MM544: Probability theory

Study Board for Natural Sciences

Teaching language: Danish or English depending on the teacher, but English if international students are enrolled
EKA: N300007102
Assessment: Second examiner: External
Grading: 7-point grading scale
Offered in: Odense
Offered in: Autumn
Level: Bachelor

STADS ID (UVA): N300007101
ECTS value: 10

Date of Approval: 12-03-2025


Duration: 1 semester

Version: Approved - active

Internal Course Code

MM544

Comment

The course is co-read with MM835.

Entry requirements

The course cannot be followed by students who have passed MM835.

Academic preconditions

The course builds on the knowledge acquired in the course MM548. Students taking the course are expected to have knowledge of measure and integration theory.

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.

The course gives an academic basis for studying the topics stochastic processes and mathematical finance, that are part of the degree.


Expected learning outcome

The learning objectives of the course is 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 exam

EKA

N300007102

Assessment

Second examiner: External

Grading

7-point grading scale

Identification

Student Identification Card - Name

Language

Normally, the same as teaching language

Examination aids

Book and notes may be used during preparation time before the oral exam

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 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

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.