MSc (Mathematics and Computing) Programme:Theory of Linear OperatorsThapar University
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Real Analysis – I
Fundamentals of Computer Science and C Programming
Discrete Mathematical Structure
Real Analysis –II
Advanced Abstract Algebra
Computer Oriented Numerical Methods
Data Based Management Systems
Computer Based Optimization Techniques
Theory of Linear Operators
Spectral Theory: Spectral Theory in Normed linear spaces, resolvent set and spectrum, spectral properties of bounded linear operators, Properties of resolvent sets and spectrum. Spectral mapping theorem for polynomials, Spectral radius of a bounded linear operator on a complex Banach space. Elementary theory of Banach algebras,
Spectral properties of compact linear operators: General Properties of compact linear operators. Spectral properties of compact linear operators on Normed spaces. Behavior of compact linear operators with respect to solvability of operator equations, Fredholm type theorem. Fredholm alternative theorem. Fredholm alternative for integral equations.
Spectral properties of bounded self adjoint linear operators: Spectral properties of bounded self adjoint linear operators on a complex Hilbert space. Positive operators. Monotone sequences theorem for bounded self adjoint operators on a complex Hilbert space. Square roots of a positive operator. Projection operators.