CMMS05 Metric and Banach Spaces 7CCMMS05 Metric and Banach Spaces
Lectures:
Two hours of lectures each week;
Tuesdays 14:00-16:00 in room S436.
Assignments:
Weakly assignments will be given during the lectures and posted on the web.
These will not be assessed and are for practice only.
However, students are strongly encouraged
to work on these assignments and to submit them.
Feedback on these assignments will be given and difficulties
will be discussed in class.
In addition, it is essential that students work through the theory as the course progresses.
Prerequisites:
A rigorous analysis course and some knowledge of linear algebra.
Assessment:
by a single 2 hour written examination in the summer term.
There is no coursework component.
Aims and objectives:
to discuss some fundamental aspects of functional analysis in Banach spaces
Syllabus:
the various topics to be discussed include metric spaces,
continuous maps, normed spaces, completeness, bounded linear maps,
compactness, Hahn-Banach theorem,
the dual space. Instruction is by formal lectures.
Books:
The course is essentially self-contained, but the following books
provide good background reading:
M. Reed & B. Simon,
Methods of modern mathematical physics, vol.1: Functional analysis.
W. Rudin, Functional Analysis.
P. Lax, Functional Analysis.
A. Kolmogorov & S. Fomin, Introductory real analysis.
E. Kreyszig, Introductory functional analysis with applications.