- Unit Coordinator: Aleksandra Achtelik
- ECTS Credits: 3
- Semester: 1
- Year: 2
- Campus: University of Silesia in Katowice
- Aims:
The aim of the module is to develope all language skills (listening, reading, speaking and writing) and to prepare students for quite easy communication in Polish, necessary while studying in Poland. Students acquire not only linguistic and communicative competence, but also sociocultural: they get to know selected aspects of Polish culture, basic habits and holidays celebrated in Poland, taking into account the pragmatic and sociolinguistic euciency.
Programme includes basic communication situations: greetings and farewells, shopping, ordering food, traveling, etc.
- ECTS Credits: 10
- Semester: 1
- Year: 2
- Campus: Leibniz University Hannover
- Language: English
- Unit Coordinator: Sylvain Rubenthaler
- Programme: InterMaths
- ECTS Credits: 6
- Semester: 1
- Year: 2
- Campus: University of Côte d'Azur
- Language: English
- Delivery: In-class
- Aims:
• This course addresses the basic methods used for simulating random variables and implementing Monte-Carlo and Quasi Monte-Carlo methods.
• Simulation of stochastic processes used in neuroscience, such as Brownian motion and solutions to stochastic differential equations, will be addressed.
• The course will introduce sampling methods in finite dimension, discretization of diffusion processes, strong and weak errors. - Content:
- Simulation
- Monte-Carlo methodes
- Discretization schemes
- Error analysis
- Pre-requisites:
Probability with measure theory, stochastic calculus, programming
- Code: DT0654
- Unit Coordinator: Matthias Schulte
- ECTS Credits: 6
- Semester: 2
- Year: 1
- Campus: Hamburg University of Technology
- Language: English
- Aims:
This course provides an introduction to probability theory and stochastic processes with special emphasis on applications and examples.
The first part covers some important concepts from measure theory, stochastic convergence and conditional expectation, while the second part deals with some important classes of stochastic processes.
- Content:
- Measure and probability spaces
- Integration and expectation
- Types of stochastic convergence
- Law of large numbers
- Central limit theorem
- Radon-Nikodym theorem
- Conditional expectation
- Martingales
- Markov chains
- Poisson processes
- Pre-requisites:
Familiarity with the basic concepts of probability
- Reading list:
- H. Bauer, Probability theory and elements of measure theory, second edition, Academic Press, 1981.
- A. Klenke, Probability Theory: A Comprehensive Course, second edition, Springer, 2014.
- G. F. Lawler, Introduction to Stochastic Processes, second edition, Chapman & Hall/CRC, 2006.
- A. N. Shiryaev, Probability, second edition, Springer, 1996.
