- 0 student
- 2 lessons
- 0 quizzes
- 10 week duration
PROGRAMME :BSc MATHEMATICS
COURSE: ABSTRACT ALGEBRA
INTRODUCTION: In Algebra, a broad division of Mathematics, Abstract Algebra is the study of Algebraic Structures which includes Groups, Rings, Fields,Vector Spaces etc. This is one of the basic pillars of Modern Mathematics and is also referred to as Modern Algebra. Because of its generality, abstract algebra is used in many fields of science.
OBJECTIVE OF THIS COURSE : This course is intended to provide a first approach to the subject of algebra by studying some basic algebraic structures , mapping between them and their substructures. It also envisages to develop basic skill and proficiency in the concepts and methods of abstract algebra.
EXPECTED LEARNING OUTCOME:
The students who succeeded in this course
- will be able to define algebraic structures
- will be able to construct substructures.
- will be able to analyze a given structure in detail.
- will be able to develop new structures based on given structures.
- will be able to compare structures.
- Will be able to demonstrate examples of structures
- Will be able to understand the concept of isomorphism
Text book :John B. Fraleigh : A First Course in Abstract Algebra ( 7th Edition) (Pearson)
- I.N. Herstein – Topics in Algebra
- Joseph A Gallian – Contemporary Abstract Algebra, Narosa Pub. House .
- Artin – Algebra , PHI
Module I-Groups and Subgroups
Binary operations, Isomorphic binary structures, Groups-definition and examples, elementary properties of groups, finite groups and group tables, subgroups, cyclic subgroups, cyclic groups, elementary properties of cyclic groups.
Module II- Permutations, Cosets, and Direct products
groups of permutations, Cayley’s theorem, orbits, cycles and the alternating groups, cosets and the theorem of Lagrange, direct products
Module III-Homomorphisms and Factor groups
Homomorphisms, properties of homomorphisms, factor groups, The Fundamental Homomorphism theorem, normal subgroups and inner automorphisms, simple groups.
Module IV-Rings and fields
Definitions and basic properties, homomorphisms and isomorphisms, Integral domains- divisors of zero and cancellation, integral domains, the characteristic of a ring. Ideals and factor rings. Homomorphisms and factor rings
0.00 average based on 0 ratings