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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
Mathematical Concentration
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Mathematical Logic
Lecturer: Markus Junker
Language: in German
Lecture: Mo, Mi, 14-16h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined and announced in class
Sit-in exam: date to be announced
This introductory course in mathematical logic consists of several parts. It the basics of predicate logic and a brief introduction to model theory and the axiom system as well as the axiom system of set theory. The aim of the lecture is to explain the recursion-theoretical content of the predicate calculus, in particular the so-called Peano-arithmetic and Gödel's incompleteness theorems.
Basic knowledge of mathematics from first semester lectures
Mathematical Concentration
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
Mathematical Concentration
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Topology
Lecturer: Heike Mildenberger
Assistant: Simon Klemm
Language: in German
Lecture: Di, Do, 10-12h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined and announced in class
Sit-in exam: date to be announced
A topological space consists of a basic set \(X\) and a family of open subsets of the basic set, which is called topology on \(X\). Examples over the basic sets \(\mathbb R\) and \({\mathbb R}^n\) are given in the analysis lectures. The mathematical subject \glqq{}Topology\grqq\ is the study of topological spaces and the investigation of topological spaces. Our lecture is an introduction to set-theoretic and algebraic topology.
Analysis I and II, Linear Algebra I
Mathematical Concentration
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Reading courses
Lecturer: All professors and 'Privatdozenten' of the Mathematical Institute
Language: Talk/participation possible in German and English
In a reading course, the material of a four-hour lecture is studied in supervised self-study. In rare cases, this may take place as part of a course; however, reading courses are not usually listed in the course catalog. If you are interested, please contact a professor or a private lecturer before the start of the course; typically, this will be the supervisor of your Master's thesis, as the reading course ideally serves as preparation for the Master's thesis (both in the M.Sc. and the M.Ed. programs).
The content of the reading course, the specific details, and the coursework requirements will be determined by the supervisor at the beginning of the lecture period. The workload should be equivalent to that of a four-hour lecture with exercises.
Reading Course
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.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"
Supplementary Module in Mathematics
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
Supplementary Module in Mathematics
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
Supplementary Module in Mathematics
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.
Supplementary Module in Mathematics
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
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Mathematics Education ‒ Functions and Analysis
Lecturer: Jürgen Kury
Language: in German
Seminar: Mi, 14-17h, SR 404, Ernst-Zermelo-Str. 1
Exemplary implementations of the theoretical concepts of central mathematical thought processes such as concept formation, modeling, problem solving and reasoning for the content areas of functions and analysis. \\ Barriers to understanding, pre-concepts, basic ideas, specific difficulties for the content areas of functions and analysis. \\ Fundamental possibilities and limitations of media, in particular of computer-aided mathematical tools mathematical tools and their application for the content areas of functions and analysis. Analysis of individual mathematical learning processes and errors as well as development individual support measures for the content areas of functions and analysis.
Required: Introduction to Mathematics Education, Knowledge about analysis and numerics
Mathematics Education for Specific Areas of Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Mathematics Education ‒ Probability Theory and Algebra
Lecturer: Katharina Böcherer-Linder
Language: in German
Seminar: Di, 9-12h, SR 226, Hermann-Herder-Str. 10
Exemplary implementations of the theoretical concepts of central mathematical thought processes such as concept formation, modeling, problem solving and reasoning for the content areas of stochastics and algebra. \\ Barriers to understanding, pre-concepts, basic ideas, specific difficulties for the content areas of stochastics and algebra.\ Basic possibilities and limitations of media, especially computer-based mathematical tools and their mathematical tools and their application for the content areas of stochastics and algebra. and algebra. \\ Analysis of individual mathematical learning processes and errors as well as development individual support measures for the content areas of stochastics and algebra.
Required: Introduction to Mathematics Education, knowledge from stochastics and algebra.
Mathematics Education for Specific Areas of Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Mathematics education seminar: High School Maths = University Maths ± x
Lecturer: Holger Dietz
Language: in German
Seminar: Do, 14-17h, -, -
As a high school student, you have no idea what it means to study mathematics. While studying mathematics at the university, the imagination of what it means to teach mathematics at school is similarly vague . This seminar would like to provide concrete insights into the practice of math teaching and tries to build on experiences e.g. B. from the practical semester.
Selected contents and aspects of mathematics lessons (from worksheet to the extension of number systems) are analyzed and questioned – not only from the point of view of the scientist, but also from the point of view of the lecturers, teachers, pupils. Mathematically simple topics often hide unexpected didactic challenges. Therefore, in addition to dealing with existing content and framework conditions, teaching should also be planned and – if possible – carried out at the school.
Basic lectures
Supplementary Module in Mathematics Education
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Mathematics education seminars at Freiburg University of Education
Lecturer: Lecturers of the University of Education Freiburg
Language: in German
For the module "Fachdidaktische Entwicklung", suitable courses can also be completed at the PH Freiburg if places are available there. Please check with Ms. Böcherer-Linder whether courses are suitable, and with the lecturers whether places are available. Courses are usually offered in German.
Supplementary Module in Mathematics Education
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Module "Research in Mathematics Education"
Lecturer: Lecturers of the University of Education Freiburg, Anselm Strohmaier
Language: in German
Part 1: Seminar 'Development Research in Mathematics Education ‒ Selected Topics': Mo, 14-16h, Mensa 3 / Zwischendeck SR 032, PH Freiburg, – please refer to the PH Freiburg course catalogue for any last-minute time or room changes.
Part 2: Seminar 'Research Methods in Mathematics Education': Mo, 10-13h, Mensa 3 / Zwischendeck SR 032, PH Freiburg, –please refer to the PH Freiburg course catalogue for any last-minute time or room changes.
Part 3: Master's thesis seminar: Development and Optimisation of a Research Project in Mathematics Education Appointments by arrangement
Registration: see course descriptions
Dates and rooms can be found in the course catalogue of the PH Freiburg
The three related courses of the module prepare students for an empirical Master thesis in mathematics didactics. The course is jointly designed by all professors at the PH with mathematics didactics research projects at secondary levels 1 and 2 and is carried out by one of these researchers. Afterwards, students have the opportunity to start Master thesis with one of these supervisors - usually integrated into larger ongoing research projects.
The first course of the module provides an introduction to strategies of empirical didactic research (research questions, research status, research designs). Students deepen their skills in scientific research and the evaluation of subject-specific didactic research. In the second course (in the last third of the semester) students are introduced to central qualitative and quantitative research methods through concrete work with existing data (interviews, student products, experimental data), students are introduced to central qualitative and quantitative research methods. The third course is an accompanying seminar for the Master thesis.
The main objectives of the module are the ability to receive mathematics didactic research in order to didactic research to clarify questions of practical relevance and to plan an empirical mathematics didactics Master thesis. It will be held as a mixture of seminar, development of research topics in groups and active work with research data. Recommended literature will be depending on the research topics offered within the respective courses. The parts can also be attended in different semesters, for example part~1 in the second Master semester and part~2 in the compact phase of the third Master semester after the practical semester.
Research in Mathematics Education
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Introduction to Programming for Science Students
Lecturer: Ludwig Striet
Language: in German
Lecture: Mo, 16-18h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates
none
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Computer exercises in Numerics
Lecturer: Patrick Dondl
Language: in German
In the practical exercises accompanying the Numerics II lecture, the algorithms developed and analysed in the lecture are implemented in practice and tested experimentally. The implementation is carried out in the programming languages Matlab, C++ and Python. Elementary programming skills are assumed.
See the lecture Numerics II.
In addition elementary programming knowledge.
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Computer Exercises
Lecturer: Peter Pfaffelhuber
Language: in English
Mo, 12-14h, SR 127, Ernst-Zermelo-Str. 1
Supplementary Module in Mathematics
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: Algebraic D-Modules
Lecturer: Annette Huber-Klawitter
Assistant: Ben Snodgrass
Language: Talk/participation possible in German and English
Seminar: Mo, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Preliminary Meeting
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.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
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Seminar on representation theory
Lecturer: Wolfgang Soergel
Language: Talk/participation possible in German and English
Seminar: Do, 10-12h, SR 125, Ernst-Zermelo-Str. 1
Preregistration: by e-mail to Wolfgang Soergel
Preliminary Meeting
Preparation meetings for talks: Dates by arrangement
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Seminar: Strong Homologies, Derived Limites, and Set Theory
Lecturer: Heike Mildenberger
Assistant: Maxwell Levine
Language: Talk/participation possible in German and English
Seminar: Di, 16-18h, SR 125, Ernst-Zermelo-Str. 1
Preliminary Meeting
Preparation meetings for talks: Dates by arrangement
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Seminar on probability theory
Lecturer: Angelika Rohde
Language: Talk/participation possible in German and English
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Seminar: String Topology
Lecturer: Nadine Große
Assistant: Maximilian Stegemeyer
Language: Talk/participation possible in German and English
Seminar: Di, 12-14h, SR 125, Ernst-Zermelo-Str. 1
Preliminary Meeting
Preparation meetings for talks: Dates by arrangement
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.Seminar: Topics in the Calculus of Variations
Lecturer: Patrick Dondl, Guofang Wang
Language: Talk/participation possible in German and English
Seminar: Mi, 16-18h, SR 125, Ernst-Zermelo-Str. 1
Preliminary Meeting SR 125, Ernst-Zermelo-Str. 1
Preparation meetings for talks: Dates by arrangement
In HISinOne: no course registration, but exam registration until 15 April 2026.
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.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.
Supplementary Module in Mathematics
Please refer to the Supplements to the Module Handbooks for the number of ECTS credits.