Type of course

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

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

Admission requirements

General admission requirements for PhD.-program at UiT.

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

Course content

The objective of the course is to introduce some of the basic notions and methods in the mathematics of modelling, numerical analysis, and optimization. These subjects have shown to be important in applied mathematics.

The main topic of the course is some methods that are used scientific computing, for example the Newton, Ritz, Galerkin, and least squares methods, polynomial approximations in Sobolev spaces, the Fourier transform, and spectral methods. Construction of numerical methods for optimization, algebraic equations, and for classical PDEs associated to wave, heat, and fluid dynamics. Methods based on rigorous numerics using interval analysis.

Objectives of the course

Knowledge:

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

• Give an account of basic concepts and definitions in the mathematics of modelling, numerical analysis, and optimization.
• Formulate results covered by the course.
• Exemplify concepts in specific cases.

Skills:

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

• Interpret concepts in specific cases.
• Describe the main features of the proofs of main theorems.

Habits of mind:

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

• Use the theory and methods of the course to solve problems in applied mathematics.

Language of instruction and examination

Teaching methods