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

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These notes are purely based on BSC and B.Tech
these are Descriptive notes I myself used these notes for Examination preparation and SCORED 90 Marks in Institute Examinations.
Bsc Second year Mathematics | As per NEP Handwritten Notes PDF

Language-English
Subject- Mathematics
Total page- 216
Type – PDF
Total MB- 57( Higher Quality )

NOTES in Good Handwriting and Clear Scanning

Hope you will find it useful😊.

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

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