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Functional Analysis
Lecturer: Guofang Wang
Language: in English
Lecture: Mo, Mi, 12-14h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined and announced in class
Sit-in exam: date to be announced
Attention: Change of time and room!
Linear functional analysis, which is the subject of the lecture, uses concepts of linear algebra such as vector space, linear operator, dual space, scalar product, adjoint map, eigenvalue, spectrum to solve equations in infinite-dimensional function spaces, especially linear differential equations. The algebraic concepts have to be extended by topological concepts such as convergence, completeness and compactness.
This approach was developed at the beginning of the 20th century by Hilbert, among others, and is now part of the methodological foundation of analysis, numerics and mathematical physics, in particular quantum mechanics, and is also indispensable in other mathematical areas.
Linear Algebra I+II, Analysis I–III
Elective in Data
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Probability Theory
Lecturer: Thorsten Schmidt
Language: in English
Lecture: Fr, 8-10h, HS II, Albertstr. 23b, Do, 12-14h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, date to be determined and announced in class
Sit-in exam: date to be announced
The problem of axiomatising probability theory was solved by Kolmogorov in 1933: a probability is a measure of the set of all possible outcomes of a random experiment. From this starting point, the entire modern theory of probability develops with numerous references to current applications.
The lecture is a systematic introduction to this area based on measure theory and includes, among other things, the central limit theorem in the Lindeberg-Feller version, conditional expectations and regular versions, martingales and martingale convergence theorems, the strong law of large numbers and the ergodic theorem as well as Brownian motion.
necessary: Analysis I+II, Linear Algebra I, Elementary Probability Theory I
useful: Analysis III
Advanced Lecture in Stochastics
Elective in Data
Probability Theory III: Stochastic Analysis
Lecturer: Angelika Rohde
Language: in English
Lecture: Di, Do, 12-14h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined and announced in class
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.
Probability Theory I and II (Stochastic Processes)
Advanced Lecture in Stochastics
Elective in Data
Algorithmic Aspects of Data Analytics and Machine Learning
Lecturer: Sören Bartels
Language: in English
Lecture: Mo, 12-14h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined and announced in class
The lecture addresses algorithmic aspects in the practical realization of mathematical methods in big data analytics and machine learning. The first part will be devoted to the development of recommendation systems, clustering methods and sparse recovery techniques. The architecture and approximation properties as well as the training of neural networks are the subject of the second part. Convergence results for accelerated gradient descent methods for nonsmooth problems will be analyzed in the third part of the course. The lecture is accompanied by weekly tutorials which will involve both, practical and theoretical exercises.
Lectures "Numerik I, II" or lecture "Basics in Applied Mathematics"
Elective in Data
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Introduction to Theory and Numerics of Stochastic Differential Equations
Lecturer: Diyora Salimova
Language: in English
Lecture: Mi, 12-14h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined and announced in class
Elective in Data
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Mathematical Physics II
Lecturer: Chiara Saffirio
Language: in English
Lecture: Mo, 14-16h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined and announced in class
Elective in Data
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Mathematical Time Series Analysis II
Lecturer: Rainer Dahlhaus
Language: in English
Lecture: Do, 10-12h, SR 127, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined and announced in class
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.
Elective in Data
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Numerical Optimization
Lecturer: Moritz Diehl
Language: in English
Tutorial / flipped classroom: Di, 14-16h, HS II, Albertstr. 23b
Sit-in exam: date to be announced
The aim of the course is to give an introduction into numerical methods for the solution of optimization problems in science and engineering. The focus is on continuous nonlinear optimization in finite dimensions, covering both convex and nonconvex problems. The course divided into four major parts:
The course is organized as inverted classroom based on lecture recordings and a lecture manuscript, with weekly alternating Q&A sessions and exercise sessions. The lecture is accompanied by intensive computer exercises offered in Python (6 ECTS) and an optional project (3 ECTS). The project consists in the formulation and implementation of a self-chosen optimization problem or numerical solution method, resulting in documented computer code, a project report, and a public presentation. Please check the website for further information.
necessary: Analysis I–II, Linear Algebra I–II
useful: Introduction to Numerics
Elective in Data
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Please note the registration modalities for the individual seminars published in the course catalogue: As a rule, places are allocated at the preliminary meeting at the end of the summer semester lecture period. You must then register for the examination in HISinOne; the registration period is expected to run from 1 March to 15 April 2026.
Seminar: Approximation Properties of Deep Learning
Lecturer: Diyora Salimova
Language: Talk/participation possible in German and English
Seminar: Mi, 14-16h, SR 226, Hermann-Herder-Str. 10
Preregistration: by e-mail to Diyora Salimova
Preliminary Meeting
Preparation meetings for talks: Dates by arrangement
Elective in Data
Mathematical Seminar
Seminar on probability theory
Lecturer: Angelika Rohde
Language: Talk/participation possible in German and English
Elective in Data
Mathematical Seminar
Seminar: Medical Data Science
Lecturer: Harald Binder
Language: Talk/participation possible in German and English
Seminar: Mi, 10:15-11:30h, HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26
Preregistration:
Preliminary Meeting HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26
In HISinOne: no course registration, but exam registration until 8 October 2025.
To answer complex biomedical questions from large amounts of data, a wide range of analysis tools is often necessary, e.g. deep learning or general machine learning techniques, which is often summarized under the term ``Medical Data Science''. Statistical approaches play an important rôle as the basis for this. A selection of approaches is to be presented in the seminar lectures that are based on recent original work. The exact thematic orientation is still to be determined.
Good knowledge of probability theory and mathematical statistics.
Elective in Data
Mathematical Seminar
Seminar: Data-Driven Medicine from Routine Data
Lecturer: Nadine Binder
Language: Talk/participation possible in German and English
Seminar: Di, 16:30-18h, HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26
Preregistration: by e-mail to Nadine Binder
Preliminary Meeting 05.02., 16:30, HS Medizinische Biometrie, 1. OG, Stefan-Meier-Str. 26
Note: Only for the degree programme "Mathematics in Data and Technology"
Imagine being able to use routine data such as diagnoses, lab results, and medication plans to answer medical questions in innovative ways and improve patient care. In this seminar, we will learn to identify relevant data, understand suitable analysis methods, and what to consider when applying them in practice. Together, we will analyze scientific studies on routine data and discuss clinical questions, the methods used, and their feasibility for implementation.
What makes this seminar special: Medical and mathematics students collaborate to understand scientific studies from both perspectives. When possible, you will work in pairs (or individually if no pair can be formed) to analyze a study from your respective viewpoints and prepare related presentations. You may test available programming code or develop your own approaches to replicate the methods and apply them to your own questions. The pairs can be formed during the preliminary meeting.
Elective in Data
Mathematical Seminar