Schedule, syllabus and examination date

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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 have good knowledge of the measure theoretic definitions of probability, independence, random variable, stochastic process, and conditional expectation
  • you master different ways to describe the distribution of a random variable
  • you have thorough knowledge of 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 understand the construction of Brownian motions and know some of their most important properties
  • master LaTeX as an electronic tool for writing mathematics

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.

Overlapping courses

10 credits overlap with STK-MAT3710 – 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 mandatory assignment must be written in (LaTeX), the typesetting software for academic writing in mathematics.

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

Master

Teaching

Every spring

Examination

Every spring

Teaching language

Norwegian