Course - Functional Analysis - TMA4230
Functional Analysis
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About the course
Course content
This course provides students with results and methods that are applicable to other areas of mathematics, and are the foundations for more advanced topics in functional analysis. The Hahn-Banach theorem, the open mapping and closed graph theorems, the Banach-Steinhaus theorem, dual spaces, weak convergence, the Banach-Alaoglu theorem, and the spectral theorem for compact operators.
Learning outcome
1. Knowledge. The student has knowledge of central concepts from functional analysis, including the Hahn-Banach theorem, the open mapping and closed graph theorems, the Banach-Steinhaus theorem, dual spaces, weak convergence, the Banach-Alaoglu theorem, and the spectral theorem for compact self-adjoint operators.
2. Skills. The student is able to apply his or her knowledge of functional analysis to solve mathematical problems.
Learning methods and activities
Lectures, exercises and a written final examination.
Further on evaluation
The retake exam may be given as an oral exam. The retake exam will be in August.
See «Teaching methods and activities».
Recommended previous knowledge
TMA4145 Linear Methods and TMA4225 Foundation of Analysis.
Course materials
To be announced at the beginning of the term.
Credit reductions
| Course code | Reduction | From |
|---|---|---|
| SIF5054 | 7.5 sp |
Subject areas
- Mathematics
- Technological subjects