MM835: Probability theory (10 ECTS)

STADS: 13013301

Level
Master's level course

Teaching period
The course is offered in the autumn semester.

Teacher responsible
Email: yuri.goegebeur@imada.sdu.dk

Timetable
Show entire timetable
Show personal time table for this course.

Comment:
Ubegrænset deltagerantal. Fælles undervisning med MM544 Sandsynlighedsteori

Prerequisites:
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

Subject overview
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

Meddeles ved kursets start.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:

1. Oral examination, external censor, grading on the Danish 7 point scale. A closer description of the exam rules will be posted under 'Course Information' on Blackboard. (10 ECTS). (13013302).

Expected working hours
The teaching method is based on three phase model.
Intro phase: 56 hours
Skills training phase: 28 hours, hereof:
 - Tutorials: 28 hours

Educational activities
Studying the course material and preparing the weekly exercises, individually or through group work.Educational form
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.

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Remarks
The course is co-read with: MM544.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.