Syllabus
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Course Code: BMAT10 2 Course Name: Algebra and Number Theory |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Rank of a matrix. Row rank and column rank of a matrix. Eigen values, eigen vectors and the characteristic equation of a matrix. Minimal polynomial of a matrix. Cayley-Hamilton theorem and its use in finding the inverse of a matrix. Unitary and Orthogonal Matrices. | |
| 2 | Applications of matrices to a system of linear (both homogeneous and non–homogeneous) equations. Theorems on consistency of a system of linear equations. Relations between the roots and coefficients of general polynomial equation in one variable. Solutions of polynomial equations having conditions on roots. | |
| 3 | Common roots and multiple roots. Nature of the roots of an equation Descarte’s rule of signs. Solutions of cubic equations (Cardon’s method). Biquadratic equations and their solutions. | |
| 4 | Divisibility, Greatest Common Divisor(GCD), Least Common Multiple (LCM). Prime numbers,
Fundamental Theorem of Arithmetic. Linear Congruences, Fermat’s theorem. Wilson’s theorem
and its converse. Linear Diophantine equations in two variables. Greatest integer function [x]. The number of divisors and the sum of divisors of a natural number n (The functions d(n) and (n)). |
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