Course Code    : PMAT 41813

Title                   : Functional Analysis

Pre-requisites   : PMAT 21553

 Learning Outcomes:

At the end of this course, the student should be able to

1. demonstrate knowledge of the functionals and its analysis under a topological background comprehending
2. understand how algebra and analysis combine to form a separate part of Pure Mathematics.

 Course Contents:

Metric spaces, Completion of metric spaces, Normed spaces, Banach spaces, Linear operators and functionals, Inner product spaces, Hilbert spaces, Fundamental theorems for normed and Banach spaces.

 Method of Teaching and Learning: A combination of lectures, tutorial discussions and presentations.

 Assessment: Based on tutorials, tests, presentations and end of course examination.

 Recommended Reading:

1. Madox, I.J., (1992) Elements of Functional Analysis, Cambridge University Press.
2. Jain, P.K., Ahuja, O.P. & Ahmad, K., (2^nd edition, 2010) Functional Analysis, New Age Science Limited
3. Kreyszig, E., (2007) Introductory Functional Analysis with Applications, John Wiley, New York.
4. Pannasamy, S., (2^nd edition, 2005) Foundations of Complex Analysis, Alpha Science International.