Mathematik - SoSe 2026

There are several model for random graphs. The famous G(n,p) model considers a graph with n vertices, where each edge is included independently with probability p. In a different model, the degree of each vertex is prescribed, and we draw uniformly at random a graph with this degree sequence. Finally, there are dynamic models, where vertices arrive one after the other and connect randomly to vertices that are already there. In this seminar we will study such models.

The password for enrollment is RG26.

Course Description

In this seminar, we will explore modern machine learning through the lens of neural networks - flexible and highly expressive models that underpin many recent advances in artificial intelligence.
We begin with a brief introduction to core concepts in machine learning, including supervised learning, loss functions, and optimization. Building on this foundation, we study several important neural network architectures, including fully connected neural networks, convolutional neural networks, residual networks, and then moving on to modern sequence models. Here we discuss in particular the attention mechanism and the transformer architectures, and discuss their importance for large language models (LLMs).

Registration key

    ML

Die Problemlabs bieten einen Raum zum gemeinsamen Arbeiten und Lernen. Ob ihr Hausaufgaben bearbeitet oder nochmal das Skript nacharbeitet ist dabei ganz euch überlassen.
An mehreren Terminen wird der Raum von ehrenamtlichen Tutor:Innen aus höheren Semestern betreut, so dass ihr bei Fragen oder Unklarheiten die nötige Unterstützung bekommt.

Anmeldeschlüssel: NoProblem

Enrolment key: omsose2026

Credits: 9 ECTS

Format: 4 hours lecture, 2 hours exercise

Target audience: MSc FiMa & Math

Time and Location:

Lectures: Tuesday 10-12, Thursday 10-12 (room B039)

Exercise Sessions: Wednesday 16-18 (room B039)

Modules:

MSc FiMa: 

• PStO 2021: WP12 Advanced Topics in Mathematics A (9 ECTS)
  
• PStO 2019: WP13 Advanced Topics in Mathematics A (9 ECTS)

• WP26 Fortgeschrittene Themen aus der Numerischen Mathematik (9 ECTS)
• WP35 Fortgeschrittene Themen aus der KI und Data Science (9 ECTS)
  

Description:

Optimization is the doctrine for finding the "best" alternative between a set of possible options in terms of a given objective function. The course is devoted to the study of the most widely used optimization methods and their convergence analysis. Throughout the lecture, the students will learn how to select the most suited optimization method for a given problem and to evaluate the expected rate of convergence of the algorithm in that specific scenario. The focus will be continuous optimization, meaning that we will consider problems with continuous variables living in a continuous vector space.

Content:

• basics of optimization;
• first order methods (gradient descent, conjugate gradient, Barzilai-Borwein and Polyak step);
• line search methods (Armijo, nonmonotone);
• second order methods (Newton, Quasi-Newton, Trust-Region);
• constrained optimization (projected gradient method, KKT conditions).
  

Mathematik II (Physik)

Einschreibeschlüssel: 26SSM2

Course Description

In this seminar, we will study one-dimensional stochastic Volterra integral equations with a particular focus on fractional kernels. For this purpose, fundamental concepts in stochastic analysis, such as semimartingales, stochastic integrals and fractional Brownian motion, will be discussed. The aim of this course is to establish the existence and uniqueness of strong solutions under Lipschitz conditions on the drift and diffusion coefficients of the stochastic Volterra equation.

Target Participants

Einschreibeschlüssel: An2S26

Enrolment key: aml26

Credits: 6 ECTS (2SWS lecture + 2SWS exercise)

Modules: 

• MSc FiMa: WP23 „Advanced Topics in Computer and Data Science B” 
  
• MSc Math: WP42 „Überblick über ein aktuelles Forschungsgebiet B” 

Description:

Real-world applications of machine learning require not only a strong theoretical foundation but also a solid knowledge of the methodologies, tools, and heuristics essential for implementing machine learning algorithms. However, the practical aspects of machine learning are often overlooked in mathematics programs. This course bridges that gap by providing students with hands-on experience in implementation and empirical analysis of machine learning algorithms — critical skills for those pursuing careers in data analysis or machine learning.

Content:

A key component of the course is extensive programming in Python, using libraries such as NumPy, Matplotlib, Pandas, and scikit-learn. We will work with real datasets, including MNIST handwritten digits, the Boston Housing dataset, Wine dataset, etc.

This lecture introduces the arbitrage theory of fixed income markets and interest rate/credit derivatives. Topics that are covered include:

• Introduction to interest rates and interest rate derivatives: bonds, various interest rates, swaps, caps, floors, swaptions, market conventions.
• Arbitrage pricing: portfolios, arbitrage, hedging valuation.
• Short-rate models.
• Affine term structure models.
• HJM models.
• Forward measures.
• LIBOR market models.
• Credit risk and Related Contracts.
• Structural Models.
• Reduced-Form Models.

More information about literature and target participants can be found here.

Einschreibeschlüssel: Grund2SS26

Einschreibeschlüssel: LinAlg2S26

pwd: araki

Einschreigeschlüssel: MiQSS26

Enrolment Key: Num2S26

Reading course on the contemporary topic of resurgence theory.

Enrolement key: "Ecalle", after Jean Écalle, the father of resurgence theory.

Wir werden typische Aufgabenstellungen beim Staatsexamen in Analysis behandeln,
Lösungsmethoden besprechen und evtl. noch etwas zugrunde liegende Theorie
wiederholen. Wir beginnen mit dem Themenbereich Funktionentheorie und
arbeiten uns dann zu den
Gewöhnlichen Differentialgleichungen durch.

Sellbsteinschreibung mit Kennwort: stexana