Lecture: Di, Do, 12-14h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined and announced in class
The lecture will probably be held in English.
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.
Teacher: Amador Martín Pizarro
Assistant: Charlotte Bartnick
Language: in English
In this course the basics of geometric model theory will be discussed and concepts such as quantifier elimination and categoricity will be introduced. A theory has quantifier elimination if every formula is equivalent to a quantifier-free formula. For the theory of algebraically closed fields of fixed characteristic, this is equivalent to requiring that the projection of a Zariski-constructible set is again Zariski-constructible. A theory is called \(\aleph_1\)-categorical if all the models of cardinality \(\aleph_1\) are isomorphic. A typical example is the theory of non-trivial \(\mathbb Q\)-vector spaces. The goal of the course is to understand the theorems of Baldwin-Lachlan and of Morley to characterize \(\aleph_1\)-categorical theories.
necessary: Mathematical Logic \
useful: Algebra and Number Theory
Elective (Option Area) (2HfB21)
Compulsory Elective in Mathematics (BSc21)
Pure Mathematics (MSc14)
Mathematics (MSc14)
Concentration Module (MSc14)
Elective (MSc14)
Elective (MScData24)
Lecture: Mi, 14-16h, SR 125, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined and announced in class
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)
Logic for Computer Science Students
Lecture: Mi, 10-12h, HS 00-026, Georges-Köhler-Allee 101
Tutorial: 2 hours, various dates
Teacher: Markus Junker
Assistant: Charlotte Bartnick
Language: in German
Proseminar: Kombinatorik
Mi, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Markus Junker
Assistant: Charlotte Bartnick
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
Mathematische Logik
Lecture: Mo, Mi, 14-16h, HS II, Albertstr. 23b
Sit-in exam 02.08., 10:00-12:00
Sit-in exam (resit) 21.02., 10:00-12:00
Teacher: Markus Junker
Assistant: Charlotte Bartnick
general:
Mathematical Concentration (MEd18, MEH21)
Pure Mathematics (MSc14)
Compulsory Elective in Mathematics (BSc21)
Modelltheorie
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)