Chapters and Topics Included on PDF
Module-I
- Groups, Subgroups and their basic properties
- Cyclic groups
- Coset decomposition
- Lagrange’s and Fermat’s theorem[7]
- Normal subgroups
- Quotient groups
Module – II
- Homomorphism and Isomorphism of groups
- Fundamental theorem of homomorphism
- Transformation and permutation group Sn (n < 5)
- Cayley’s theorem
- Group automorphism
- Inner automorphism
- Group of automorphisms
Module – III
- Definition and basic properties of rings
- Ring homomorphism
- Subring
- Ideals
- Quotient ring
- Polynomial ring
- Integral domain
- Field
Module – IV
- Definition and examples of Vector space
- Subspaces
- Sum and direct sum of subspaces
- Linear span, Linear dependence, linear independence and their basic
- properties
- Basis
- Finite dimensional vector space and dimension
- Existence theorem
- Extension theorem
- Invariance of the number of elements
- Dimension of sum of subspaces
- Quotient space and its dimension
Module – V
- Linear transformation and its representation as a matrix
- Algebra of linear transformation
- Rank-Nullity theorem
Reviews
There are no reviews yet.