Introduction

This course introduces concepts of ring and group theory. The main objective of this course is to prepare students for courses that require a good background in Group Theory, Rings, Galois Theory, Symmetric group and permutation group, etc.

Prerequisite

Modern Algebra-I

Learning Outcomes

After completing this course, the student will be able to:

1. Define and state some of the main concepts and theorems of Function Analysis
2. Apply their knowledge of the subject in the investigation of examples
3. Prove basic proportions concerning functional analysis.

Course Contents:

1. Finite and finitely generated Abelian groups
2. Definition and examples of solvable and nilpotent groups
3. Fields, finite fields
4. Field extension
5. Galois theory
6. Galois theory of equations
7. Construction with straight-edge and compass
8. Splitting field of polynomials
9. The Galois groups, some results on finite groups
10. The symmetric group as Galois group
11. Construct able regular n-gones
12. The Galois group as a permutation group.

Recommended Books

1. Nicholson. Intermediate Microeconomics. Ist ed. ( NY: TheDrydon Press, 1994).
2. Ames, D.B. Introduction to Abstract Algebra. 1sted.( Pennsylvania :
   International textbook co, 1968).

.

Suggested Books

1. Northcott D.D. The first course of Homological Algebra. 1st ed. ( Cambridge
   University Press, 1973).
2. Jacobson N. Basic Algebra I. 1st ed. ( NY: Freeman and Co, 1985).

RESEARCH PROJECT /PRACTICALS/LABS/ASSIGNMENTS

The projects assigned in this course follow as assignments the exercises related to the topics from the suggested book. Moreover, students have to apply the theorems learned to some important groups/rings/fields.

ASSESSMENT CRITERIA

Sessional: 20 (Presentation / Assignment 10, Attendance 05, Quiz 05)

Mid-Term Exam:   30

Final-Term Exam: 50

Key Dates and Time of Class Meeting

Monday                                                                                     12:30 pm-14:00 pm

Tuesday                                                                                     12:30 pm-14:00 pm

Commencement of Classes                                                   January 13, 2020

Mid Term Examination                                                            March 09-13, 2020

Final Term Examination                                                          May 04-08, 2020

Declaration of Result                                                              May 19, 2020