Mathematical Institute, University of Freiburg, Teaching

Course program in Winter term 2025/2026

1b. Advanced 4-hour Lectures

Complex Analysis

Time and place

Lecture: Di, Do, 8-10h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Sit-in exam: date to be announced

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: Stefan Kebekus
Assistant: Andreas Demleitner
Language: in German

Previous knowledge

Analysis I and II, Linear Algebra I

Usability

Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)
Pure Mathematics (MSc14)
Elective (MSc14)
Elective (MScData24)

Course program in Summer term 2025

1a. Mandatory Lectures of the Study Programmes

Linear Algebra II

Time and place

Lecture: Di, Do, 8-10h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours, various dates

Teaching

Teacher: Stefan Kebekus
Assistant: Christoph Brackenhofer
Language: in German

Content

Linear algebra II is the continuation of the lecture linear algebra I from the winter semester and one of the basic courses of math studies. Central topics are: Jordan’s normal form of endomorphisms, symmetrical bilinear forms with especially the Sylvester’s theorem, Euclidian and Hermitian vector spaces, skalar products, orthonormal bases, orthogonal and (self-) adjugated , spectral theorem, principal axis theorem.

Previous knowledge

Linear Algebra I

Usability

Linear Algebra (2HfB21, BSc21, MEH21)
Linear Algebra (MEB21)
Linear Algebra II (BScInfo19, BScPhys20)

Course program in Winter term 2024/25

1a. Mandatory Lectures of the Study Programmes

Linear Algebra I

Time and place

Lecture: Mo, Do, 8-10h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours, various dates
Sit-in exam 27.02., 09:00-12:00, HS Rundbau, Albertstr. 21, GHS Physik, Hermann-Herder-Str. 3a, GHS Biologie, Schänzlestr. 1
Sit-in exam (resit) 26.04., 09:00-13:00, HS Rundbau, Albertstr. 21

Teaching

Teacher: Stefan Kebekus
Assistant: Marius Amann
Language: in German

Content

Linear Algebra I is one of the two introductory lectures in the mathematics degree program that form the basis for further courses. Topics covered include: fundamental concepts (in particular fundamental concepts of set theory and equivalence relations), groups, fields, vector spaces over arbitrary fields, basis and dimension, linear mappings and transformation matrix, matrix calculus, linear systems of equations, Gaussian elimination, linear forms, dual space, quotient vector spaces and homomorphism theorem, determinant, eigenvalues, polynomials, characteristic polynomial, diagonalizability, affine spaces. The background to the mathematical content is explained in terms of ideas and the history of mathematics.

Previous knowledge

Required: High school mathematics. \ Attendance of the preliminary course (for students in mathematics) is recommended.

Usability

Linear Algebra (2HfB21, BSc21, MEH21)
Linear Algebra (MEB21)
Linear Algebra I (BScInfo19, BScPhys20)

Course program in Summer term 2024

Course program in Winter term 2023/24

Algebra und Zahlentheorie

Time and place

Lecture: Mo, Mi, 8-10h, HS Weismann-Haus, Albertstr. 21a
Sit-in exam 26.02., 09:00-11:30

Teaching

Teacher: Stefan Kebekus
Assistant: Andreas Demleitner
general: ,

Usability

Algebra and Number Theory (2HfB21, MEH21)
Compulsory Elective in Mathematics (BSc21)
Pure Mathematics (MSc14)
Introduction to Algebra and Number Theory (MEB21)