MM506: Probability theory I (5 ECTS)

STADS: 13000601

Level
Bachelor course

Teaching period

Third quarter (Elective for Scient. students).
Third quarter on third academic year (Compulsory for Mat.Øk. students).

Teacher responsible
Email: steenth@imada.sdu.dk

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

Comment:
Obligatorisk kursus for mat.øk.-studerende. Valgfrit kursus for scient.-studerende.

Tidsmæssig placering: Tredje kvartal (Valgfrit for Scient. studerende). Tredje kvartal på 3. studieår (Obligatorisk for Mat.Øk. studerende).

02.02.2006:
Udover de allerede planlagte forelæsninger og øvelser er der skemalagt yderligere tidspunkter i ovennævnte fag:
Forelæsning: tirsdag kl. 14-16 lokale U49E (uge 6-11)
Øvelser: mandag kl. 08-10 lokale U49C (uge 6-11)

Prerequisites:
None

Academic preconditions:
The students must know contents of the course MM517.

Course introduction
To give the students a solid introduction to the mathematical treatment of probability theory based on abstract measure- and integration theory. The course presents fundamental elements of probability theory as it evolved during the twentieth century.

Competencies:
Probability theory is the mathematical foundation for theoretical statistics, and it has also found numerous applications in other branches of mathematics, e.g. functional analysis.
Having completed the course successfully, the students can be expected to

• have a fundamental understanding of the mathematical formulation of stochastic phenomena.

• be able to establish simple stochastic models for various phenomena observed in nature and society.

• have experience in performing basic probability calculations.

• be prepared for advanced courses in probability theory and its applications in both applied math. (mathematical finance, statistics etc.) and in pure math. (Banach spaces, operator algebras etc.).

Expected learning outcome


Subject overview
1. The mathematical description of a stochastic experiment

2. Distributions on the positive integers.

3. Distributions on the reals.

4. Multi-dimensional observations: joint and marginal distributions.

5. Moments, mean and standard deviation.

6. The characteristic function.

7. Weak convergence of probability measures.

Literature

• Ernst Hansen: Sandsynlighedsregning på Målteoretisk Grundlag, HCØ tryk.

Syllabus
See syllabus.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
(a) A number of mandatory assignments during the course. These assignments must be passed in order to take the exam.

(b) A 30 minutes oral exam. External examiner, grades according to the 13-point marking scale.

Examination only when the course has been taught. Examination in opposition terms only after acceptance from the Study board.

Expected working hours
The teaching method is based on three phase model.

(a) Forelæsninger (25 timer).
(b) Eksaminatorier (25 timer).
Educational activities

Language
No recorded information about the language used in the course.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.