620-312 Linear Analysis

Note

Students may only gain credit for one of 620-312 and 618-302 (1997 Handbook).

Credit Points

Coordinator

Prerequisites

620-311 (1997 Handbook 618-301).

Semester

Contact

Subject Description

Students completing this subject should comprehend

• fundamental concepts about measures and Lebesgue integration with respect to a variety of measures;
• how basic concepts of linear algebra can be generalised to infinite dimensional situations using techniques from analysis;
• how these concepts arise in many branches of mathematics, as for example, in partial differential equations, operations research and probability, but also in areas of theoretical physics such as quantum mechanics;

have developed the ability to

• give rigorous mathematical arguments at an advanced level;
• apply abstract concepts to solving problems in other areas of mathematics such as differential equations;

and appreciate

• the necessity for a rigorous theoretical foundation of concepts used frequently in mathematics and physics.

Linear spaces and operators: Normed and inner product spaces, Hilbert spaces, abstract Fourier series; linear functionals and operators; dual spaces. Measure and integration: Introduction to measure and integration; dominated convergence and applications.

Assessment

Up to 24 pages of written assignments and a three-hour end-of-semester written examination.