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Algebra [1]

Paper Code: 
24CMAT411
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 ideas about rings, integral domains and fields.

 

Course Outcomes: 

 Course

Learning outcomes

(at course level)

Learning and teaching strategies

Assessment

Strategies

Course Code

Course Title

 

 

 

 

 

 

 

24CMAT

411

 

 

 

 

Algebra

(Theory)

 

 

 

 

 

 

CO67: Construct group, subgroup, related properties and theorems.

CO68: Differentiate between cyclic group, permutation group, quotient group and normal subgroup.

CO69: Identify homomorphism and isomorphism of groups.

CO70: Construct rings, sub-rings, related properties and theorems, Ideal and characteristic of a ring and their uses in the security system.

CO71: Apply the knowledge of integral domain, fields and subfields and their applications.

CO72: Contribute effectively in course-specific interaction.

Approach in teaching:

Interactive Lectures, Discussion, Power Point Presentations, Informative videos

 

Learning activities for the students:

Self learning assignments, Effective questions, presentations, Assigned tasks

 

 

 

Quiz,

Individual projects,

Open Book Test, 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: 
  • 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, Abstract Algebra: Theory and Applications, Stephen F. Austin, state University, 2013.
  • Robert M. Thrall and Leonard Tornheim, Vector Spaces and Matrices, Dover Publications Inc. New York, 2011.

e- RESOURCES

 

JOURNALS

 

Academic Year: 
2024-2025 [8]

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Source URL: https://maths.iisuniv.ac.in/courses/subjects/algebra-9

Links:
[1] https://maths.iisuniv.ac.in/courses/subjects/algebra-9
[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/2024-2025