Module description
In this module, with its sibling M02, we will introduce basic mathematical concepts and objects, e.g. functions and matrices. We will use them to formulate and understand fundamental techniques such as interpolation or the solution of linear systems. For additional information see the Moodle page: https://moodle.fernuni.ch/course/view.php?id=4139
Contacts
Lecturer: Sofia Botti
Assistant: Shega Likaj
Course Organization
We will provide you with several different learning activities and formats:
- Lecture notes: They provide you with all the details that you need to know at the end of the semester. It is important that you read these notes regularly and try to understand everything.
- Video lectures: The video lectures will provide only a general overview of the topics and will pick up on certain aspects of the topics covered in the lecture notes, but they will not go into the full level of detail.
- Weekly exercises session: We will do an exercise session in which will discuss problems that are mostly relevant for the homework assignments or preparatory exercises will be solved. Here you will also have the opportunity to ask live questions. It is highly recommended to attend the weekly exercise meetings, that will take place every Wednesday afeternoon from 17:45 to 19:00 at the following link https://fernuni.zoom.us/j/66920953220?pwd=yFbjUveoTwWjfvcAp754vL0So1Ypau.1.
- Forum: The forum in Moodle is for discussions among yourselves, but we will also have a regular look there and support you in case you have problems.
Five times per semester, there is an interactive lecture on Zoom given by Sofia Botti.
Partecipation is highly recommended.
https://fernuni.zoom.us/j/66920953220?pwd=yFbjUveoTwWjfvcAp754vL0So1Ypau.1.
All exercise sessions and interactive lectures will be recorded and made accessible on Switch Tube.
Schedule
A tabular overview of the course schedule is as follows:| Study Week | Dates | Topic/Lecture |
|---|---|---|
| 1 | Sep 1 — Sep 6 | Basics - Sets, Functions, Numbers, Absolute Value |
| 2 | Sep 8 — Sep 13 | Induction and Relations |
| Sep 13 | Lecture 1 | |
| 3 | Sep 15 — Sep 20 | Groups, Construction of Z, Minimim and Maximum |
| 4 | Sep 22 — Sep 27 | Floating Point and b-adic Representation |
| 5 | Sep 29 — Oct 4 | Practical Floating Point System |
| 6 | Oct 6 — Oct 11 | Condition Number and Landau Symbol |
| Oct 11 | Lecture 2 | |
| 7 | Oct 13 — Oct 18 | Polynomial Interpolation |
| Oct 20 — Oct 24 | Break | |
| 8 | Oct 27 — Nov 1 | Divided Differences |
| 9 | Nov 3 — Nov 8 | Linear Systems and Gaussian Elimination |
| Nov 8 | Lecture 3 | |
| 10 | Nov 10 — Nov 15 | LU-Decomposition and Matrix Norms8 |
| 11 | Nov 17 — Nov 22 | Symmetry and Cholesky |
| 12 | Nov 24 — Nov 29 | Linear Independence and Orthogonality |
| Nov 29 | Lecture 4 | |
| 13 | Dec 1 — Dec 6 | Cubic Splines |
| 14 | Dec 8 — Dec 13 | Approximation and Normal Equations |
| Dec 13 | Lecture 5 |
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.
Grading & Exam
The exam takes place 10 January 2026 online on Zoom.
To be admitted to the examination, 50% of each and every one of the 14 assignments must be attempted. Two "free" assignments that won't be counted towards your grade are allowed, with the restriction that these two assignments cannot be consecutive. If you complete all 14 assignments, the ones with the lowest two grades won't be counted. The bonus assignment gives you some extra points.
Final grade = 30% x Average Assignment Grade + 70% x Final Grade