Algebra

Paper Code: 
MAT501
Credits: 
3
Contact Hours: 
45.00
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

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

MAT 501

 

 

 

 

 

 

Algebra

(Theory)

 

 

 

 

 

 

The students will be able to –

 

CO60: Students will describe group, subgroup, related properties and theorems.

CO61: Students will differentiate between cyclic group, permutation group, quotiant group and normal subgroup.

CO62: Students will identify homomorphism and isomorphism of groups.

CO63: Students will describe rings, sub-rings, related properties and theorems, Ideal and characteristic of a ring and their uses in security system.

CO64: Students will use the knowledge of field, sub-field, related properties and theorems in encryption and description.

CO65: Students will 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 the group, Fundamental theorem of homomorphism of the 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: 
  • I.N. Herstein, Topics in Algebra, Wiley Eastern Ltd., New Delhi, 2008.
  • A.R.Vasishtha, J. N. Sharma and A.K. Vasishtha, Linear Algebra, Krishna Prakashan, 2010.
  • Joseph Gallian, Contemporary Abstract Algebra, Cengage Learning USA, 2013.
References: 
  • 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.
  • K. C. Sarangi, Elements of Abstract Algebra, RBD, Jaipur, 2009.
  • Robert M. Thrall and Leonard Tornheim, Vector Spaces and Matrices, Dover Publications Inc. New York, 2011.
 
Academic Year: 
2022-2023
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