MM835: Probability theory

The Study Board for Science

Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N310006102
Assessment: Second examiner: External
Grading: 7-point grading scale
Offered in: Odense
Offered in: Autumn
Level: Master

STADS ID (UVA): N310006101
ECTS value: 10

Date of Approval: 12-03-2025


Duration: 1 semester

Version: Approved - active

Comment

The course is co-read with: MM544.

Entry requirements

The course cannot be chosen by students, who passed MM544.

Academic preconditions

Students taking the course are expected to have knowledge of measure and integration theory as taught in MM548.

Course introduction

The aim of the course is to enable the student to work in a rigorous way with probability models. Such models are of interest in their own right, but are also important for studies in areas like theoretical statistics, stochastic processes, mathematical finance and insurance. The course consists of three main blocks: (i) fundamental concepts, (ii) convergence of random variables and (iii) conditional expectation and martingales.

Expected learning outcome

The learning objectives of the course are that the student demonstrates the ability to:

  • reproduce definitions in probability theory within the scope of the course's syllabus
  • reproduce results in probability theory, together with their proofs, within the scope of the course's syllabus
  • apply the theory to solve problems in probability theory
  • relate the results within the scope of the course's syllabus to each other

Content

The following main topics are contained in the course: Random variables, probability measures, distribution functions, expectation, independence, characteristic functions, convergence of random variables, central limit theorems, conditional expectation, martingales.

Literature

See itslearning for syllabus lists and additional literature references.

Examination regulations

Exam element a)

Timing

January

Tests

Oral examination

EKA

N310006102

Assessment

Second examiner: External

Grading

7-point grading scale

Identification

Student Identification Card - Name

Language

Normally, the same as teaching language

Examination aids

To be announced during the course

ECTS value

10

Indicative number of lessons

84 hours per semester

Teaching Method

Planned lessons:
Total number of planned lessons: 84
Hereof:
Common lessons in classroom/auditorium: 84

The course introduces the topics at a general level in lectures and exercises sessions will be devoted to work on exercises based on the topics presented in previous lectures.

Other planned teaching activities:
Studying the course material and preparing the weekly exercises, individually or through group work.

Teacher responsible

Name E-mail Department
Yuri Goegebeur Yuri.Goegebeur@imada.sdu.dk Data Science

Timetable

Administrative Unit

Institut for Matematik og Datalogi (matematik)

Team at Registration

NAT

Offered in

Odense

Recommended course of study

Profile Education Semester Offer period

Transition rules

Transitional arrangements describe how a course replaces another course when changes are made to the course of study. 
If a transitional arrangement has been made for a course, it will be stated in the list. 
See transitional arrangements for all courses at the Faculty of Science.