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)
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)
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)
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)
Mi, 16-17h, HS II, Albertstr. 23b
Teacher: David Criens, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt
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)
Mo, 14-16h, Raum 232, Ernst-Zermelo-Str. 1
Teacher: Peter Pfaffelhuber
Assistant: Jakob Stiefel
general:
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)
Fr, 13-14h, HS II, Albertstr. 23b
Teacher: David Criens, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt
Fr, 12-13h, HS II, Albertstr. 23b
Teacher: Harald Binder, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt, Jens Timmer
Lecture: Mo, Mi, 12-14h, HS II, Albertstr. 23b
Teacher: Peter Pfaffelhuber
Assistant: Moritz Ritter
general:
Compulsory Elective in Mathematics (BSc21)
Lecture: Do, 12-14h, HS Weismann-Haus, Albertstr. 21a
Teacher: Peter Pfaffelhuber
Assistant: Jakob Stiefel
general:
Compulsory Elective in Mathematics (BSc21)
Fr, 13-14h, HS II, Albertstr. 23b
Teacher: David Criens, Peter Pfaffelhuber
Fr, 12-13h, HS II, Albertstr. 23b
Teacher: Harald Binder, Peter Pfaffelhuber, Jens Timmer
Mo, 10-12h, HS 00-036, Georges-Köhler-Allee 101
Teacher: Peter Pfaffelhuber
Assistant: Jakob Stiefel
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)
Fr, 13-14h, HS II, Albertstr. 23b
Teacher: Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt
Fr, 12-13h, HS II, Albertstr. 23b
Teacher: Harald Binder, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt, Jens Timmer
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)
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
Fr, 13-14h, HS II, Albertstr. 23b
Teacher: Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt
Fr, 12-13h, HS II, Albertstr. 23b
Teacher: Harald Binder, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt, Jens Timmer
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)
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)
Fr, 13-14h, -, -
Teacher: Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt
Teacher: Peter Pfaffelhuber
Assistant: Jakob Stiefel
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
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)
Fr, 13-14h, , online
Teacher: Peter Pfaffelhuber, Philipp Harms, Angelika Rohde, Thorsten Schmidt
Fr, 12-13h, , online
Teacher: Harald Binder, Philipp Harms, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt, Jens Timmer
Lecture: Mo, Mi, 10-12h, SR 127, Ernst-Zermelo-Str. 1
Teacher: Peter Pfaffelhuber
Assistant: Jakob Stiefel
general:
Compulsory Elective in Mathematics (BSc21)
Fr, 13-14h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Philipp Harms, Angelika Rohde, Thorsten Schmidt, Peter Pfaffelhuber
Teacher: Peter Pfaffelhuber
Assistant: Timo Enger
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
Lecture: Mi, Mo, 12-14h, HS II, Albertstr. 23b
Teacher: Peter Pfaffelhuber
Assistant: Timo Enger
general:
Compulsory Elective in Mathematics (BSc21)
Fr, 13-14h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Philipp Harms, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt
Fr, 12-13h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Harald Binder, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt, Jens Timmer, Philipp Harms
Do, 11-12h, Raum 232, Ernst-Zermelo-Str. 1
Teacher: Peter Pfaffelhuber
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)
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)
Fr, 13-14h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Philipp Harms, Peter Pfaffelhuber, Angelika Rohde, Thorsten Schmidt
Fr, 12-13h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Harald Binder, Peter Pfaffelhuber, Angelika Rohde, Jens Timmer