Table of contents

The course is connected to the following study programs

  • Industrial Mathematics, Bachelor's Programme

Teaching language

Norwegian or English

Recommended previous knowledge

60 sp in mathematics including MA-227

Learning outcomes

Upon successful completion of the course, the student will be able to

  • Explain and apply the Lebesgue integral for positive measures, included product measures.
  • Explain the convergence theorems (the monotone case, Fatou’s lemma and the dominated case) as well as the Tonelli-Fubini theorem.
  • Apply measure- and integration theory at fundamental parts of probability theory.
  • Know the measure theoretic definitions of probability, independence, random variable, stochastic process and conditional expectation, as well as various ways of describing the probability distribution of random variables.
  • apply methods in order to treat and describe limits of sequences of random variables, in particular the law of great numbers, the central limit theorem and convergence of martingales.
  • Have knowledge of how filtrations and conditional expectations are used to represent information.
  • Treat martingales and Markov chains in discrete time.
  • Have knowledge of basic properties of Brownian motions.

Contents

Lebesgue integral when measure and sigma-algebra are given, convergence theorems, product measure and integration on product spaces. Probability described by measure theoretic concepts, with themes like distribution and density, filtrations, conditional expectations, convergence of seuences of random variables, laws of great numbers, the central limit theorem, Markov chains, martingales in discrete time and Brownian motion.

Teaching and learning methods

Lectures, group work, project with applications to industrial mathematics and compulsory submissions. The subject has an expected scope of work of around 267 hours.

Examination requirements

Mandatory hand-ins must be approved. See Canvas for details.

Examinations

Individual, oral exam

Student evaluation

The person responsible for the course decides, in cooperation with student representative, the form of student evaluation and whether the course is to have a midway or end of course evaluation in accordance with the quality system for education, chapter 4.1.

Offered as a free-standing course

Yes. Subject to availability or capacity.

Admission for external candidates

No
Last updated from FS (Felles studentsystem) Oct. 15, 2026 9:32:31 AM