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Course content

MAT2400 is a generalization and continuation of the mathematical analysis from MAT1100 and MAT1110 and the linear algebra from MAT1120. The theory is generalized from finite dimensional spaces to spaces that may be infinite dimensional, and whose elements typically are functions, rather than numbers or what you are used to think of as vectors. Key concepts are convergence, continuity, differentiability, completeness, and compactness. The theory is applied to problems from differential equations and Fourier analysis. MAT2400 gives training in mathematical reasoning and lays the theoretical foundation for further studies in mathematical analysis.

Learning outcome

After completing the course you:

  • are familiar with the theory of metric spaces, you can give arguments related to convergence, continuity, completeness, and compactness in such spaces, and you are familiar with several ways in which the theory may be applied, to study sequences of functions and to show the existence of solutions to ordinary differential equations;
  • have a basic knowledge of normed vector spaces and continuous linear maps between such spaces, and you know the basic theory of differentiation of maps between normed vector spaces, including the theorems about inverse and implicit functions;
  • have knowledge about inner product spaces, and how to express elements as linear combinations of elements of an orthonormal basis, in particular how functions may be represented as Fourier series, and you can explain various forms of convergence of such series;
  • can present your own mathematical arguments in a clear and well-organized way, with correct notation and terminology, and you can relate abstract concepts to concrete examples.

Admission

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.

Prerequisites

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, MAT1110 – Calculus and linear algebra and MAT1120 – Linear algebra.

Overlapping courses

10 credits overlap with MAT1300 – Analysis I (discontinued)

*The information about overlaps for discontinued courses may not be complete. If you have questions, please contact the Department. 

Teaching

4 hours of lectures and 2 hours of problem solving in plenum per week. In addition there will be exercise solving groups during the week, with guidance available.

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

Examination

2 mandatory assignments.

Final written examinations.

 

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.

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.

Evaluation

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

Credits

10

Level

Bachelor

Teaching

Every spring

Examination

Every spring

Teaching language

Norwegian (English on request)