algebra through the utilization of class lectures, class activities, directed questions and responses, assigned problem sets, and regular in-class quizzes and tests. As a result of this course the student will gain an understanding of the course concepts, develop problem-solving skills directly related to the course content, and acquire techniques to establish the validity of mathematical statements.

 

 Course Evaluation:                    290-3-3-.13  (1) (a) 1

 

The grading components for this course consist of the following activities:

1. Quizzes                                            20% of Grade

2. Homework Assignments                    5% of Grade

3. Tests                                                50% of Grade

4. Final Exam (Comprehensive)            25% of Grade

 

Final grades are assigned by the percentage of the total points earned for the course.

 90 - 100% A        80 - 89% B          70 - 79% C       60 - 69% D       below 60% F

 

 

ABSTRACT ALGEBRA I

 Course Content:

 
Unit 1: Basic Properties of the Integers
 
1. Mathematical Induction

2. Multiples and Divisors, Primes in Z

3. The Division Algorithm

4. Common Divisors

5. Euclid's Algorithm

6. Common Multiples

7. Unique Factorization in Z

 

Unit 2: Groups
 
1. Permutations in a Finite Set

2. Multiplication of Permutations

3. Abstract Groups

4. Cycle Notation

5. Subgroups in a Group

6. Additive Notation, Modular Arithmetic

7. Cyclic Groups

8. Even and Odd Permutations

9. Groups of Symmetries

10. The Alternating Groups

11. Cosets of a Subgroup

12. Quotient Groups

 

Unit 3: Sets and Mappings
 
1. Mappings

2. Group Isomorphisms

3. Group Homomorphisms

4. Cayley's Theorem

5. Cartesian Products, Direct Products

 

 

 

 

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