MAT2100 – Elementary Real Analysis

Schedule, syllabus and examination date

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Changes in the course due to coronavirus

Autumn 2020 and Spring 2021 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.

Please note that there may be changes in the form of examination for some courses taught Spring 2021. We aim to bring both the course description and the semester page of all courses up to date with correct information by 1 February 2021.

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

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 axiomatic theory of real numbers and have a good understanding of topological concepts like openness, closedness, compactness, convergence, 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 convergence 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
  • are able to present your own mathematical arguments with correct use of notation and terminology in a clear and well-organized way.

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)

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


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

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


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

This course has several mandatory assignments, where at least 2 must be approved before you can sit the final exam.

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) Jan. 27, 2021 9:21:20 PM

Facts about this course

Teaching language