Page 71 - CatalogNEP-PS

 better, and classify them as abelian, cyclic and permutation groups.
 Explain the significance of the notion of cosets, normal subgroups and homomorphisms.
 Understand the fundamental concepts of rings, subrings, fields, ideals, and factor rings.

THEORY (45 Hours)

UNIT-I: Introduction to Groups (12 Hours)
Modular arithmetic; Definition and examples of groups, Elementary properties of groups, Order
of a group and order of an element of a group; Subgroups and its examples, Subgroup tests;
Center of a group and centralizer of an element of a group.
UNIT-II: Cyclic Groups, Permutation Groups and Lagrange’s Theorem (18 Hours)
Cyclic groups and its properties, Generators of a cyclic group; Group of symmetries; Permutation
groups, Cyclic decomposition of permutations and its properties, Even and odd permutations and
the alternating group; Cosets and Lagrange‘s theorem; Definition and examples of normal
subgroups, Quotient groups; Group homomorphisms and properties.
UNIT-III: Rings, Integral Domains, and Fields (15 Hours)
Definition, examples and properties of rings, subrings, integral domains, fields, ideals and factor
rings; Characteristic of a ring; Ring homomorphisms and properties.

*TUTORIAL (15 Hours (1 Hour per week))

SUGGUESTED READINGS:

1. M.Artin,AbstractAlgebra,2ndEd.,Pearson,2011.
th
2. JosephAGallian,ContemporaryAbstractAlgebra,4 Ed.,Narosa,1999.
3. GeorgeEAndrews,NumberTheory,HindustanPublishingCorporation,1984.
4. I.N. Herstein: ―Topics in Algebra‖, Wiley Eastern Company, New Delhi, 1975.
nd
5. Hoffman and R. Kunze; Linear Algebra, 2 Edition, Prentice Hall of India, Delhi.
6. Vivek Shahi and Vikas Bisht: Algebra, Narosa Publishing House.
nd
7. P.B. Bhattacharya, S.K. Jain and S.R. Nagpaul; Basic Abstract Algebra (2 Edition)
8. Spectrum- Abstract Algebra, Sharma Publications, Jalandhar
9. A Text Book of Abstract Algebra, S. Dinesh & Co, Jalandhar

Maths.311 Elementary Linear Algebra 3+1*

LEARNING OBJECTIVES:

The objective of the course is:
 To introduce the concept of vectors in .
 Understanding the nature of solution of system of linear equations.
 To view the × matrices as a linear function from to and vice versa.
 To introduce the concepts of linear independence and dependence, rank and linear
transformations has been explained through matrices.

LEARNING OUTCOMES:

This course will enable the students to:
 Visualize the space in terms of vectors and the interrelation of vectors with
matrices.
 Familiarize with concepts of bases, dimension, and minimal spanning sets in vector
spaces.

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