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Title- Algebra (Code-09050101)

B.Sc. (Hons. Mathematics) – 1st semester

S.No.

Topic

Domain

Hours as per UGC

 

 

1

  • Symmetric ,Skew- Symmetric matrices
  • Hermitian ,Skew- Hermitian matrices
  • Elementary operations on matrices
  • Rank of matrices ,inverse of matrices
  • L.D and L.I. of rows and columns
  • Eigen values, eigenvectors and Char. Equation of a matrix
  • Minimal polynomial of a matrix
  • Cayley Hamilton Theorem and find inverse of a matrix.

Must know

15

 

 

2

  • Homogeneous and non Homogeneous
  • Application of matrices to a system of linear equations,
  • Theorems on consistency of a system of linear equation
  • Unitary and orthogonal matrices,
  •  Bilinear and Quadratic forms of matrices

Must Know

12

 

 

3

  • Relation between the roots and coefficients of general polynomial equation in one variable,
  • Solutions of polynomial equation having conditions on roots,
  • Common roots and multiple roots,
  • Transformation of equation.

Must know

 10

 

4

 

  • Nature of roots of an equation,
  • Descartes’ rule of sign
  • Solution of cubic equation
  • Bi-quadratic equations and their solutions

Nice to know

8

 Book Recommended :

  •  H.S. Hall and S.R. Knight: Higher Algebra. H.M. Publications 1994.
  •  Shanti Narayan : A text Book of Matrices.
  • Chandrika Prasad : Text Book on Algebra and Theory of Equations. Pothishala Private Ltd. Allahabad.
  • Titu Andreescu and Dorin Andrica, Complex Number from A to Z Birkhauser. 2006
  • Madhumangal Pal:Abstrat Algebra.PHI I  earning Private Limited Delhi. 2013
  • David C.Lay. Linear Algebra and us Applications 3rd Ed.. Pearson Education Asia.
  • Indian Reprint. 2007.
  • G.H.hardy Pure Mathematics. Universal Book Stall, New Delhi. 1989.
  • I.S. Luther and I.B.S.Passi. Algebra vol – 1. 11. Narosa Publishing House New Delhi
Admissions Open 2019-20