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
Entry requirements
Academic preconditions
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
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
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.