Linear Algebra II
Lecture: Di, Do, 8-10h, HS Rundbau, Albertstr. 21
Tutorial: 2 hours, various dates
Teacher: Stefan Kebekus
Assistant: Christoph Brackenhofer
Language: in German
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.
Linear Algebra I
Linear Algebra (2HfB21, BSc21, MEH21)
Linear Algebra (MEB21)
Linear Algebra II (BScInfo19, BScPhys20)
Lecture: Di, Do, 10-12h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Teacher: Annette Huber-Klawitter, Amador Martín Pizarro
Assistant: Christoph Brackenhofer
Language: in German
Semi-algebraic geometry is about properties of subsets of \(**R**^n\), which are given by inequalities of the form [ f(x1, \dots, xn)\geq 0] for polynomials \(f\in**R**[X_1,\dots,X_n]\).
The theory has many different facets. On the one hand, it can be seen as a version of algebraic geometry over \(\mathbf{R}\) (or even more generally over so-called real closed fields). On the other hand, the properties of these fields are a central tool for the model-theoretic proof of Tarski-Seidenberg's theorem on quantifier elimination in real closed fields. Geometrically, this is interpreted as a projection theorem.
From this theorem, a proof of Hilbert's 17th problem easily follows, which was solved by Artin in 1926.
\textit{Is every real polynomial \(P \in \mathbf{R}[x_1, \dots, x_n]\), which takes a non-negative value for every \(n\)-tuple in \(\mathbf{R}^n\), a sum of squares of rational functions (i.e., quotients of polynomials)?}
In the lecture, we will explore both aspects. Necessary tools from commutative algebra or model theory will be discussed according to the prior knowledge of the audience.
Required: Algebra and Number Theory \ Recommended: Knowledge in commutative algebra and algebraic geometry (cf. Kommutative Algebra und Einführung in die algebraische Geometrie), model theory
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective (MScData24)
Lecture: Di, Do, 8-10h, HS II, Albertstr. 23b
oram exam (resit) 04.12., 00:00-00:00
Teacher: Annette Huber-Klawitter
Assistant: Christoph Brackenhofer
Mathematical Concentration (MEd18, MEH21)
Compulsory Elective in Mathematics (BSc21)
Di, 14-16h, SR 127, Ernst-Zermelo-Str. 1
Teacher: Annette Huber-Klawitter
Assistant: Christoph Brackenhofer
Undergraduate Seminar (2HfB21, BSc21, MEH21, MEB21)
Lecture: Di, Do, 8-10h, HS Rundbau, Albertstr. 21
Teacher: Annette Huber-Klawitter
Assistant: Christoph Brackenhofer, Pedro Núñez
general: ,
Linear Algebra II (BScInfo19, BScPhys20)
Lecture: Di, Do, 10-12h, HS Weismann-Haus, Albertstr. 21a
Sit-in exam (resit) 19.06., 10:00-13:00
Teacher: Amador Martín Pizarro
Assistant: Christoph Brackenhofer
general: ,
Algebra and Number Theory (2HfB21, MEH21)
Compulsory Elective in Mathematics (BSc21)
Pure Mathematics (MSc14)
Introduction to Algebra and Number Theory (MEB21)