MM835: Probability theory

Study Board of 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: 25-04-2019


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.

Course introduction

The aim of the course is to enable the student to work in a rigorous way with probability models, which is important in regard to the study of theoretical statistics.
The course builds on the knowledge acquired in the courses MM548, and gives an academic basis for studying the topics stochastic processes and mathematical finance, that are part of the degree.

In relation to the competence profile of the degree it is the explicit focus of the course to:
  • Give the competence to plan and execute scientific projects at a high level, and to manage work and development situations that are complex, unpredictable and that require new solving skills. 
  • Give skills to study, analyse, model and solve problems on a high level of abstraction using logical and structured argumentation.
  • Give knowledge about advanced models and methods in mathematics

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, the normal and multivariate normal distribution, 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

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

In order to enable students to achieve the learning objectives for the course, the teaching is organised in such a way that there are 84 lectures, class lessons, etc. on a semester. These teaching activities are reflected in an estimated allocation of the workload of an average student as follows: 

  • Intro phase (lectures) - 56 hours
  • Training phase: 28 hours

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.
Activities during the studyphase. 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 Educational Law & Registration

NAT

Offered in

Odense

Recommended course of study

Profile Education Semester Offer period