COURSE SUMMARY
Course Title:
Modern Algebra
Course Code:
18MAT222
Year Taught:
2018
2019
Semester:
4
Degree:
Integrated Degree
School:
School of Arts and Sciences
Campus:
Mysuru

'Modern Algebra' is a course offered at the School of Arts and Sciences, Amrita Vishwa Vidyapeetham, Mysuru campus.

#### Scope and Objectives

To enable students to understand fundamental concepts of algebra and apply results from elementary group theory to solve contemporary problems.

#### Syllabus

Unit I:

Introduction to Groups. Symmetries of a Square.The Dihedral Groups.Definition and Examples of Groups.Elementary Properties of Groups Finite Groups; Subgroups, Terminology and Notation. Subgroup Tests, Examples of Subgroups.
Chapters 2 and 3.

Unit II:

Cyclic Groups, Properties of Cyclic Groups. Classification of Subgroups of Cyclic Groups, Permutation Groups, Properties of Permutations, Isomorphisms, Definition and Examples. Cayley's Theorem, Properties of Isomorphisms.
Chapters 4-7.

Unit III:

Automorphisms, Cosets and Lagrange''s Theorem, Application of Cosets to Permutation Groups.Normal Subgroups, Factor Groups, Applications of Factor Groups. Group Homomorphisms, Definition and Examples,Properties of Homomorphisms, The First Isomorphism Theorem.
Chapters 11-13

Unit IV:

Rings-Motivation and Definition, Examples of Rings.Properties of Rings.Subrings.Integral Domains.
Chapters 23-24

Unit V:

Quotient Rings and Ideals. Homomorphism of rings and rings of polynomials.
Chapters 28-30.

#### Textbook

1. A First course in abstract algebra, Johan B. Fraleigh, third edition, Narosa, 2000.

#### References

1. Garrett Birkoff and Saunders Mac Lane, ‘A Survey of Modern Algebra’, Universities Press, 2003.
2. I. N. Herstein, ‘Topics in Algebra’, Second Edition, John Wiley and Sons, 2000.
3. M.Artin, ‘Algebra’, Prentice Hall inc., 1994..