Computer exercises in Statistics
Mo, 14-16h, PC-Pool Raum 201, Hermann-Herder-Str. 10
Teacher: Sebastian Stroppel
Language: in German
This computer exercise course is aimed at students who have already attended the lectures Elementary Probability Theory I and II or are attending the second part this semester. Computer-based methods will be discussed to deepen the understanding of the lecture material and demonstrate further application examples. For this purpose, the programming language python is used. After an introduction to python, methods of descriptive statistics and graphical analysis of data will be considered, the numerical generation of random numbers will be explained and parametric and non-parametric tests and linear regression methods will be discussed. Previous knowledge of python and/or programming skills are not required.
Analysis I+II, Linear Algebra I+II, Elementary Probability Theory I+II (part II can be followed in parallel).
Computer Exercise (2HfB21, MEH21, MEB21)
Elective (Option Area) (2HfB21)
Supplementary Module in Mathematics (MEd18)
Elective (MScData24)
Di, 12-14h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Peter Pfaffelhuber
Assistant: Sebastian Stroppel
Language: in English
Lean4 is both, a programming language and an interactive theorem prover. By the latter, we mean software that is able to check mathematical proofs. It is interactive since the software tells you what remains to be proven after every line of code. The course is an introduction to this technique, with examples from various fields of mathematics. Lean4 is special since researchers all over the world are currently building a library of mathematical theories, which contains at the moment around 1.5 million lines of code. I aim to cover basics from calculus, algebra, topology and measure theory in Lean4.
Analysis 1, 2, Linear algebra 1
Computer Exercise (2HfB21, MEH21, MEB21)
Elective (Option Area) (2HfB21)
Supplementary Module in Mathematics (MEd18)
Elective (MSc14)
Elective (MScData24)
Lecture: Mo, Mi, 14-16h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Ernst August v. Hammerstein
Assistant: Sebastian Stroppel
Language: in English
The lecture builds on basic knowledge about Probability Theory. The fundamental problem of statistics is to infer from a sample of observations as precise as possible statements about the data-generating process or the underlying distributions of the data. For this purpose, the most important methods from statistical decision theory such as test and estimation methods are introduced in the lecture. \\ Key words hereto include Bayes estimators and tests, Neyman-Pearson test theory, maximum likelihood estimators, UMVU estimators, exponential families, linear models. Other topics include ordering principles for reducing the complexity of models (sufficiency and invariance). Statistical methods and procedures are used not only in the natural sciences and medicine, but in almost all areas in which data is collected and analyzed This includes, for example, economics (“econometrics”) and the social sciences (especially psychology). However, in the context of this lecture, we will focus less on applications, but---as the name suggests---more on the mathematical justification of the methods.
Required: Probability Theory (in particular measure theory and conditional probabilities/expectations)
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Advanced Lecture in Stochastics (MScData24)
Elective in Data (MScData24)