### Instruction

Name | Cr | Method of study | Time | Location | Organiser |
---|---|---|---|---|---|

Probability theory I | 5 Cr | Lecture Course | 3.9.2019 - 17.10.2019 | ||

Probability theory I | 5 Cr | Lecture Course | 4.9.2018 - 18.10.2018 | ||

Probability theory I | 5 Cr | General Examination | 8.8.2018 - 8.8.2018 | ||

Probability theory I | 5 Cr | General Examination | 13.6.2018 - 13.6.2018 | ||

Probability theory I | 5 Cr | General Examination | 23.5.2018 - 23.5.2018 | ||

Probability theory I | 5 Cr | General Examination | 14.3.2018 - 14.3.2018 | ||

Probability theory I | 5 Cr | General Examination | 10.1.2018 - 10.1.2018 | ||

Probability theory I | 5 Cr | Lecture Course | 5.9.2017 - 17.10.2017 |

### Target group

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.

### Prerequisites

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

### Learning outcomes

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

### Timing

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

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

### Contents

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

### Activities and teaching methods in support of learning

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

### Study materials

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

### Assessment practices and criteria

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

### Recommended optional studies

Vector analysis II, Probability II.

### Completion methods

Exam, other methods will be described later