PMAT 21015

>< Type/ Status : Core
>< Title : Discrete Mathematics II
>< Pre-requisites : PMAT 11025
>< Objectives :
At the end of this course, the student will acquire the basics of vector spaces and linear transformations and will be able to apply them to solve problems in diverse areas.
>< Course Content :

Vector Spaces: Vector Spaces, Subspaces, Linear independence, Basis and dimension, Linear transformations, Kernel and image of a linear transformation, dimension theorem, Inner product, Gram-Schmidt orthogonalization process, Orthogonal complement, Orthogonal projections.

Applications of Linear Transformations: Lines and planes, Quadratic forms, Conic sections, Quadratic surfaces, Least squares, Differential equations and other applications.

Eigenvalues and Eigenvectors: Polynomials of matrices and linear operators, Eigenvalues and eigenvectors, Diagonalization, Characteristic polynomial, Cayley-Hamilton theorem, Minimum polynomial, Jordan Canonical Form, Rational canonical form.

>< Methodology : A combination of lectures and tutorial discussions
>< Scheme of Evaluation : Based on tutorials, tests and end of course examination
>< Recommended Reading :
1. Johnsonbaugh, R. (1990). Discrete Mathematics, Macmillan.
2. Khanna, V.K. & Bhambri, S.K. (1998). A Course in Abstract Algebra, Vikas, India.
3. Aggarwal, R.S. & Matharu, R.S. (1991). Linear Algebra, S. Chands, India.
4. Narayan, S. & Pal, S. (1992). A text book of Modern Abstract Algebra, S . Chands, India.

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