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Algebra [1]

Paper Code: 
25CMAT401
Credits: 
4
Contact Hours: 
60.00
Max. Marks: 
100.00
Objective: 

This course will enable the students to -

  1. Construct groups, Subgroups and group homomorphism. 
  2. Develop the ideas about the rings, Integral domains and fields.
  3. Apply the concept of group theory and ring theory in realistic problems.

 

Course Outcomes: 

 Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

25CMAT 401

 

 

 

 

 

 

Algebra

(Theory)

 

 

 

 

 

 

CO34: Construct group, cyclic group, permutation group, Related properties and theorems.

CO35: Differentiate between Subgroup Quotient group and normal subgroup.

CO36: Identify homomorphism and isomorphism of groups.

CO37: Construct rings, Sub-rings, Related properties, theorems and their uses in the security system.

CO38: Apply the knowledge of integral domain, Fields and subfields and their applications.

CO39: Contribute effectively in course-specific interaction.

 

Approach in teaching:

Interactive Lectures, Discussion, PowerPoint Presentations, Informative videos

 

Learning  activities for the students:

Self learning assignments, Effective questions, Assigned tasks

 

Quiz, Individual or group project,

Open Book Test, Continuous Assessment, Semester End Examination

 

Unit I: 
Groups
12.00
 Definition of a group with examples and related properties, Order of elements in a group and related theorems, Cyclic group, Permutation group
 
Unit II: 
Subgroups
12.00
Subgroups, Cosets, Lagrange’s theorem, Normal subgroup, Quotient group.
 
Unit III: 
Homomorphism
12.00
Homomorphism of groups, Types of homomorphism, Cayley theorem, Fundamental theorem of homomorphism of group. 
 
Unit IV: 
Ring
12.00
Definition, Types, Examples, Subrings and elementary properties of rings.
 
Unit V: 
Integral domain and Field:
12.00
Integral domain, Field, Subfield and their related properties, Characteristic of a ring and field.
 
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.

 

e- RESOURCES

 

Academic Year: 
2025-2026 [8]

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Source URL: https://maths.iisuniv.ac.in/node/1436

Links:
[1] https://maths.iisuniv.ac.in/node/1436
[2] https://nptel.ac.in/courses/111106113
[3] https://nptel.ac.in/courses/111102009
[4] https://onlinecourses.nptel.ac.in/noc21_ma42/preview
[5] https://www.journals.elsevier.com/journal-of-algebra
[6] https://www.worldscientific.com/worldscinet/jaa
[7] https://www.springer.com/journal/10469
[8] https://maths.iisuniv.ac.in/academic-year/2025-2026