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### Description

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.

Differential equations, probability theory

Elements of complex analysis

Construction and analysis of models in form of non-autonomous differential equations, delay-differential equations, stochastic differential equations; single-type and multi-type birth-death processes; semi-large systems

Recommended time/stage of studies for completion: 1. or 2. year

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

This is a course about population models that cannot be properly described or analysed in a purely deterministic way because of the presence of noise. We consider two kinds of noise depending on its origin: The noise may be exogenous, i.e., due to autonomous processes external to the population itself and affecting it by causing population parameters to fluctuate in time. Especially in small populations, the noise may also be endogenous, i.e., due to stochastic demographic in the number of births and deaths within any given interval of time.

Lectures and exercise classes

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

Exam, other methods will be described later

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