Elementary Probability Theory I
Lecture: Fr, 10-12h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, every other week, various dates
Sit-in exam: date to be announced
Requirements on examinations, assessments and coursework will be described in the supplements of the module handbooks to be published as part of the course cataloque by end of October.
Teacher: Thorsten Schmidt
Assistant: Simone Pavarana
Language: in German
Stochastic is, to put it loosely, the “mathematics of chance”, about which---possibly contrary to first impressions---many precise and not at all random statements can be formulated and proven. The aim of the lecture is to give an introduction to stochastic modeling, to explain some basic concepts and results of Stochastic and to illustrate them with examples. It is also intended as a motivating preparation for the lecture “Probability Theory” in the summer semester, especially for students in the B.Sc. in Mathematics. Topics covered include: Discrete and continuous random variables, probability spaces and measures, combinatorics, expected value, variance, correlation, generating functions, conditional probability, independence, weak law of large numbers, central limit theorem. The lecture Elementary Probability Theory~II in the summer semester will mainly be devoted to statistical topics. If you are interested in a practical, computer-supported implementation of individual lecture contents, participation in the regularly offered practical excercise “Praktischen Übung Stochastik" is also recommended (in parallel or subsequently).
Required: Linear Algebra I, Analysis I and II. \
Note that Linear Algebra I can be attended in parallel.
Elementary Probabilty Theory (2HfB21, MEH21)
Elementary Probability Theory I (BSc21, MEB21, MEdual24)
Lecture: Mi, 12-14h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Teacher: Thorsten Schmidt
Assistant: Simone Pavarana
Language: in English
In this lecture we will study new and highly efficient tools from machine learning which are applied to stochastic problems. This includes neural SDEs as a generalisation of stochastic differential equations relying on neural networks, transformers as a versatile tool not only for languages but also for time series, transformers and GANs as generator of time series and a variety of applications in Finance and insurance such as (robust) deep hedging, signature methods and the application of reinforcement learning.
The prerequisites are stochastics, for some parts we will require a good understanding of stochastic processes. A (very) short introduction will be given in the lectures – so for fast learners it would be possible to follow the lectures even without the courses on stochastic processes.
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective in Data (MScData24)