03 / Teaching
At the blackboard.
Course materials, exercise classes and moments when an abstract idea became tangible.
Basel · Spring 2022
Einführung
in die Topologie
Introduction to topology
12 exercise sheets
12 solutions
1 bonus challenge
Everything for the course.
Lecture notes and exercises in German, with solutions collected by sheet.
All sheets and solutions
- Sheet 01Exercises Solutions
- Sheet 02Exercises Solutions
- Sheet 03Exercises Solutions
- Sheet 04Exercises Solutions
- Sheet 05Exercises Solutions
- Sheet 06Exercises Solutions
- Sheet 07Exercises Solutions
- Sheet 08Exercises Solutions
- Sheet 09Exercises Solutions
- Sheet 10Exercises Solutions
- Sheet 11Exercises Solutions
- Sheet 12Exercises Solutions
- BonusExercises
A moment from my topology teaching
A painting that needs
both nails.
I once used a painting hung by a string around two nails to explain the fundamental group of the twice-punctured plane. Remove either nail and the painting falls.
The string represents the nontrivial commutator aba−1b−1. Filling either puncture kills its generator and makes this word trivial.
Try the algebra behind the trick
aba⁻¹b⁻¹ ≠ 1
Both punctures are present: the commutator is nontrivial.
The display tracks the group word; the comic shows the physical demonstration.A moment from my topology teaching
Two angles.
Then a doughnut break.
When I taught the product topology, I brought doughnuts for the students during the break. A circle has one angular coordinate; a torus has two.
Products U × V of open subsets of the two circles form a basis for the product topology. The surface of a doughnut models a torus.
The parametrization
Changing either angle moves along one circle factor.
Exercise classes I have led alongside the following courses.
University of Basel
- Lineare Algebra IICourse instructor: Philipp Habegger
- Komplexe DynamikCourse instructor: Harry Schmidt
- Algebraische ZahlentheorieCourse instructor: Philipp Habegger
- Lineare Algebra IICourse instructor: Philipp Habegger
- ZahlentheorieCourse instructor: Harry Schmidt
- Lineare Algebra IICourse instructor: Jérémy Blanc
University of Mainz
- Lineare AlgebraCourse instructor: Theo de Jong
- ZahlentheorieCourse instructor: Axel Stäbler
- Algebra IICourse instructor: Moritz Rahn
- Algebra IICourse instructor: Ariyan Javanpeykar
- Lineare Algebra und Geometrie IICourse instructor: Ariyan Javanpeykar
Two substitute lectures
Algebra II · Mainz · Summer 2017