Abstract Algebra
Paper Code:
MAT501
Credits:
3
Contact Hours:
45.00
Max. Marks:
100.00
Objective:
o To introduce basics in mathematics.
o To introduce and develop abstract concepts
Unit I:
I
9.00
Definition of a group with examples and simple properties. Order of elements in a Group and related theorem.
Unit II:
II
9.00
Subgroups, Cyclic groups, Permutation groups, Alternating groups.
Unit III:
III
9.00
Cosets, Lagrange’s theorem, Normal subgroups, Quotient group.
Unit IV:
IV
9.00
Homomorphism and Isomorphism, The Fundamental theorem of homomorphism. Rings.
Unit V:
V
9.00
Subrings. Ideal of a ring, Characteristic of a ring, Integral domain, Fields: their simple properties.
Essential Readings:
- K. C. Sarangi, Elements of Abstract Algebra, RBD, Jaipur.
- P.B. Bhattacharya, S.K. Jain and S.R. Nagpaul, Basic Abstract Algebra, Cambridge University Press.
- G. C. Sharma, Modern Algebra, Shivlal Agarwal & Co. Agra.
References:
- Deepak Chatterjee, Abstract Algebra. PHI. Ltd.New Delhi.
- I.N. Herstein, Topics in Algebra, Wiley Eastern Ltd., New Delhi.
- Malcolm Birkoff, Abstract Algebra, Cambridge University Press.
Academic Year:
