Preliminary course catalogue - changes and additions are likely.
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Algebra and Number Theory
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
Elective
Algebraic Topology
Lecture: Di, Do, 10-12h, SR 404, Ernst-Zermelo-Str. 1
Tutorial: 2 hours, date to be determined
Teacher: Maximilian Stegemeyer
Language: in German
Elective
Complex Analysis
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
Elective
Model Theory
Lecture: Di, Do, 12-14h, SR 404, Ernst-Zermelo-Str. 1
Teacher: Amador Martín Pizarro
Assistant: Charlotte Bartnick
Elective
Calculus of Variations
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
Elective
Learning by Teaching
Organisation: Susanne Knies
Language: in German
What characterizes a good tutorial? This question will be discussed in the first workshop and tips and suggestions will be given. Experiences will be shared in the second workshop.
Elective
Computer exercises for 'Introduction to Theory and Numerics of Partial Differential Equations'
Teacher: Patrick Dondl
Language: in English
Elective
Computer exercises for 'Theory and Numerics of Partial Differential Equations'
Please note the registration modalities for the individual seminars published in the comments to the course catalog: As a rule, places are allocated after pre-registration by e-mail at the preliminary meeting at the end of the lecture period of the summer semester. You must then register online for the exam; the registration period runs from August 1, 2025 to October 8, 2025.
Seminar: Minimal Surfaces
Seminar: Mi, 16-18h, SR 125, Ernst-Zermelo-Str. 1
Preregistration:
Preliminary Meeting
Preparation meetings for talks: Dates by arrangement
Teacher: Guofang Wang
Elective
Seminar
Seminar: Di, 14-16h, SR 125, Ernst-Zermelo-Str. 1
Teacher: Wolfgang Soergel
Assistant: Damian Sercombe
Elective