Algebra

Paper Code: 
CMAT 511
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to -

  1. Develop the ideas about group, field, ring and their homomorphism. 
  2. Understand the introduction to vector space.

Course Outcomes (COs):

 Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

CMAT 511

 

 

Algebra

(Theory)

 

 

 

 

 

 

The students will be able to –

 

CO75: describe group, subgroup, related properties and theorems.

CO76: differentiate between cyclic group, permutation group, quotient group and normal subgroup.

CO77: identify homomorphism and isomorphism of groups.

CO78: describe rings, sub-rings, related properties and theorems, Ideal and characteristic of a ring and their uses in the security system.

CO79: use the knowledge of field, sub-field, related properties and theorems in encryption and description.

CO80: describe vector spaces and their applications in real life problems.

 

 

Approach in teaching:

 

Interactive Lectures, Discussion, Power Point Presentations, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions, presentations, Giving tasks

 

 

Quiz, Poster Presentations,

Power Point Presentations, Individual and group projects,

Open Book Test, Semester End Examination

 

 

 

 

Unit I: 
I
9.00
Definition of a group with examples and related properties, Order of elements in a group and related theorems, Subgroup.
 
Unit II: 
II
9.00
Cyclic group, Permutation group, Cosets, Lagrange’s theorem, Normal subgroup, Quotient group.
 
Unit III: 
III
9.00
Homomorphism and Isomorphism of group, Fundamental theorem of homomorphism of group. Ring: Definition, examples and elementary properties, Subring.
 
Unit IV: 
IV
9.00
Integral domain, Field, Subfield and their related properties, Ideal of a ring, Characteristic of a ring.
 
Unit V: 
V
9.00
Vector space: Definition and examples, Subspace, Linear combination of vectors, Linear span, Linearly dependent and independent vectors and their properties, Bases and dimension(Definition and examples only).
 
Essential Readings: 
  • A.R.Vasishtha, J. N. Sharma and A.K. Vasishtha, Linear Algebra, Krishna Prakashan, 2010.
  • K. C. Sarangi, Elements of Abstract Algebra, RBD, Jaipur, 2009.
  • I.N. Herstein, Topics in Algebra, Wiley Eastern Ltd., New Delhi, 2008.
  • Joseph Gallian, Contemporary Abstract Algebra, Cengage Learning USA, 2013.
References: 
  • G. C. Sharma and Shivlal Agarwal, Modern Algebra,& Co. Agra, 1998.
  • Deepak Chatterjee, Abstract Algebra, PHI. Ltd. New Delhi, 2001.
  • P. B. Bhattacharya , S.K. Jain and S. R. Nagpaul, Basic Abstract Algebra, Cambridge University Press, 2001.
  • Thomas W.Judson and Robert A. Beezer, Abstract Algebra: Theory and Applications, 2015.
  • Robert M. Thrall and Leonard Tornheim, Vector Spaces and Matrices, Dover Publications Inc. New York, 2011.
 
Academic Year: 
2022-2023
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