# MSc (Mathematics and Computing) Programme:Theory of Linear Operators

Thapar UniversityPrice on request

Price on request

£ 1,000 - (Rs 82,438)

Free

£ 399 - (Rs 32,893)

## Important information

- Master
- Patiala

Starts | Location |
---|---|

On request |
PatialaThapar University P.O Box 32, 147004, Punjab, India See map |

## Course programme

Semester I

Real Analysis – I

Linear Algebra

Complex Analysis

Fundamentals of Computer Science and C Programming

Discrete Mathematical Structure

Differential Equations

Semester II

Real Analysis –II

Advanced Abstract Algebra

Computer Oriented Numerical Methods

Data Structures

Data Based Management Systems

Operating Systems

Semester III

Topology

Computer Based Optimization Techniques

Computer Networks

Mechanics

Seminar

Semester IV

Functional Analysis

Dissertation

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.