This course is discontinued

MAT9340 – Elementary functional analysis

Course content

The course gives an introduction to functional analysis, which is a branch of analysis in which one develops analysis in infinite dimensional vector spaces. The central concepts which are studied, are normed spaces with emphasis on Banach and Hilbert spaces, and continuous linear maps (often called operators) between such spaces. Spectral theory for compact operators is studied in detail, and applications are given to integral and differential equations.

Learning outcome

The course will be useful for all students who are aiming at writing a master thesis in mathematics (or applied mathematics) with spesialization in analysis.


PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.

If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.

PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.


Recommended previous knowledge

Knowledge corresponding to MAT1110 – Calculus and Linear Algebra, MAT1120 – Linear Algebra, MAT2400 – Real Analysis, MAT2410 – Introduction to Complex Analysis should be taken together with MAT3300 – Measure and integration (discontinued)/MAT4300 – Measure and integration (discontinued) if you haven`t taken this course previously.


4 hours of lectures/exercises per week.


Depeding on the number of students, the exam will be either oral or written. What form the exam will take will be announced by the teaching staff within October 15th.

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 pass/fail scale. Read more about the grading system.

Explanations and appeals

Resit an examination

Students who due to illness or other valid reason of absence were unable to sit for their final exams may apply for participation in deferred examinations. Deferred examinations are arranged either later in the same semester or early in the semester following the exam in question. Documentation of valid reasons for absence from the regular exam must be submitted upon application to participate in deferred examinations.

Students who have failed an exam, who withdraw during an exam, and students who wish to retake an exam to achieve a better grade may not participate in deferred exams, but may retake the exam when it is regularly scheduled.

Information about deferred and new examination (also called repeat examination) is found here

More information about examination at the Faculty of Mathematics and Natural Sciences can be found here

Special examination arrangements

Application form, deadline and requirements for special examination arrangements.

Facts about this course






Autumn 2009

This version of the course was held for the last time Autumn 2009. MAT4340 – Elementary functional analysis (discontinued) will still be held.


Autumn 2009

Teaching language


The course is given in English. If no students have asked for the course in English within the first lecture, it may be given in Norwegian.