Functional Analysis

Doctorate level

Theoretical. (Åpen for UiT sine ph.d.-studenter (kategori 1) og åpen for følgende kategorier av enkeltemnestudenter:

- kategori 2: Deltakarar på UiT sitt førstelektorprogram som fyller utdanningskravet.

- kategori 3: Doktorgradsstudentar frå andre universitet.

- kategori 4: Personar med minimum mastergrad eller tilsvarande som ikkje er doktorgradsstudentar.)

Application code: 9301

Last dates for course registration and registration for examination are September 1 for the fall semester, and February 1 for the spring semester.

PhD students or holders of a Norwegian master´s degree of five years or 3+ 2 years (or equivalent) may be admitted (categories 3 and 4 above). PhD students must upload a document from their university stating that they are registered PhD students. This group of applicants does not have to prove English proficiency and are exempt from semester fee.

Holders of a Master´s degree must upload a Master´s Diploma with Diploma Supplement / English translation of the diploma. Applicants from listed countries must document proficiency in English. To find out if this applies to you see the following list:

Proficiency in English must be documented - list of countries.

For more information on accepted English proficiency tests and scores, as well as exemptions from the English proficiency tests, please see the following document: Proficiency in English - PhD level studies.

The course will be cancelled if less than five participants.

The students shall learn some of the central concepts of functional analysis and methods, and be able to apply these.

The Hahn-Banach theorem, open mapping and closed graph theorems, the Banach-Steinhaus theorem, dual spaces, weak convergence, the Banach-Alaoglu theorem, and the spectral theorem for bounded self-adjoint operators, applications to PDE and numerical methods

General admission requirements for PhD.-program at UiT.

Offered irregularly. The course will be cancelled if less than five participants.

Knowledge:

After passing the course, the student is expected to be able to

• Demonstrate understanding of the central concepts of functional analysis.
• Show knowledge of where the forefront of knowledge within the field is.

Skills:

After passing the course, the student is expected to be able to

• Carry out research of high international standard connected application of functional analysis.
• Handle complex academic issues and challenge established knowledge and practice connected to application of functional analysis.

Habits of mind:

After passing the course, the student is expected to be able to

• Formulate mathematics in a way that enable communication of research and development in applied functional analysis on high level.
• Give oral presentation and participate in debates concerning functional analysis in international forums.

Anbefalte forkunnskaper

TEK-8002 Principles of Mathematical Analysis

Language of instruction and examination

Schedule

Re-sit examination