Time and place

Lecture: Di, Do, 10-12h, HS Weismann-Haus, Albertstr. 21a
Tutorial: 2 hours, various dates
Sir-in Exam: Date to be announced

Teacher: Wolfgang Soergel
Assistant: Damian Sercombe
Language: in German

This lecture continues the linear algebra courses. It treats groups, rings, fields and applications in the number theory and geometry. The highlights of the lecture are the classification of finite fields, the impossibility of the trisection of angles with circle and ruler, the non-existence of a solution formula for the general equations of fifth degree and the quadratic reciprocity law.

Required: Linear Algebra~I and II

Pure Mathematics
Elective

Time and place

Lecture: Di, Do, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined

Teacher: Maximilian Stegemeyer
Language: in German

Pure Mathematics
Elective
Mathematics
Concentration Module

Time and place

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

Teacher: Stefan Kebekus
Language: in German

Complex analysis deals with functions \(f : \mathbb C \to \mathbb C\) , which map complex numbers to complex numbers. Many concepts of Analysis~I can be directly transferred to this case, e.\,g. the definition of differentiability. One might expect that this would lead to a theory analogous to Analysis~I but much more is true: in many respects you get a more elegant and simpler theory. For example, complex differentiability on an open set implies that a function is even infinitely often differentiable, and this is further consistent with analyticity. For real functions, all these notions are different. However, some new ideas are also necessary: For real numbers \(a\), \(b\) one integrates for \[\int_a^b f(x) \mathrm dx\] over the elements of the interval \([a, b]\) or \([b, a]\). However, if \(a\), \(b\) are complex numbers, it is no longer so clear clear how such an integral is to be calculated. One could, for example, in the complex numbers along the line that connects \(a, b \in \mathbb C\), or along another curve that leads from \(a\) to \(b\). Does this lead to a well-defined integral term or does such a curve integral depend on the choice of the curve?

Required: Analysis I+II, Linear Algebra I

Pure Mathematics
Elective

Time and place

Lecture: Di, Do, 12-14h, SR 404, Ernst-Zermelo-Str. 1

Teacher: Amador Martín Pizarro
Assistant: Charlotte Bartnick

Pure Mathematics
Elective
Mathematics
Concentration Module

Time and place

Lecture: Mo, Mi, 10-12h, HS II, Albertstr. 23b
Tutorial: 2 hours, date to be determined

Teacher: Guofang Wang
Assistant: Florian Johne
Language: in German

Pure Mathematics
Elective
Mathematics
Concentration Module

Time and place

Lecture: Do, 14-16h, SR 226, Hermann-Herder-Str. 10
Tutorial: 2 hours, date to be determined

Teacher: Maxwell Levine
Language: in English

Pure Mathematics
Elective
Mathematics
Concentration Module