Teacher: Peter Pfaffelhuber
Assistant: Samuel Adeosun
Language: in English

Measure Theory is the foundation of advanced probability theory. In this course, we build on knowledge in analysis and provide all necessary results for later classes in statistics, probabilistic machine learning and stochastic processes. It contains set systems, constructions of measures using outer measures, the integral, and product measures.

Required: Basic courses in analysis, and an understanding of mathematical proofs.

Elective in Data (MScData24)

Time and place

Lecture: Mo, Di, 12-14h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours, various dates

Teacher: Peter Pfaffelhuber
Language: in German

Time and place

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)

Time and place

Questions sesssion / flipped classroom: Mo, 10-12h, HS II, Albertstr. 23b
Letcure (4 hours): asynchronous videos

Teacher: Peter Pfaffelhuber
Assistant: Samuel Adeosun
Language: in English

A stochastic process \((X_t)_{t\in I}\) is nothing more than a family of random variables, where \(I\) is some index set modeling time. Simple examples are random walks, Markov chains, Brownian motion and derived processes. The latter play a particularly important role in the modeling of financial mathematics or questions from the sciences. We will first deal with martingales, which describe fair games. After constructing the Poisson process and Brownian motion, we will focus on properties of Brownian motion. Infinitesimal characteristics of a Markov process are described by generators, which allows a connection to the theory of partial differential equations. Finally, a generalization of the law of large numbers is discussed with the ergodic theorem for stationary stochastic processes. Furthermore, insights are given into a few areas of application, such as biomathematics or random graphs.

Required: Probability Theory I

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)

Time and place

Exercise session: Mi, 10-12h, HS II, Albertstr. 23b

Oral exam 28.02.

Teacher: Peter Pfaffelhuber
Assistant: Samuel Adeosun
Language: in English

Measure Theory is the foundation of advanced probability theory. In this course, we build on knowledge in analysis and provide all necessary results for later classes in statistics, probabilistic machine learning and stochastic processes. It contains set systems, constructions of measures using outer measures, the integral, and product measures.

Required: Basic courses in analysis, and an understanding of mathematical proofs.

Elective in Data (MScData24)

Time and place

Lecture: Mo, 12-14h, HS II, Albertstr. 23b

Teacher: Peter Pfaffelhuber
Assistant: Samuel Adeosun

Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)
Applied Mathematics (MSc14)

Time and place

Mi, 16-17h, HS II, Albertstr. 23b

Teacher: David Criens, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt

Time and place

Fr, 12-13h, SR 404, Ernst-Zermelo-Str. 1

Teacher: Harald Binder, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt, Jens Timmer

Teacher: Peter Pfaffelhuber
Assistant: Jakob Stiefel
general:

Compulsory Elective in Mathematics (BSc21)

Time and place

Mo, 14-16h, Raum 232, Ernst-Zermelo-Str. 1

Teacher: Peter Pfaffelhuber
Assistant: Jakob Stiefel
general:

Time and place

Do, 10-12h, SR 125, Ernst-Zermelo-Str. 1

Teacher: Peter Pfaffelhuber, Thorsten Schmidt
Assistant: Ernst August von Hammerstein

Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)

Time and place

Fr, 13-14h, HS II, Albertstr. 23b

Teacher: David Criens, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt

Time and place

Fr, 12-13h, HS II, Albertstr. 23b

Teacher: Harald Binder, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt, Jens Timmer

Time and place

Lecture: Mo, Mi, 12-14h, HS II, Albertstr. 23b

Teacher: Peter Pfaffelhuber
Assistant: Moritz Ritter
general:

Compulsory Elective in Mathematics (BSc21)

Time and place

Lecture: Do, 12-14h, HS Weismann-Haus, Albertstr. 21a

Teacher: Peter Pfaffelhuber
Assistant: Jakob Stiefel
general:

Compulsory Elective in Mathematics (BSc21)

Time and place

Fr, 13-14h, HS II, Albertstr. 23b

Teacher: David Criens, Peter Pfaffelhuber

Time and place

Fr, 12-13h, HS II, Albertstr. 23b

Teacher: Harald Binder, Peter Pfaffelhuber, Jens Timmer

Time and place

Mo, 10-12h, HS 00-036, Georges-Köhler-Allee 101

Teacher: Peter Pfaffelhuber
Assistant: Jakob Stiefel

Time and place

Do, 10-12h, SR 125, Ernst-Zermelo-Str. 1

Teacher: Peter Pfaffelhuber
Assistant: Timo Enger

Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)

Time and place

Fr, 13-14h, HS II, Albertstr. 23b

Teacher: Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt

Time and place

Fr, 12-13h, HS II, Albertstr. 23b

Teacher: Harald Binder, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt, Jens Timmer

Time and place

Lecture: Do, 10-12h, HS II, Albertstr. 23b
22.03., 10:00-12:00
Sit-in exam (resit) 27.04., 14:00-16:00

Teacher: Peter Pfaffelhuber
Assistant: Timo Enger
general:

Further Chapters in Analysis (MEd18, MEH21, MEdual24)

Time and place

Mo, 12-14h, HS II, Albertstr. 23b
24.02., 00:00-00:00

Teacher: Peter Pfaffelhuber
Assistant: Jakob Stiefel
general:

Applied Mathematics (MSc14)
Mathematical Concentration (MEd18, MEH21)
Compulsory Elective in Mathematics (BSc21)

Teacher: Peter Pfaffelhuber

Time and place

Fr, 13-14h, HS II, Albertstr. 23b

Teacher: Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt

Time and place

Fr, 12-13h, HS II, Albertstr. 23b

Teacher: Harald Binder, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt, Jens Timmer

Time and place

Fr, 11-12h, , online
09.08., 10:00-12:00
Sit-in exam (resit) 22.02., 00:00-00:00

Teacher: Peter Pfaffelhuber
Assistant: Jakob Stiefel
general:

Elementary Probabilty Theory (2HfB21, MEH21)

Time and place

Fr, 10-11h, , online
09.08., 10:00-12:00
Sit-in exam (resit) 22.02., 00:00-00:00

Teacher: Peter Pfaffelhuber
Assistant: Jakob Stiefel
general:

Elementary Probabilty Theory (2HfB21, MEH21)

Teacher: Peter Pfaffelhuber
Assistant: Ernst August von Hammerstein

Supplementary Module in Mathematics (MEd18)

Time and place

Fr, 13-14h, -, -

Teacher: Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt

Teacher: Peter Pfaffelhuber
Assistant: Jakob Stiefel

Time and place

Fr, 12-13h, -, -

Teacher: Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt

Teacher: Peter Pfaffelhuber
Assistant: Jakob Stiefel
general: ,

Elementary Probabilty Theory (2HfB21, MEH21)

Teacher: Peter Pfaffelhuber
Assistant: Timo Enger

Time and place

Fr, 10-12h, Raum 232, Ernst-Zermelo-Str. 1

Teacher: Peter Pfaffelhuber
Assistant: Timo Enger

Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)

Time and place

Fr, 13-14h, , online

Teacher: Peter Pfaffelhuber, Philipp Harms, Angelika Rohde, Thorsten Schmidt

Time and place

Fr, 12-13h, , online

Teacher: Harald Binder, Philipp Harms, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt, Jens Timmer

Time and place

Lecture: Mo, Mi, 10-12h, SR 127, Ernst-Zermelo-Str. 1

Teacher: Peter Pfaffelhuber
Assistant: Jakob Stiefel
general:

Compulsory Elective in Mathematics (BSc21)

Time and place

Fr, 13-14h, SR 404, Ernst-Zermelo-Str. 1

Teacher: Philipp Harms, Angelika Rohde, Thorsten Schmidt, Peter Pfaffelhuber

Teacher: Peter Pfaffelhuber
Assistant: Timo Enger

Time and place

Fr, 12-13h, SR 404, Ernst-Zermelo-Str. 1

Teacher: Harald Binder, Philipp Harms, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt, Jens Timmer

Teacher: Peter Pfaffelhuber
Assistant: Timo Enger

Time and place

Lecture: Mi, Mo, 12-14h, HS II, Albertstr. 23b

Teacher: Peter Pfaffelhuber
Assistant: Timo Enger
general:

Compulsory Elective in Mathematics (BSc21)

Time and place

Fr, 13-14h, SR 404, Ernst-Zermelo-Str. 1

Teacher: Philipp Harms, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt

Time and place

Fr, 12-13h, SR 404, Ernst-Zermelo-Str. 1

Teacher: Harald Binder, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt, Jens Timmer, Philipp Harms

Time and place

Do, 11-12h, Raum 232, Ernst-Zermelo-Str. 1

Teacher: Peter Pfaffelhuber

Time and place

Lecture: Fr, 10-12h, HS Weismann-Haus, Albertstr. 21a
27.02., 10:00-12:00

Teacher: Peter Pfaffelhuber, Simone Hermann
Assistant: Ernst August von Hammerstein
general:

Further Chapters in Analysis (MEd18, MEH21, MEdual24)

Time and place

Lecture: Di, Do, 12-14h, HS Weismann-Haus, Albertstr. 21a
08.03., 10:00-13:00
Sit-in exam (resit) 12.04., 10:00-13:00

Teacher: Peter Pfaffelhuber
Assistant: Simone Hermann
general: ,

Mathematical Concentration (MEd18, MEH21)
Compulsory Elective in Mathematics (BSc21)
Applied Mathematics (MSc14)

Time and place

Fr, 13-14h, SR 404, Ernst-Zermelo-Str. 1

Teacher: Philipp Harms, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt

Time and place

Fr, 12-13h, SR 404, Ernst-Zermelo-Str. 1

Teacher: Harald Binder, Peter Pfaffelhuber, Angelika Rohde, Jens Timmer