Time and place

Lecture: Di, Do, 10-12h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined and announced in class
Programming exercise: 2 hours, date to be determined

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

Teaching

Teacher: N.N., Peter Pfaffelhuber, Diyora Salimova
Assistant: Samuel Ayomide Adeosun
Language: in English

Content

This course provides an introduction into the basic concepts, notions, definitions and results in probability theory, numerics and optimization, accompanied with programming projects in Python. Besides deepen mathematical skills in principle, the course lays the foundation of further classes in these three areas.

Previous knowledge

None that go beyond admission to the degree programme.

Usability

Basics in Applied Mathematics (MScData24)

Time and place

Lecture: Mo, 16-18h, HS II, Albertstr. 23b
Exercise session: Mi, 16-18h, HS II, Albertstr. 23b

The requirements for examinations, assessments and coursework are set out in the latest updates to the module handbooks, which will be published from the end of October as part of the annotated course catalogue.

Teaching

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

Previous knowledge

Analysis, Linear Algebra

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Specialisation Module (MSc14)
Elective (MSc14)
Elective in Data (MScData24)

Time and place

Di, 12-14h, SR 127, Ernst-Zermelo-Str. 1

Cannot be credited together with Prorgramming Exercises in Stochastics in Python.

Teaching

Teacher: Peter Pfaffelhuber
Assistant: Samuel Ayomide Adeosun

Content

This course is designed for students without prior knowledge in programming, but students who have already taken a first programming course might benefit as well . We will start with basic syntax and the standard library of python, including data types, functions, loops, regular expressions, and interacting with the operating system. For data analysis we learn dataframes using packages such as pandas (and relatives), see how we can interact with freely available APIs, make plots using matplotlib, and use numpy and scipy for standard procedures including numerical computations.

Within this course, you will pick a programming task of your interest, and implement your ideas based on your gained knowledge.

Previous knowledge

none

Usability

Elective (MScData24)
Computer Exercise (2HfB21, MEH21, MEB21)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

29.09.–02.10.; begins on 29.09. at 10h15 in HS Physiologie.

Teaching

Teacher: Peter Pfaffelhuber
Assistant: Samuel Ayomide Adeosun
Language: in German

Content

Optional offer for first-year students of mathematics: The pre-course gives a taste of studying mathematics and is intended to make it easier to get started, but it is not a prerequisite for the degree programme.

Time and place

Exercise session: Do, 12-14h, SR 218, Ernst-Zermelo-Str. 1, first appointment is on October 15.
Lecture: asynchronous (videos)

• The first in person activity of this lecture are the exercises on Wednesday, 15.10. at 10 h.
• 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.

Teaching

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

Content

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.

Previous knowledge

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

Usability

Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Time and place

Lecture: Mi, 14-16h, HS II, Albertstr. 23b, Do, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined and announced in class

Teaching

Teacher: David Criens
Assistant: Samuel Ayomide Adeosun
Language: in English

Content

This lecture builds the foundation of one of the key areas of probability theory: stochastic analysis. We start with a rigorous construction of the It^o integral that integrates against a Brownian motion (or, more generally, a continuous local martingale). In this connection, we learn about It^o's celebrated formula, Girsanov’s theorem, representation theorems for continuous local martingales and about the exciting theory of local times. Then, we discuss the relation of Brownian motion and Dirichlet problems. In the final part of the lecture, we study stochastic differential equations, which provide a rich class of stochastic models that are of interest in many areas of applied probability theory, such as mathematical finance, physics or biology. We discuss the main existence and uniqueness results, the connection to the martingale problem of Stroock-Varadhan and the important Yamada-Watanabe theory.

Previous knowledge

Probability Theory I and II (Stochastic Processes)

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Specialisation Module (MSc14)
Elective (MSc14)
Advanced Lecture in Stochastics (MScData24)
Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Time and place

Do, 14-16h, PC-Pool Raum -100, Hermann-Herder-Str. 10

Teaching

Teacher: Carola Sophia Heinzel
Assistant: Samuel Ayomide Adeosun
Language: in English

Content

This course introduces the foundational concepts and practical skills necessary for understanding and implementing machine learning models, with a particular focus on deep learning and neural networks. Students will progress from basic programming skills in Python , with a focus on the PyTorch library, to advanced topics such as training multi-layer perceptrons, optimization techniques, and transformer architectures. By the end of the course, participants will have the ability to implement and analyze neural networks, apply optimization strategies, and understand modern transformer-based models for tasks such as text generation and time series analysis.

Previous knowledge

Basic knowledge in programming and basic knowledge in stochastics.

Usability

Computer Exercise (2HfB21, MEH21, MEB21)
Elective (Option Area) (2HfB21)
Supplementary Module in Mathematics (MEd18)
Elective (MSc14)
Elective (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Time and place

Q&A sesssion / flipped classroom: Mo, 10-12h, HS II, Albertstr. 23b
Exercise session: Mi, 12-14h, SR 127, Ernst-Zermelo-Str. 1
Lecture: asynchronous (videos)

Teaching

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

Content

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.

Previous knowledge

Required: Probability Theory I

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Applied Mathematics (MSc14)
Mathematics (MSc14)
Specialisation Module (MSc14)
Elective (MSc14)
Advanced Lecture in Stochastics (MScData24)
Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Time and place

Oral exam 28.02.

Teaching

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

Content

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.

Previous knowledge

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

Usability

Elective in Data (MScData24)

Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.

Time and place

Lecture: Mo, 12-14h, HS II, Albertstr. 23b
Exercise session: Mi, 16-18h, SR 127, Ernst-Zermelo-Str. 1

Teaching

Teacher: Peter Pfaffelhuber
Assistant: Samuel Ayomide Adeosun

Usability

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

Time and place

Lecture: Mo, 10-12h, HS 1098, KG I

Teaching

Teacher: Ernst August v. Hammerstein
Assistant: Samuel Ayomide Adeosun