6 ECTS credits
150 h study time
Offer 1 with catalog number 4013327FNR for all students in the 2nd semester at a (F) Master - specialised level.
1. Topological and locally convex vector spaces
2. The weak* and weak topology
3. Krein-Milman theory
4. Fundamental theorems of functional analysis
5. Fixed point theorems
Notes will be provided. Supplementary references will be mentioned throughout the course.
The student is familiar with basic concepts of abstract functional analysis, in particular with respect to the notion of weak topologies. The student can correctly formulate the main theorems of the course, and can clarify why the hypotheses of the theorems are necessary. In particular, the student can provide easy examples to elucidate the theorems in the course, and can show with counterexamples why certain hypotheses in the theorems are necessary. The student is also capable of independantly making connections between the different parts of the course, and is capable to give insightful answers to theoretical questions.
The final grade is composed based on the following categories:
Oral Exam determines 100% of the final mark.
Within the Oral Exam category, the following assignments need to be completed:
Exam:
- Oral exam with written preparation
- No external aids can be used (closed book exam)
- Open questions about the theory and its application in easy examples
This offer is part of the following study plans:
Master of Mathematics: Fundamental Mathematics (only offered in Dutch)
Master of Mathematics: Education (only offered in Dutch)
Master of Teaching in Science and Technology: wiskunde (120 ECTS, Etterbeek) (only offered in Dutch)