6 ECTS credits
150 h study time

Offer 1 with catalog number 4013327FNR for all students in the 1st semester at a (F) Master - specialised level.

Semester
1st semester
Enrollment based on exam contract
Impossible
Grading method
Grading (scale from 0 to 20)
Can retake in second session
Yes
Taught in
Dutch
Partnership Agreement
Under interuniversity agreement for degree program
Faculty
Faculty of Sciences and Bioengineering Sciences
Department
Mathematics
Educational team
Andreas Debrouwere
Kenny De Commer (course titular)
Tan Lu
Activities and contact hours
30 contact hours Lecture
30 contact hours Seminar, Exercises or Practicals
Course Content

1) Topological vector spaces and locally convex vector spaces

2) Fundamental theorems of functional analysis

3) The weak* and weak topology

4) Introduction to the theory of distributions

5) Applications in the theory of differential operators

6) Applications in representation theory

Course material
Digital course material (Required) : Functionaalanalyse, Kenny De Commer
Additional info

Notes will be provided. Supplementary references will be mentioned throughout the course.

Learning Outcomes

General competencies


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. 

Grading

The final grade is composed based on the following categories:
Oral Exam determines 60% of the final mark.
Written Exam determines 40% of the final mark.

Within the Oral Exam category, the following assignments need to be completed:

  • Oral exam with a relative weight of 1 which comprises 60% of the final mark.

Within the Written Exam category, the following assignments need to be completed:

  • Written exam with a relative weight of 1 which comprises 40% of the final mark.

Additional info regarding evaluation

Oral examination:

 

  • Oral with written preparation
  • Closed book
  • Open questions about theory and the associated context

 

Written exam:

  • Open book
  • Exercises that aim at mastering the methods and techniques of functional analysis.
     
Allowed unsatisfactory mark
The supplementary Teaching and Examination Regulations of your faculty stipulate whether an allowed unsatisfactory mark for this programme unit is permitted.

Academic context

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)