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

Thapar University
In Patiala

Price on request
You can also call the Study Centre
17523... More
Compare this course with other similar courses
See all

Important information

  • Master
  • Patiala
Description

Important information
Venues

Where and when

Starts Location
On request
Patiala
Thapar 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.


Compare this course with other similar courses
See all