MAT3400 – Linear Analysis with Applications

Schedule, syllabus and examination date

Course content

The course provides advanced knowledge in measure and integration theory together with a basic introduction to functional analysis. Covered topics include Banach and Hilbert spaces, the Hahn-Banach theorem, dual spaces, orthonormal bases, Jacobi’s transformation theorem, Lp-spaces and their duals, construction and decomposition of measures, Lebesgue-Stieltjes measures, the Riesz-Markov theorem, product measures and the Fubini-Tonelli theorems, the Radon-Nikodym theorem, the fundamental theorem of calculus, the Fourier transform and the Plancherel theorem, characteristic functions and conditional expectations.

Learning outcome

After completing the course you

  • are used to work with measure spaces and integration of measurable functions
  • have a good understanding of the most frequently used tools of Lebesgue integration such as convergence theorems and Fubini-Tonelli theorems
  • have a good understanding of various function spaces and their duals
  • are acquainted with basic notions of functional analysis
  • are familiar with fundamental tools of Fourier analysis
  • are prepared for more advanced courses on differential equations, harmonic, stochastic and functional analysis

Admission to the course

Students who are admitted to study programmes at UiO must each semester register which courses and exams they wish to sign up for in Studentweb.

Special admission requirements

In addition to fulfilling the Higher Education Entrance Qualification, applicants have to meet the following special admission requirements:

  • Mathematics R1 (or Mathematics S1 and S2) + R2

And in addition one of these:

  • Physics (1+2)
  • Chemistry (1+2)
  • Biology (1+2)
  • Information technology (1+2)
  • Geosciences (1+2)
  • Technology and theories of research (1+2)
  • Social economy (1+2)

The special admission requirements may also be covered by equivalent studies from Norwegian upper secondary school or by other equivalent studies (in Norwegian).

Overlapping courses

Teaching

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

The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.

Examination

Final written exam which counts 100 % towards the final grade.

This course has 1 mandatory assignment that must be approved before you can sit the final exam.

It will also be counted as one of the three attempts to sit the exam for this course, if you sit the exam for one of the following courses: MAT4400 – Linear Analysis with Applications

Examination support material

No examination support material is allowed.

Language of examination

Courses 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:

More about examinations at UiO

You will find further guides and resources at the web page on examinations at UiO.

Last updated from FS (Felles studentsystem) Nov. 6, 2026 1:11:26 AM

Facts about this course

Level
Bachelor
Credits
10
Teaching
Spring
Examination
Spring
Teaching language
English

Contact

Department of Mathematics