MAT2100 – Elementary Real Analysis

Schedule, syllabus and examination date

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Course content

MAT2100 covers the theoretical basis for one variable mathematical analysis and gives a comprehensive introduction to the central concepts and proof techniques.  The course extends the theory of MAT1100 – Calculus emphasizing the theoretical aspects of the theory.  Students that  want to pursue a masters degree in mathematical analysis (including partial differential equations. mathematical optimization, stochastic analysis and mathematical finance) are recommended to take MAT2400 – Real Analysis instead (or in addition). 

Learning outcome

After completing the course you:

  • will know the axionatic theory of real numbers and have a good understanding of topological concepts like openness, closedness, compactness, convergense and continuity on the real line;
  • will have an understanding of the concept of cardinality and know the difference between countable and uncountable sets;
  • will be able to use the basic theorems on continuous and differentiable functions on the real line;
  • will be able to explain the definition of the Riemann integral and the connection between integration and differentiation;
  • will know the different forms of convergense for sequences and series of functions and the basic theory of power series and Fourier series;
  • are able to explain the basic theory of metric spaces;
  • area ble to present your own mathematical arguments with correct use of notation and terminology in a clear and well organized way.


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.

If you are not already enrolled as a student at UiO, please see our information about admission requirements and procedures.


Formal prerequisite knowledge

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)

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

Recommended previous knowledge

MAT1100 – Calculus and MAT1110 – Calculus and Linear Algebra


4 hours of lectures and 2 hours of problem sessions in groups per week.

The number of groups offered can be adjusted during the semester, depending on attendance.


2 mandatory assignments

Final oral examination.

Examination support material

No examination support material is allowed.

Language of examination

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.

Explanations and appeals

Resit an examination

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

Withdrawal from an examination

It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.

Special examination arrangements

Application form, deadline and requirements for special examination arrangements.


The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.

Facts about this course






Every spring


Every spring

Teaching language