Functional Analysis

Lecturer: A.L. Pinchuck

Prerequisites

Real analysis (M3.3) or an equivalent course is a necessary prerequisite for this course and knowledge of metric spaces would be advantageous.

Description

Functional analysis is the branch of mathematics, and specifically of analysis, concerned with the study of vector spaces and operators acting upon them. Functional analysis is essentially a mixture of linear algebra and the techniques of analysis, and has important applications in probability theory, approximation theory and mathematical physics amongst other areas.

This course is an introduction to the field in which we study normed linear spaces, Hilbert spaces, bounded linear operators, dual spaces and the most well known and far reaching results in functional analysis such as the Hahn-Banach theorem, Baire’s category theorem, the uniform boundedness principle, the open mapping theorem and the closed graph theorem.

Textbook

None prescribed. Complete course notes will be provided.

Tutorials

One tutorial per week.

Tests/Exams

Two tests and one final examination.

Last Modified: Fri, 15 Jul 2011 14:57:09 SAST