Functional Analysis I
Syllabus, Master's level, 1MA043
This course has been discontinued.
- Code
- 1MA043
- Education cycle
- Second cycle
- Main field(s) of study and in-depth level
- Mathematics A1N
- Grading system
- Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
- Finalised by
- The Faculty Board of Science and Technology, 15 March 2007
- Responsible department
- Department of Mathematics
Entry requirements
BSc with 50 credit points Mathematics including Linear Algebra II and Transform Methods
Learning outcomes
In order to pass the course (grade 3) the student should be able to
Higher grades, 4 or 5, require a higher level of proficiency. The student should be able to solve problems of greater complexity, i.e. problems requiring a combination of ideas and methods for their solution, and be able to give a more detailed account of the proofs of important theorems and by examples and counter-examples be able to motivate the scope of various results. Requirements concerning the student's ability to present mathematical arguments and reasoning are greater.
Content
Topology in metric spaces. Normed spaces. Banach spaces, inner product spaces, Hilbert spaces. Linear maps. Basic functional analytic theorems: Hahn–Banach's theorem, Banach–Steinhaus' theorem, the open map and the closed graph theorems. Compactness and weak convergence. Operators on Hilbert spaces. Geometry in Hilbert spaces. The spectral theory for compact symmetric operators.
Instruction
Lectures and problem solving sessions.
Assessment
Written and, possibly, oral examination at the end of the course. Moreover, compulsory assignments may be given during the course.