Abstract Algebra & Linear Algebra | As per NEP, BSc Second Year Mathematics Handwritten Notes PDF Download

Description

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