### Discription

This course aims to provide a first approach to the subject of algebra, which is one of the basic pillars of modern mathematics.  Abstract algebra is a broad field of mathematics, concerned with algebraic structures such as groups, rings and fields.

### Learning Outcomes

After successful completion of the course, student is able to

1. demonstrate insight into abstract algebra with focus on axiomatic theories
2. apply algebraic ways of thinking
3. demonstrate knowledge and understanding of fundamental concepts including groups, subgroups, normal subgroups, homomorphisms and isomorphisms
4. demonstrate knowledge and understanding of rings, fields and their properties
5. understand and prove fundamental results and solve algebraic problems using appropriate techniques

### Contents

1. Cyclic groups.
2. Cosets decomposition of a group.
3. Lagrange’s theorem and its consequences.
4. Conjugacy classes.
5. Centralizers and Normalizers.
6. Normal Subgroups.
7. Homomorphism of groups.
8. Cayley’s theorem.
9. Quotient groups.
10. Fundamental theorem of homomorphism.
11. Isomorphism theorems.
12. Endomorphism and automorphisms of groups.
13. Commutator subgroups.
14. Permutation groups.
15. p-Subgroups.
16. Sylow’s theorems.
17. Definition and examples of rings.
18. Special classes of rings.
19. Fields.
20. Ideals.
21. Ring homomorphism.

### Recommended Books

1. Gallian, J. A. (2017). Contemporary abstract algebra (9th ed.). New York: Brooks/Cole.
2. Malik, D. S., Mordeson, J. N., & Sen, M. K. (1997). Fundamentals of abstract algebra. New York: WCB/McGraw-Hill.

### Suggested Books

1. Roman, S. (2012). Fundamentals of group theory (1st ed.). Basel: Birkhäuser.
2. Rose, H. E. (2006). A course on finite groups (1st ed.). London: Springer-Verlag.
3. Fraleigh, J. B. (2003). A first course in abstract algebra (7th ed.). Boston: Addison-Wesley Publishing Company.

### 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 Meetings

Tuesday                                                   11:00 AM -12:30 AM

Wednesday                                              09:30 AM -11:00 AM

Commencement of Classes                                                   October 26, 2020

Mid Term Examination                                                           December 28, 2020 to January 01, 2021

Final Term Examination                                                         March 01, 2021 to March 05, 2021

Declaration of Result                                                             March 12, 2021