MAT4400 – Linear Analysis with Applications

Schedule, syllabus and examination date

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Changes in the course due to coronavirus

Autumn 2020 the exams of most courses at the MN Faculty will be conducted as digital home exams or oral exams, using the normal grading scale. The semester page for your course will be updated with any changes in the form of examination.

See general guidelines for examination at the MN Faculty autumn 2020.

Course content

MAT4400 gives an introduction to measure and integration theory, and to operator theory (on Hilbert spaces). Covered topics include: elementary measure and integration theory, including convergence theorems, Lp-spaces and their completeness, and Carathéodory’s extension theorem. Adjoint operators, orthogonal projections, compact operators and Hilbert-Schmidt operators. The spectral theorem for compact self-adjoint operators. Applications to Sturm-Liouville theory and Fredholm theory.

Learning outcome

After completing the course you:

  • are used to work with sigma-algebras and with measures on sigma-algebras. In particular you are familiar with the most important sigma-algebras on the real line and with the Lebesgue measure on these;
  • have a good understanding of measure spaces and of integrable functions, know how to compute the integral of many integrable functions and are acquainted with convergence theorems for integrals;
  • know what an Lp-space is and what Hölder’s inequality says;
  • are able to determine the adjoint of a bounded linear operator on a Hilbert space and decide if the operator is self-adjoint, and know well examples of self-adjoint operators, such as orthogonal projections onto closed subspaces;
  • are familiar with compact operators and their most important properties, and are well aware of what is meant by the Fredholm alternative, in particular in connection with certain Integral equations;
  • have a good understanding of the spectral theorem for compact self-adjoint operators and know how it can be used to solve certain Sturm-Liouville problems.

Admission to the course

Students at UiO register for courses and exams in Studentweb.

Overlapping courses


6 hours of lectures/exercises every week throughout the semester.


1 mandatory assignment written with a typesetting software for mathematics, e.g. LaTeX.

Final written examination.

Examination support material

No examination support material is allowed.

Language of examination

Subjects taught in English will only offer the exam paper in English. You may write your examination paper in Norwegian, Swedish, Danish or English.

Grading scale

Grades are awarded on a scale from A to F, where A is the best grade and F is a fail. Read more about the grading system.

Resit an examination

This course offers both postponed and resit of examination. Read more:

Special examination arrangements, use of sources, explanations and appeals

See more about examinations at UiO

Last updated from FS (Common Student System) Oct. 27, 2020 5:16:57 PM

Facts about this course

Teaching language