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Abstract Algebra [1]

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: 
  1. K. C. Sarangi, Elements of Abstract Algebra, RBD, Jaipur.
  2. P.B. Bhattacharya, S.K. Jain and S.R. Nagpaul, Basic Abstract Algebra, Cambridge University Press.
  3. G. C. Sharma, Modern Algebra, Shivlal Agarwal & Co. Agra.
 
References: 
  1. Deepak Chatterjee, Abstract Algebra. PHI. Ltd.New Delhi.
  2. I.N. Herstein, Topics in Algebra, Wiley Eastern Ltd., New Delhi.
  3. Malcolm Birkoff, Abstract Algebra, Cambridge University Press.
Academic Year: 
2014-2015 [2]

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[1] https://maths.iisuniv.ac.in/courses/subjects/abstract-algebra-2
[2] https://maths.iisuniv.ac.in/academic-year/2014-2015