MAU34203 Functional analysis
| Module Code | MAU34203 |
|---|---|
| Module Title | Functional analysis |
| Semester taught | Semester 1 |
| ECTS Credits | 5 |
| Module Lecturer | Prof. Florian Naef |
| Module Prerequisites | MAU22200 Advanced analysis |
Assessment Details
- This module is examined in a 2-hour examination at the end of Semester 1.
- Continuous assessment contributes 20% towards the overall mark.
- Re-assessment, if needed, consists of 100% exam.
Contact Hours
11 weeks of teaching with 3 lectures per week.
Learning Outcomes
On successful completion of this module, students will be able to
- Give appropriate definitions, theorems and proofs related to the topics introduced in this module, including topics in general topology, elementary theory of Banach spaces and linear operators.
- Solve problems requiring manipulation or application of one or more of the concepts and results introduced in this module.
- Formulate mathematical arguments in appropriately precise terms related to the concepts and results introduced in this module.
- Apply their knowledge in mathematical domains where functional analytic techniques are relevant.
Module Content
- General topology: Review of metric spaces, definition of topological spaces, open/closed sets, boundary, continuity, limits of sequences, compactness, bases, second countability, separability, sub-bases, weak and product topologies, neighbourhood bases, first countability.
- Normed and Banach spaces: Definitions and examples of Banach spaces and bounded linear operators, series in Banach spaces, convergence and absolute convergence, basic concepts from Lebesgue integration, Hölder's and Minkowski's inequalities.
- Baire category theorem and some of its consequences, open mapping theorem, application to Fourier series.