Analysis I/II
In der Analysis-Vorlesung für Mathematik- und Physikstudierende wurde 2016/17 und 2017/18 einerseits ein neues interaktives Skript eingesetzt, des Weiteren wurden die Studenten motiviert ihre L?sungen vor den Kollegen zu pr?sentieren, und schlussendlich wurde in der Prüfung h?herer Stellenwert auf mathematische Inhalte im Vergleich zu Rechnungen gelegt.
Keywords
Course description
Project description
Professor Einsiedler’s Analysis I/II courses (BSc in Maths, Physics or Int. Disc.) in the academic years 2016/17 and 2017/18 included the following novel aspects:
Script:
- A new script was written jointly with the assistant Andreas Wieser and was received very well by the students, see https://people.math.ethz.ch/~einsiedl/Analysis-Skript.pdf
- This script was converted into an e-script, see https://wp-prd.let.ethz.ch/WP0-CIPRF9693/
- An integral part of the text (both in pdf, but more prominently in the e-script) are GeoGebra-applets which are meant to visualize various aspects of the theory or portions of the proofs.
- The e-script version contains several innovative activities that foster students understanding and motivation. At the end of each chapter they can use an applet to review the terminology and main facts (programmed by a dedicated student). Furthermore, students could publicly ask questions in the margin of the eSkript, which were answered by teaching assistants or Professor Einsiedler.
Exercises:
- Students were asked to volunteer online for presenting solutions to their homework, were then selected randomly by an algorithm, and had to present their solutions in the exercise classes. This was meant to train both their mathematical skills but equally important the soft skill of presenting scientific (here mathematical) ideas.
- Direct feedback in the form of Schnellübungen was given as well.
- The students collected in this way points during the semester that were counted as Lernelemente towards the final grade.
Exam:
In the past the exam in Analysis has frequently been so heavy in calculations that it was possible to pass the exam with good grades in these parts and without any theoretical knowledge from the lecture. As far as one can tell this standard had developed without any conscious decision but by evolution of the exam over decades.
Professor Einsiedler’s take on this was, that this makes sense for service courses but not at all for mathematics bachelor students, who are supposed to master the theory as well. Hence the exam was redesigned to a mix of problems which was in alignment with the actual learning objectives and made it impossible to pass without theoretical knowledge.
Aftermath:
- Professor Einsiedler received the Golden Owl in 2018 (most likely for the above Analysis courses).
- Both the script and the new nature of the final exam have been taken over by the current lecturer Professor Jossen.
- The e-script version of the script is with 107’959 views one of the most popular e-scripts at ETHZ and has also been recommended by some German universities as a source.
