Algebra
This course will enable the students to -
- Develop the ideas about group, field, ring and their homomorphism.
- Understand the introduction to vector space.
Course Outcomes (COs):
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Course |
Learning outcomes (at course level) |
Learning and teaching strategies |
Assessment Strategies |
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|---|---|---|---|---|
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Paper Code |
Paper Title |
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MAT 501 |
Algebra(Theory)
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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.
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Approach in teaching:
Interactive Lectures, Discussion, Power Point Presentations, Informative videos
Learning activities for the students: Self learning assignments, Effective questions, presentations, Giving tasks
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Quiz, Poster Presentations, Power Point Presentations, Individual and group projects, Open Book Test, Semester End Examination
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Definition of a group with examples and related properties, Order of elements in a group and related theorems, Subgroup.
Cyclic group, Permutation group, Cosets, Lagrange’s theorem, Normal subgroup, Quotient group.
Homomorphism and Isomorphism of group, Fundamental theorem of homomorphism of group. Ring: Definition, examples and elementary properties, Subring.
Integral domain, Field, Subfield and their related properties, Ideal of a ring, Characteristic of a ring.
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).
- K. C. Sarangi, Elements of Abstract Algebra, RBD, Jaipur, 2009.
- I.N. Herstein, Topics in Algebra, Wiley Eastern Ltd., New Delhi, 2008.
- G. C. Sharma and Shivlal Agarwal, Modern Algebra,& Co. Agra, 1998.
- Joseph Gallian, Contemporary Abstract Algebra, Cengage Learning USA, 2013.
- 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.
- A.R.Vasishtha, J. N. Sharma and A.K. Vasishtha, Linear Algebra, Krishna Prakashan, 2010.
- Robert M. Thrall and Leonard Tornheim, Vector Spaces and Matrices, Dover Publications Inc. New York, 2011.
