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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: hcpetersen@imada.sdu.dk

Timetable
Group Type Day Time Classroom Weeks Comment
Common I Tuesday 10-12 U21 36,39
Common I Tuesday 10-12 U67 37-38,40,46-50
Common I Tuesday 10-12 U61 41
Common I Tuesday 10-12 U17 43
Common I Tuesday 10-12 U142 44-45
Common I Wednesday 12-14 U10 36-41,43,45-50
Common I Wednesday 12-14 U92 44
O1 TE Thursday 10-12 U62 37-41,43-45,47-49
O1 TE Friday 10-12 U9 46
Show entire timetable
 Show personal time table for this course.

Comment:
Ubegrænset deltagerantal.Samlæses med MM544

Prerequisites:
None.

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. Report and oral examination. The report is evaluated as a part of the oral exam. Evaluated by external marking and graded by the Danish 7-mark scale (10 ECTS).
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

Educational form
Activities during the study phase: Studying the course material and preparing the weekly exercises, individually or through group work.

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.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.