### Opetus

Nimi Op Opiskelumuoto Aika Paikkakunta Järjestäjä
Probability theory I 5 Cr Luentokurssi 3.9.2019 - 17.10.2019
Probability theory I 5 Cr Luentokurssi 4.9.2018 - 18.10.2018
Probability theory I 5 Cr Yleinen tentti 8.8.2018 - 8.8.2018
Probability theory I 5 Cr Yleinen tentti 13.6.2018 - 13.6.2018
Probability theory I 5 Cr Yleinen tentti 23.5.2018 - 23.5.2018
Probability theory I 5 Cr Yleinen tentti 14.3.2018 - 14.3.2018
Probability theory I 5 Cr Yleinen tentti 10.1.2018 - 10.1.2018
Probability theory I 5 Cr Luentokurssi 5.9.2017 - 17.10.2017

### Kohderyhmä

Optional course.

Master's Programme in Mathematics and Statistics is responsible for the course.

The course belongs to the Mathematics and Applied mathematics module.

The course is available to students from other degree programmes.

### Edeltävät opinnot tai edeltävä osaaminen

Analysis I-II, Topology I, Vector analysis I, Measure and integral

### Osaamistavoitteet

The course gives a firm theoretical ground for Probability and introduces some of its classical results

### Ajoitus

Recommended time/stage of studies for completion: 1. year

Term/teaching period when the course will be offered: varying

### Sisältö

Measure theoretic foundations of probability, independence, laws of large numbers, characteristic functions and the central limit theorm, Gaussian measures, recurrence/transience of random walks

### Oppimista tukevat aktiviteetit ja opetusmenetelmät

Lectures and exercise classes, possibly other methods like reading assignments+discussion

### Oppimateriaali

Lecture notes; D. Williams: "Probability with martingales", R. Durrett: "Probability: theory and examples"

### Arviointimenetelmät ja -kriteerit

Exam and excercises, Course will be graded with grades 1-5

### Suositeltavat valinnaiset opinnot

Vector analysis II, Probability II.

### Toteutus

Exam, other methods will be described later