Key facts
Details for course being taught in current academic year
Level 3 - 15 credits - spring term
E-learning links
Resources
Timetable Link
Lecturer's website
Course description
Course outline
Banach spaces. Banach fixed-point theorem, Baire’s Theorem, continuous linear maps on Banach spaces, Banach-Steinhaus theorem, open mapping and closed graph theorems, Hahn-Banach Theorem. Compactness of sets, Hilbert spaces. Orthogonal expansions. Riesz-Fischer Theorem.
Pre-requisite
Measure and Integration, or equivalent.
Learning outcomes
At the end of the course a successful student should
* know the basic facts and the definitions about Hilbert and Banach
spaces and their duals;
* be able to state and sketch the ideas of the proofs of the following
basic theorems and principles: Baire, Banach-Steinhaus, Hahn-
Banach, closed graph, open mapping; contraction mapping.
Assessments
| Type | Timing | Weighting |
|---|---|---|
| Coursework | 10.00% | |
| Problem Sets | Spring Week 10 | 50.00% |
| Problem Sets | Spring Week 10 | 50.00% |
| Unseen Examination | Summer Term (2 hours) | 90.00% |
Resit mode of assessment
| Type | Timing | Weighting |
|---|---|---|
| Unseen Examination | Summer Vacation (2 hours ) | 100.00% |
Timing
Submission deadlines may vary for different types of assignment/groups of students.
Weighting
Coursework components (if listed) total 100% of the overall coursework weighting value.
Teaching methods
| Term | Method | Duration | Week pattern |
|---|---|---|---|
| Spring Term | LECTURE | 2 hours | 1111111111 |
| Spring Term | LECTURE | 1 hour | 1010101010 |
| Spring Term | WORKSHOP | 1 hour | 0101010101 |
How to read the week pattern
The numbers indicate the weeks of the term and how many events take place each week.