MM302 : Abstract Algebra 1

Department

Department of Mathematics

Academic Program

Bachelor in mathematics

Type

Compulsory

Credits

Prerequisite

MM213 MM215

Overview

This course introduces students to the basic concepts of binary operations and their properties. It also deals with the group and the cosets to know their basic properties. This course aims to develop the student's ability to define Lagrange's theory and its applications, as well as to know the regular subgroup and its basic properties, the simple group, the quotient group, and homomorphisms in groups (examples and elementary properties), the reciprocal group and its elementary properties. The course focuses on the group properties, and applications, the subgroup, the symetric group, as well as their elementary properties.

Intended learning outcomes

By the end of the course, the student should be able to

1- Identify binary operations and their properties

2- Define the concept of groups and subgroups

3- Explain morphology and symmetry in groups

4- Explain some basic concepts and theorems in the symmetric group

5- Connects binary operations and their properties

6- Prove some theorems in groups and subgroups

7- Explain the morphology and symmetry of groups

8- Discuss and evaluate his knowledge of symmetric groups

9- Solve a number of exercises and problems with more than one idea about binary operations and their properties

10- He applies exercises and questions to groups and subgroups

11- It gives solutions to new, different, and multiple problems in morphology and symmetry in groups

12- Employ the properties of symmetric groups

Teaching and learning methods

. 1- Theoretical lectures

. 2- Discussion and dialogue

. 3- Brain storming

. 4- Using mathematical proof methods

. 5- Exercises and multi-idea problem-solving

Methods of assessments

. 1- A written exam (essay + objective) = 25 marks, or its assessment is left to the course instructor

2- Short tests (written or oral), demonstration tasks, applications, exercises, and presentation = 15 marks, or the assessment is left to the course instructor.

3- Written final exam (essay + objective) = 60 marks

Course Contents

tutorial	Lecture	credit	Subject	Week
1	2	3	Binary Operation and its properties – Group and its basic properties	1
1	2	3	Subgroup and The Cyclic Group and its properties	2
1	2	3	Symmetric Group and its basic properties	3
1	2	3	Cosets - Lagranges Theorem and its applications	4
			First midterm exam	5
1	3	4	Normal Subgroup and its basic properties	5-6
1	2	3	Simple Group – Quotient Group	7
1	3	4	Groups Homomorphism: Examples and basic properties	8-9
	2	2	The study of homomorphism on Subgroup and Normal Subgroup	9-10
			Second midterm exam	10
1	2	3	Kernal of homomorphism and its properties	11
1	2	3	First basic theorem of Isomorphism	12
1	2	3	Symmetry on groups	13
1	2	3	Symmetric group and its properties	14
			Final exam

References

References Title	Publisher	Version	Author
First Course in Abstract Algebra	Publications Management	1998	John B. Farleigh

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