Lecture: Di, Do, 12-14h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined
Sir-in Exam: Date to be announced
Teacher: Amador Martín Pizarro
Assistant: Stefan Ludwig
Language: in German
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
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)
Pure Mathematics (MSc14)
Elective (MSc14)
Elective (MScData24)
Lecture: Mi, 14-16h, SR 125, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined
Teacher: Amador Martín Pizarro
Assistant: Charlotte Bartnick
Language: in German
Groups without any non-trivial normal subgroup are called simple groups. Similar to prime numbers for the natural numbers, simple groups form the building blocks for finite groups. It is easy to see that Abelian finite simple groups are cyclic. Non-Abelian examples are alternating groups and Lie-type groups.
The classification of finite simple groups is far beyond the scope of this course. However, we will illustrate some of the recurring ideas of classification and, in particular, prove the following result of Brauer and Fowler:
Theorem: Let G be a finite group of even order such that the centre is of odd order. Then there is an element \(g \neq 1_G\) with \(|G| < |C_G (g)|^3\) .
This theorem had a particularly large impact on the classification of finite simple groups, as it suggests that these could be classified by examining the centralisers of elements of order 2.
Algebra and Number Theory
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Supplementary Module in Mathematics (MEd18)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective (MScData24)
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)
Logic for Philosophy Students
Lecture: Mi, 10-12h, HS 3117, KG III
Tutorial: 2 hours, various dates
Teacher: Amador Martín Pizarro
Assistant: Stefan Ludwig
Language: in German
Lecture: Di, Do, 12-14h, HS II, Albertstr. 23b
Teacher: Amador Martín Pizarro
Assistant: Xier Ren
Pure Mathematics (MSc14)
Mathematical Concentration (MEd18, MEH21)
Compulsory Elective in Mathematics (BSc21)
Di, 14: 30-16h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Amador Martín Pizarro, Heike Mildenberger
Do, 15-16h, HS II, Albertstr. 23b
Teacher: Nadine Große, Amador Martín Pizarro
Do, 14-15h, HS II, Albertstr. 23b
Teacher: Annette Huber-Klawitter, Markus Junker, Amador Martín Pizarro
Lecture: Do, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Amador Martín Pizarro
Assistant: Charlotte Bartnick
general:
Lecture: Mi, 10-12h, HS 00-026, Georges-Köhler-Allee 101
Teacher: Amador Martín Pizarro
Assistant: Charlotte Bartnick
Di, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Amador Martín Pizarro
Di, 14-16h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Heike Mildenberger, Amador Martín Pizarro
Do, 15-16h, HS II, Albertstr. 23b
Teacher: Amador Martín Pizarro, Nadine Große
Do, 14-15h, HS II, Albertstr. 23b
Teacher: Annette Huber-Klawitter, Markus Junker, Amador Martín Pizarro
Lecture: Di, Do, 12-14h, HS II, Albertstr. 23b
Teacher: Amador Martín Pizarro
Assistant: Francesco Gallinaro
general:
Di, 14: 30-16h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Amador Martín Pizarro, Heike Mildenberger
Do, 14-15h, HS II, Albertstr. 23b
Teacher: Annette Huber-Klawitter, Markus Junker, Amador Martín Pizarro
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)
Lecture: Mo, Mi, 14-16h, HS II, Albertstr. 23b
Teacher: Amador Martín Pizarro
Assistant: Charlotte Bartnick
general:
Mathematical Concentration (MEd18, MEH21)
Compulsory Elective in Mathematics (BSc21)
Di, 14-16h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Heike Mildenberger, Amador Martín Pizarro
Lecture: Di, Do, 12-14h, HS II, Albertstr. 23b
Teacher: Amador Martín Pizarro
Assistant: Michael Lösch
general:
Mathematical Concentration (MEd18, MEH21)
Pure Mathematics (MSc14)
Compulsory Elective in Mathematics (BSc21)
Di, 14: 30-16h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Amador Martín Pizarro, Heike Mildenberger
Lecture: Di, Do, 12-14h, SR 125, Ernst-Zermelo-Str. 1
Teacher: Amador Martín Pizarro
Assistant: Rémi Jaoui
general:
Compulsory Elective in Mathematics (BSc21)
Mathematical Concentration (MEd18, MEH21)
Lecture: Mi, 10-12h, HS 1199, KG I
Teacher: Amador Martín Pizarro
Assistant: Michael Lösch
Di, 14-16h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Amador Martín Pizarro, Heike Mildenberger
Do, 12-14h, , online
29.07., 15:00-19:00
Teacher: Amador Martín Pizarro
Assistant: Michael Lösch
general: ,
Linear Algebra II (BScInfo19, BScPhys20)
Di, 14: 30-16h, bbb-Raum "Philidor", online
Teacher: Amador Martín Pizarro, Heike Mildenberger
Do, 12-14h, , online
23.02., 13:00-17:00
Sit-in exam (resit) 13.09., 14:00-19:00
Teacher: Amador Martín Pizarro
Assistant: Michael Lösch
general: ,
Linear Algebra I (BScInfo19, BScPhys20)
Lecture: Mi, 10-12h, -, -
19.02., 10:00-13:00
Teacher: Amador Martín Pizarro
Assistant: Nadja Hempel
Mi, 15-16: 30h, bbb-Raum "Sprechstunde Prof. Martin Pizarro", online
Teacher: Amador Martín Pizarro
Assistant: Nadja Hempel
Mi, 16-18h, , online
Teacher: Heike Mildenberger, Amador Martín Pizarro
Lecture: Di, Do, 12-14h, HS II, Albertstr. 23b
27.07., 10:00-12:00
Teacher: Amador Martín Pizarro
Assistant: Daniel Palacin
Pure Mathematics (MSc14)
Mathematical Concentration (MEd18, MEH21)
Compulsory Elective in Mathematics (BSc21)
Lecture: Mi, 12-14h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Amador Martín Pizarro
Assistant: Michael Lösch
general:
Compulsory Elective in Mathematics (BSc21)
Mi, 16-18h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Amador Martín Pizarro, Heike Mildenberger
Lecture: Di, Do, 12-14h, HS II, Albertstr. 23b
Teacher: Amador Martín Pizarro
Assistant: Daniel Palacin
general:
Mathematical Concentration (MEd18, MEH21)
Compulsory Elective in Mathematics (BSc21)
Lecture: Mi, 10-12h, HS 00-026, Georges-Köhler-Allee 101
Teacher: Amador Martín Pizarro
Assistant: Michael Lösch
Mi, 16-18h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Amador Martín Pizarro
Lecture: Mo, Mi, 12-14h, HS II, Albertstr. 23b
02.08., 10:00-13:00
Teacher: Amador Martín Pizarro
Assistant: Michael Lösch
general: ,
Compulsory Elective in Mathematics (BSc21)
Pure Mathematics (MSc14)
Mathematical Concentration (MEd18, MEH21)
Teacher: Amador Martín Pizarro
Assistant: Michael Lösch
Compulsory Elective in Mathematics (BSc21)
Mo, 14-16h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Amador Martín Pizarro, Heike Mildenberger
Lecture: Di, Do, 12-14h, HS II, Albertstr. 23b
Teacher: Amador Martín Pizarro
Assistant: Daniel Palacin Cruz
general:
Compulsory Elective in Mathematics (BSc21)
Lecture: Mo, 10-12h, HS 00-026, Georges-Köhler-Allee 101
Teacher: Amador Martín Pizarro
Assistant: Michael Lösch
Mi, 16-18h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Heike Mildenberger, Amador Martín Pizarro