Lecture notes and other writings

Feedback and self-assessment
in undergraduate student seminars in mathematics

with Manuel Luethi, ETH Learning and Teaching Journal, Vol 2, No 1, 2020. Link here

Abstract

In this article we will discuss bachelor’s seminars in mathematics at ETH. Most students (in these seminars) are neither used to individually preparing material from textbooks nor to discussing advances mathematics with fellow students. As these seminars usually follow a single thread, it is often impossible to quickly catch up on the content of past lectures. Hence there is also the risk that students only focus on their own talks, which often results in badly aligned talks. To overcome these problems, we implemented two tweaks to the standard setup. These are extensive meetings with the organizers and few mandatory exercises. We will evaluate the success of these measures and, where success is scarce, propose further measures to possibly address these problems.

Analysis I/II

with Manfred Einsiedler. A (most likely) outdated complete version is available here, the updated work-in-progress is here.

These are extensive lecture notes in German for the first year course in analysis at ETH Zurich. They were mostly developed in the academic years 2016-2017 (see this link) and 2017-2018 (see this and this link) and have been used henceforth (see for example this link). The topics covered are roughly the following:

Introduction to logic and set theory.
Real numbers, continuity.
Riemann integral for functions in one variable.
Sequences, convergence, series, power series.
Differential calculus for functions in one variable, the fundamental theorem of calculus.
Metric spaces.
Differential calculus for functions in several variables.
Implicit function theorem, inverse function theorem and an introduction to differential geometry (submanifolds of $\mathbb{R}^n$ and Lagrange multipliers).
Riemann integral for functions in several variables.
Path and surface integrals, Gauss' Theorem and Stokes' Theorem.
Ordinary differential equations.

What is... the shape of a lattice?

These are by now slightly outdated colloquial notes for a talk I gave in the “What is…?”-seminar of the Zurich Graduate School of Mathematics.

On the "Banana"-Trick of Margulis

Short and very preliminary notes explaining the thickening trick developed by G.A. Margulis in a specific instance. These were used in the seminar “Homogeneous Dynamics and Counting Problems” mentioned elsewhere.

Arithmeticity of lattices in higher rank real groups

Preliminary notes for a talk I gave in an informal reading course in Zurich, fall 2019. The aim of these notes is to deduce arithmeticity of lattices in higher-rank real groups from Margulis’ superrigidity result.