Study programmes of mathematical focus areas
- Not all courses can be offered every year; please refer to the overview of regularly offered lectures.
- The main areas of focus of the individual lecturers can be found on the staff pages and the working group pages.
- In BSc Mathematics and MSc Mathematics, all focus areas (except Didactics of Mathematics) can be chosen equally.
- In the Polyvalent dual major Bachelor and in the MEd Mathematics, theses can be written either in a subject area (mathematics or in the second subject) or in a subject area didactics. In the latter case, the typical course of study is described below.
- In the MSc Mathematics in Data and Technology, in principle all specializations (except didactics of mathematics) can be chosen. However, applied analysis and numerics, mathematical stochastics and financial mathematics, as well as related areas, are particularly suitable.
Last edited by Carolin Mann on 02/04/2026 at 12:00:42.
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This focus area deals with number fields and their generalizations, with the particular aim of gaining insights into the solvability of equations. Due to the wide range of interests covered by this focus area, a variety of study paths are possible. The specific structure of your studies can be discussed at any time with one of the lecturers in this focus area.
In addition to introductory student seminars and advanced student seminars, the focus area offers the following lectures:
- Algebra and Number Theory (in the winter semester)
- Commutative Algebra and Introduction to Algebraic Geometry (in the summer semester)
- Various advanced lectures, e.g., Algebraic Number Theory (every two years in the summer semester), Representation Theory, Algebraic Geometry (offered irregularly)
In addition, there are courses that also belong to the geometry major:
- Function theory (winter semester), Topology (every two years in the summer semester), Differential geometry (winter semester)
- Function theory II (e.g., Riemann surfaces, modular forms), Algebraic topology, Differential topology (offered irregularly)
As a rule, it is advisable to take the courses in the following order:
Bachelor
- Algebra and Number Theory
- Commutative Algebra and Introduction to Algebraic Geometry
- Seminar
Master
- Advanced lecture in algebra (one or more)
- Student Seminar(s)
- In addition to advancing your knowledge, you should also expand your foundation, e.g., by taking Algebra and Number Theory , Commutative Algebra , Function Theory , or Topology .
The lecture Commutative Algebra can also be taken without Algebra and Number Theory. The advanced lectures usually build on Algebra and Number Theory and/or Commutative Algebra. Supplementary knowledge can be acquired through guided self-study ( Scientific Work ).
Prerequisites
- for a bachelor's thesis: usually two courses (lectures, introductory student seminars, advanced student seminars) from the area of specialisation.
- for a master's thesis: additionally two to three courses from the area of specialisation.
Last edited by Carolin Mann on 02/04/2026 at 12:01:55.
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This focus area also covers the study of multi-valued functions and solutions to differential equations. Specialisation in the field of Analysis usually includes the following courses. Alternative study plans should be discussed with one of the lecturers in the focus area.
Bachelor's degree:
- 3rd semester: Analysis III
- 4th semester: Functional Analysis
- 5th and 6th semesters: one or two advanced lectures in analysis, such as Introduction to Partial Differential Equations , Partial Differential Equations , Variational Calculus (all offered irregularly)
- 6th semester: Seminar and bachelor's thesis
Master's degree:
(if starting in the winter semester; otherwise corresponding changes)
- 7th and 8th semesters: advanced lectures in analysis such as Geometric Analysis , Geometric Measure Theory , Partial Differential Equations II (all offered irregularly)
- 8th and 9th semesters: one seminar each
- 10th semester: Master's thesis
Useful additions to the Bachelor's and Master's programmes are the lectures Curves and Surfaces (every two years in the summer semester), Differential Geometry and Function Theory (both in the winter semester).
Last edited by Carolin Mann on 02/04/2026 at 12:03:02.
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In this focus area, methods for the systematic, computational solution of mathematical problems are designed. A specialisation in the field of Applied Analysis / Numerics usually includes the following courses. Alternative study programmes should be discussed with one of the lecturers in the focus area.
Bachelor's degree:
- 3rd semester: Analysis III , Numerical Methods I
- 4th semester: Functional Analysis , Numerical Methods II , Numerical Methods for Differential Equations
- 5th semester: Introduction to the Theory and Numerical Methods of Partial Differential Equations
- 6th semester: Student seminar and bachelor's thesis, and one further lecture, e.g. Mathematical Modeling, or Algorithmic Data Analysis
Master's degree:
(if starting in the winter semester; otherwise, corresponding changes)
- 7th and 8th semesters: advanced lectures such as Theory and Numerics for Partial Differential Equations , Nonlinear Functional Analysis (all offered irregularly)
- 9th semester: Special lecture or Scientific Work ; seminar from the area of specialisation
- 10th semester: Master's thesis
For the numerically oriented lectures, participation in the practical exercises offered is recommended. Students who are more interested in theory are advised to take additional lectures in one of the areas Theory of partiel Differential Equations, Variational Calculus, Differential Geometry and Optimisation in their 7th–9th semesters.
Last edited by Carolin Mann on 02/04/2026 at 12:04:01.
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For example, it investigates the curvature properties of curves and surfaces and their higher-dimensional generalizations. A specialisation in geometry and topology usually includes the following courses. Alternative study programmes should be discussed with one of the lecturers in the focus area.
Bachelor's degree:
- 4th semester: Topology or Curves and Surfaces or _ Functional Analysis_
- 5th semester: depending on the offer Differential Geometry, Algebraic Topology
- 6th semester: Topology or Functional Analysis (if not taken in the 4th semester)
- 5th/6th semester: Student seminar and bachelor's thesis
Master's degree:
(if starting in the winter semester; otherwise corresponding changes)
- 7th–9th semester: one or two advanced lectures from the focus area, e.g., Differential Geometry II (in one of its various forms), Differential Topology , Algebraic Topology (all offered irregularly). As an alternative to a lecture: in the 9th semester, a reading course.
- 8th–9th semester: one or two student seminars from the area of specialisation
- 9th–10th semester: Master's thesis
Depending on your interests, useful additions to the Bachelor's and Master's programmes include: Function Theory (winter semester), lectures on analysis, lectures on algebraic geometry and Lie groups, lectures on mathematical physics.
Last edited by Carolin Mann on 02/04/2026 at 12:05:10.
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Mathematical logic formulates, among other things, the axiomatic laws of mathematics and examines the provability of mathematical statements. Specialisation in the field of mathematical logic usually includes the following courses. Alternative study programmes should be discussed with the academic advisor of the Department of Mathematical Logic or one of the lecturers in the specialisation area.
Bachelor's degree:
- 4th semester: Mathematical Logic
- 5th Semester: (depending on availability) Set Theory or Model Theory
- 6th semester: Student seminar and bachelor's thesis
The lecture Mathematical Logic, which is offered regularly in the summer semester, is the minimum requirement for a bachelor's thesis; a student seminar and/or an additional lecture in the field of mathematical logic is desirable.
As a rule, the lectures Set Theory and Model Theory alternate in the winter semester; sometimes both are held. In the summer semester, there are sometimes follow-up lectures.
Master's degree:
(if starting in the winter semester; otherwise corresponding changes)
- 7th and 8th semesters: If not already taken in the bachelor's programme: Set Theory and/or Model Theory and, if offered, advanced lectures in mathematical logic, otherwise reading courses. Supplementary: advanced lectures in pure mathematics, e.g., Commutative Algebra, Topology, Algebraic Number Theory
- 9th semester: Scientific Work (reading course), student seminar in the area of specialisation
- 10th semester: Master's thesis
Useful additions are applications, for example advanced algebra, algebraic geometry, set-theoretical topology.
Last edited by Carolin Mann on 02/04/2026 at 12:06:07.
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Stochastics models random events and develops methods for optimally dealing with randomness or large amounts of data. A specialisation in Mathematical Stochastics and Financial Mathematics usually includes the following courses. Alternative study paths are best discussed with the academic advisor of the Department of Mathematical Stochastics or one of the lecturers in the specialisation area.
Bachelor's degree:
- 3rd semester: Stochastics I , Analysis III
- 4th semester: Probability Theory Useful additions are Stochastics II and the Practical Exercise in Stochastics .
- 5th semester: Probability Theory II (formerly: Stochastic Processes ) or Probabilistic Machine Learning
- 6th semester: Student seminar and bachelor's thesis
The measure theory taught in the Analysis III lecture is a prerequisite for understanding the advanced stochastics lectures (except Probabilistic Machine Learning) starting with Probability Theory. Measure theory is usually briefly reviewed in the Probability Theory lecture.
Master's degree:
(if starting in the winter semester; otherwise, corresponding changes)
- 7th semester: If offered: Mathematical Statistics or Probability Theory II, if not already taken in the bachelor's programme
- 8th semester: Probability Theory III (formerly: Stochastic Integration and Financial Mathematics or Stochastic Analysis )
- 9th semester: Scientific Work (reading course), student seminar from the area of specialisation
- 10th semester: Master's thesis
Last edited by Carolin Mann on 02/04/2026 at 12:08:31.
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Mathematics education deals with the learning and teaching of mathematics. Insights are gained from the combination of empirical research, practical school experience and theory. The course content in mathematics education prepares students for a career in teaching and for research as part of a Master’s thesis. Mathematics education has several related disciplines, including educational sciences and, in particular, mathematics itself. For this reason, the introduction to mathematics education is ideally recommended for the 5th semester, or from the 3rd semester at the earliest.
Polyvalent dual major Bachelor’s degree:
- Introduction to Mathematics Education
Master of Education:
- Teaching Methods for Functions and Calculus
- Teaching Methods for Algebra and Probability and Statistics
- Students who do not wish to write a Master’s thesis in Mathematics Education should attend the student seminar on subject-specific didactic development (topics vary depending on the lecturer).
- Students who wish to write a Master’s thesis in Mathematics Education must first attend the courses on subject-specific didactic research at the University of Education Freiburg. (Please note: Plan well in advance, as the teaching placement semester must also be completed).
NEW: Linking subject-specific knowledge with subject didactics: From the 2025 winter semester onwards, the course Schulmathematische Aspekte der Analysis und Linearen Algebra can be taken as a mathematical supplement (offered only in the winter semester).
Last edited by Carolin Mann on 02/04/2026 at 12:09:55.
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Medical Statistics
Students with a strong background in probability theory and mathematical statistics may enrol in the Medical Data Science seminar, which is offered every semester. This student seminar focuses on current methodological research into the analysis and modelling of data from biomedical research, particularly deep learning and, more generally, machine learning techniques, such as large language models (LLMs). The integration of statistical methods with computer science methods, including the underlying mathematical principles, plays a key role in this context.
Bachelor’s and Master’s theses may be assigned based on this student seminar.
Optimisation
The following lectures from the Faculty of Engineering are offered as part of the mathematics degree programmes:
- Numerical Optimisation (Summer Semester): This course covers optimisation problems in science and engineering. The focus is on continuous, non-linear optimisation problems in finite-dimensional spaces, which are either convex or non-convex.
- Numerical Optimal Control (Winter Semester): The emphasis is on both discrete-time and continuous-time optimal control in continuous state spaces.
Bachelor’s and Master’s theses may be assigned based on these two lectures.