Module description
The Differential Geometry module provides an introduction into the study of curved spaces using techniques from Analysis.
Contact
Lecturer: Thomas Mettler
Assistant: Tim Maruhn
Lecture Notes
The module is based on lecture notes available in both PDF and HTML formats. While both versions contain identical core content, the HTML version includes solutions to the exercises in the lecture notes, additional multiple-choice questions, and some animations. You are currently viewing the HTML version of the module.
Schedule
Exercise sessions will be held via Zoom on weeknight evenings during the semester. To help us schedule a time that works for everyone, please complete the scheduling poll located in the Exercise Sheets section of the module's Moodle page. During the exercise session, you can ask questions, receive help with the current exercise sheet, and discuss solutions to the previous one. The exercise sheet must be submitted by the following Monday at 10:00 via upload on Moodle.
Five times per semester, there is an interactive lecture on Zoom given by Thomas Mettler.
https://fernuni.zoom.us/my/thomas.mettler
A tabular overview of the course schedule is as follows:
| Study Week | Dates | Events |
|---|---|---|
| 1 | Feb 23 — Feb 27 | Begin course |
| Feb 28 | Lecture 1 | |
| 2 | Mar 2 — Mar 6 | Ex. Session 1 |
| 3 | Mar 9 — Mar 13 | Ex. Sheet 1 due, Ex. Session 2 |
| 4 | Mar 16 — Mar 20 | Ex. Sheet 2 due, Ex. Session 3 |
| Mar 21 | Lecture 2 | |
| 5 | Mar 23 — Mar 27 | Ex. Sheet 3 due, Ex. Session 4 |
| 6 | Mar 30 — Apr 3 | Ex. Sheet 4 due, Ex. Session 5 |
| Apr 6 — Apr 10 | Break | |
| 7 | Apr 13 — Apr 17 | Ex. Sheet 5 due, Ex. Session 6 |
| Apr 18 | Lecture 3 | |
| 8 | Apr 20 — Apr 24 | Ex. Sheet 6 due, Ex. Session 7 |
| 9 | Apr 27 — May 1 | Ex. Sheet 7 due, Ex. Session 8 |
| May 2 | Lecture 4 | |
| 10 | May 4 — May 8 | Ex. Sheet 8 due, Ex. Session 9 |
| 11 | May 11 — May 15 | Ex. Sheet 9 due, Ex. Session 10 |
| 12 | May 18 — May 22 | Ex. Sheet 10 due, Ex. Session 11 |
| 13 | May 25 — May 29 | Ex. Sheet 11 due, Ex. Session 12 |
| May 30 | Lecture 5 | |
| 14 | Jun 1 — Jun 5 | Ex. Sheet 12 due, Ex. Session 13 |
Grading & Exam
The exam takes place 27 June 2026 online on Zoom.
To be admitted to the examination, you must meaningfully work on at least 75% of the exercise sheets (9 out of 12). This can be done by solving the exercises correctly or by showing a clear effort in attempting to solve them. In general, don't worry about meeting this requirement, as we will be generous in evaluating whether an exercise sheet has been meaningfully attempted.
Each exercise is graded with 0 to 3 points. The nine exercise sheets with the highest points will amount for 10% of your final grade. The remaining 90% are determined through an oral exam.
During the oral exam, you are expected to demonstrate a thorough understanding of the lecture notes, videos, and exercise sheets. You may be asked to state definitions or theorems, explain proofs, or perform calculations, often involving all these elements. The exam will last between 20 to 30 minutes, depending on the time needed to assign an accurate grade. Ensure you have a computer or tablet ready for writing and screen sharing.
Recordings
All exercise sessions and interactive lectures will be recorded and made accessible on Switch Tube. Additionally, all recordings will be embedded within the HTML version of the lecture notes.
Online Meeting Room
Outside of the exercise classes, the Zoom room linked below can always be used by students for online meetings:
https://fernuni.zoom.us/my/tim.maruhn
Moodle Page
https://moodle.fernuni.ch/course/view.php?id=4253
Last Update: Tue 20 January 2026 - 13:18 on tmD