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Course content

The course gives an introduction to probability theory in a measure theoretic setting. Among the topics discussed are: Probability measures, σ-algebras, conditional expectations, convergence of random variables, the law of large numbers, characteristic functions, the central limit theorem, filtrations, martingales in discrete time, Brownian motion

Learning outcome

After having completed the course:

  • you know the measure theoretic definitions of probability, independence, random variable, stochastic process, and conditional expectation
  • you know different ways to describe the distribution of a random variable
  • you know methods for treating and describing limits of sequences of random variables
  • you are familiar with how filtrations and conditional expectations are used to represent information, and can work with discrete time martingales
  • you know the construction of Brownian motions and some of their most important properties.

Admission

Students admitted at UiO must apply for courses in Studentweb. Students enrolled in other Master's Degree Programmes can, on application, be admitted to the course if this is cleared by their own study programme.

Nordic citizens and applicants residing in the Nordic countries may apply to take this course as a single course student.

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

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

Recommended previous knowledge:

Overlapping courses

10 credits overlap with STK-MAT4710 – Probability theory

Teaching

4 hours lectures/exercises each week throughout the semester.

Examination

1 mandatory assignment that has to be approved to attend the exam.

The final written exam counts 100% for the grade.

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

Students who can document a valid reason for absence from the regular examination are offered a postponed examination at the beginning of the next semester.

Re-scheduled examinations are not offered to students who withdraw during, or did not pass the original examination.

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.

The course  STK-MAT3710 – Probability theory overlaps 10 ECTS with STK-MAT4710 – Probability theory and number of times one can take the exam applies to these courses combined.

Special examination arrangements

Application form, deadline and requirements for special examination arrangements.

Facts about this course

Credits

10

Level

Bachelor

Teaching

Autumn 2019

Examination

Autumn 2019

Teaching language

Norwegian