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#### Algebra (Code-09050101)B.Sc. Mathematics (Hons) – 1st semester

S.No.

Content of the topics

Learning      Objectives

Teaching Guidelines

Methodology

Time (Hours)

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 Characteristic equation of a matrix Minimal polynomial of a matrix Cayley Hamilton Theorem and find inverse of a matrix.
Student will be able to study  limit, Continuity & differentiability of function Lecture should be effective so that student will be able to grasp the topics easily

Assignment/  seminar/       Class tests/  Presentation

14

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
Student will be able to study of Asymptotes, Curvature and Points of infixion Lecture should be effective so that student will be able to grasp the topics easily

Assignment/  seminar/       Class tests/  Presentation

15

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.
Student will be able to trace the curves & study Reduction formulae , Rectification Lecture should be effective so that student will be able to grasp the topics easily

Assignment/  seminar/       Class tests/  Presentation

8

4

 Nature of roots of an equation, Descartes’ rule of sign Solution of cubic equation Bi-quadratic equations and their solutions
Student will be able to find the area and Volumes  of curves Lecture should be effective so that student will be able to grasp the topics easily

Assignment/  seminar/       Class tests/  Presentation

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