ALGEBRA
Paper Code:
MAT501
Credits:
3
Contact Hours:
45.00
Max. Marks:
100.00
9.00
Definition of a group with examples and related properties, Order of elements in a group and related theorems, Subgroup.
9.00
Cyclic group, Permutation group, Cosets, Lagrange’s theorem, Normal subgroup, Quotient group.
9.00
Homomorphism and isomorphism of group, Fundamental theorem of homomorphism of group. Ring: Definition, examples and elementary properties, Subring.
9.00
Integral domain, Field, Subfield and their related properties, Ideal of a ring, Characteristic of a ring.
9.00
Vector space: Definition with 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:
- 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, Shivlal Agarwal, Modern Algebra, & Co. Agra, 1998.
- 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 & Robert A. Beezer, Abstract Algebra: Theory and Applications, 2015.
- A.R. Vasishtha, J. N. Sharma, A.K. Vasishtha, Linear Algebra, Krishna Prakashan, 2010.
- Robert M. Thrall and Leonard Tornheim, Vector Spaces and Matrices, Dover Publications Inc. New York, 2011.
Academic Year:
